From @uxc.cso.uiuc.edu,@wri.UUCP,@uunet:simon@alberta Tue Feb 14 00:28:05 1989 To: mathgroup Subject: Where is the mdefs.h file in release 1.1 for the Mac II ? Status: RO Do you know if this file, mentioned on page 157 of the Mathematica book, is? Could it be posted to sci.math.symbolic on usenet if there has been an oversight? Thanks ------------------- Simon Tortike, Department of Mining, Metallurgical and Petroleum Engineering, The University of Alberta, Edmonton, AB, CANADA T6G 2G6. simon@alberta.uucp || Tel. +1 403 492-3338 From stevec Tue Feb 14 00:40:34 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA01694; Tue, 14 Feb 89 00:40:07 CST Date: Tue, 14 Feb 89 00:40:07 CST From: stevec (Steve Christensen) Message-Id: <8902140640.AA01694@yoda.ncsa.uiuc.edu> To: @wri.UUCP@newton, alberta!simon Subject: Re: Where is the mdefs.h file in release 1.1 for the Mac II ? Cc: stevec Status: RO This file is included in the Sun version, but not in the Mac II version I have. I will check with WRI and see if I can post it and find out why it is not in the Mac version. Steve Christensen From stevec@yoda Thu Mar 2 12:10:21 1989 Received: from spock.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA08659; Thu, 2 Mar 89 12:10:20 CST Received: from yoda.ncsa.uiuc.edu by spock.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA18645; Thu, 2 Mar 89 12:04:59 CST Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA08649; Thu, 2 Mar 89 11:57:17 CST Date: Thu, 2 Mar 89 11:57:17 CST Message-Id: <8903021757.AA08649@yoda.ncsa.uiuc.edu> To: mathgroup@yoda Subject: Statistical and Econometric Modeling From: "GSBACD::PHD_IVO" Status: RO While I cannot afford Mathematica on my Mac-II-maybe if I sell it and buy myself a NeXT-I would like to be on the mailing list to figure out how useful it would be. In particular, I would like to see discussion of usage of M. for statistical and econometric modeling. Since magazines claim that M. is a memory hog, I guess one would need virtual memory to use M. for large-scale statistical projects, wouldn't one? ivo welch phd_ivo@gsbacd.uchicago.edu From stevec Sun Mar 5 01:29:10 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA10872; Sun, 5 Mar 89 01:28:59 CST Date: Sun, 5 Mar 89 01:28:59 CST From: stevec (Steve Christensen) Message-Id: <8903050728.AA10872@yoda.ncsa.uiuc.edu> To: mathgroup Subject: Archives Status: RO I have placed several files in the MathGroup archives on the ftp.ncsa.uiuc.edu (128.174.20.50) machine. These are available via anonymous ftp. In the Symbolic/Mathematica/MathGroup_Mail_Archive will be a file called MathGroupMail1 which will contain messages like this one, that is, messages that go out to the mailing list. I will continuously add to this file until it contains about 50 messages, then I will start MathGroupMail2, and so forth. In the Symbolic/Mathematica/Sci.Math.Symbolic directory, I have placed a file called Archive1 which currently contains those Mathematica related messages from the sci.math.symbolic newsgroup on the net and our local uiuc.mathematica notesfiles. Archive1 contains messages in a digest form that appear from September 1988 to early February 1989. Archive2 will contain a second digest as messages appear in those two newsgroups or elsewhere in other newsgroups. This is a service for those of you who do not have access to sci.math.symbolic. In Symbolic/Mathematica/Packages are two .m files, one .h file and a pointer to the Cocklear package from Apple. There are now over 300 email addresses on the MathGroup list, some of which are mailboxes for whole insitutions like UC-Berkeley. I am in contact with some of the Mathematica vendor representatives and am adding them to the list. I hope to have every vendor have representatives on the list so that they can be constantly aware of what is going on in the Mathematica world. We have a fair number of Mathematica experts on the list. If you are doing significant work with Mathematica and would be willing to talk about your application in your region of the world, please let me an the mailing list know. There is a demand for speakers for local user groups, university departments and industrial research labs. Finally, the usual reminder - The value of a user group and mailing list comes from an active participation. Please do not hesitate to send mail on your applications, experiences, bugs, packages, etc. often. Please pass this on to other Mathematica users who may not be on the list yet. Steve Christensen steve@ncsa.uiuc.edu 14008@ncsavmsa.bitnet mathgroup@wri.com From stevec Tue Mar 7 13:02:52 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA12000; Tue, 7 Mar 89 13:00:32 CST Date: Tue, 7 Mar 89 13:00:32 CST From: stevec (Steve Christensen) Message-Id: <8903071900.AA12000@yoda.ncsa.uiuc.edu> To: mathgroup Subject: Archives Status: RO First: I will be moving to new offices on March 8 and so my machines will be down for a time. If you send mail to me or mathgroup, your message may get reflected back if there is a problem getting my machines back on the network here. Please try again the next day if you have a problem. I have placed several files in the MathGroup archives on the ftp.ncsa.uiuc.edu (128.174.20.50) machine. These are available via anonymous ftp. [Some of you - especially in Europe - have problems getting to this machine using its name, try ftp 128.174.20.50 instead.] In the Symbolic/Mathematica/MathGroup_Mail_Archive will be a file called MathGroupMail1 which will contain messages like this one, that is, messages that go out to the mailing list. I will continuously add to this file until it contains about 50 messages, then I will start MathGroupMail2, and so forth. In the Symbolic/Mathematica/Sci.Math.Symbolic directory, I have placed files called Archive1 and Archive2 which currently contain those Mathematica related messages from the sci.math.symbolic newsgroup on the net and our local uiuc.mathematica notesfiles. Archive1 contains messages in a digest form that appear from September 1988 to early February 1989. Archive2 contains a second digest for February. This is a service for those of you who do not have access to sci.math.symbolic. In Symbolic/Mathematica/Packages are two .m files, one .h file and a pointer to the Cocklear package from Apple. There are now over 300 email addresses on the MathGroup list, some of which are mailboxes for whole insitutions like UC-Berkeley. I am in contact with some of the Mathematica vendor representatives and am adding them to the list. I hope to have every vendor have representatives on the list so that they can be constantly aware of what is going on in the Mathematica world. We have a fair number of Mathematica experts on the list. If you are doing significant work with Mathematica and would be willing to talk about your application in your region of the world, please let me an the mailing list know. There is a demand for speakers for local user groups, university departments and industrial research labs. Finally, the usual reminder - The value of a user group and mailing list comes from an active participation. Please do not hesitate to send mail on your applications, experiences, bugs, packages, etc. often. Please pass this on to other Mathematica users who may not be on the list yet. Steve Christensen steve@ncsa.uiuc.edu 14008@ncsavmsa.bitnet mathgroup@wri.com From stevec Mon Mar 13 14:05:17 1989 To: mathgroup Subject: Modelling of vascular systems Status: RO [As messages come into the Mailing List that indicate Mathematica users with specific interests, I will send them out so that users with similar applications can communicate. --smc] Hi! i just read your 'news' listing about the mathematica mailing list. I would like to be added to this list please. I am involved in the modelling of vascular systems at the capillary and arteriolar level and I am trying to model oxygen transport mechanisms in muscle tissue. I am also interested in modelling blood vessel geometries and in the investigation of 3D reconstructions of serial sections of electron microscope images of the blood vessels. Thanks for your anticipated cooperation, and I look forward to exciting times with Mathematica. Dev ........................................................................... Devkumar R. Sainani Department of Medical Biophysics Telephone: (519) 661-3100 or University of Western Ontario, and (519) 663-3799 or John P. Robarts Research Institute (519) 663-5777 EXT. 4440 London, Ontario, Canada N6A 5C1 Canada : Dev@uwovax.uwo.ca BITNET : Dev@uwovax.bitnet UUCP : Dev@julian.uucp (...!watmath!julian!Dev) From stevec Mon Mar 13 14:08:44 1989 To: mathgroup Subject: Mathematica/Hypercard Question Status: RO We are considering the possibility of using Mathematica on a Mac II to build a marketing model workstation. I have been told that it might be possible to access Mathematica from within Hypercard. Could you direct me to someone with experience (expertise) in that domain? Stephane From lwyse@bucasb.BU.EDU Tue Mar 14 13:02:19 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA01239; Tue, 14 Mar 89 13:02:17 CST Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA22346; Tue, 14 Mar 89 12:59:57 CST Return-Path: Received: from bu-it.BU.EDU by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA22533; Tue, 14 Mar 89 12:59:51 CST Received: from COCHLEA.BU.EDU by bu-it.BU.EDU (5.58/4.7) id AA24822; Tue, 14 Mar 89 13:55:35 EST Received: by cochlea.bu.edu (4.0/4.7) id AA01652; Tue, 14 Mar 89 13:55:51 EST Date: Tue, 14 Mar 89 13:55:51 EST From: lwyse@bucasb.BU.EDU Message-Id: <8903141855.AA01652@cochlea.bu.edu> To: steve@ncsa.uiuc.edu Subject: mathematica/TeX question for mathgroup Status: RO I am having trouble "Splice"ing TeXForms into a Tex document. Mathematica automatically converts even not-so-long expressions into "short" form (abbreviating by elliding out middle terms and replacing them with a count of them between angle brackets.) This short form is then spliced into my TeX document in beautiful TeX notation. Has anybody foung an elegant solution to this? thanx, lonce From stevec Tue Mar 14 13:50:27 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA01319; Tue, 14 Mar 89 13:45:27 CST Date: Tue, 14 Mar 89 13:45:27 CST From: stevec (Steve Christensen) Message-Id: <8903141945.AA01319@yoda.ncsa.uiuc.edu> To: mathgroup Subject: email address Status: RO Administrative note: Some of you may be using the address steve@spock.ncsa.uiuc.edu or similar address with "spock" in it. Please do not use this address any longer. Spock is a Sun-3 that is being taken out of the mail line. If you have used this old address recently, it is likely that your mail did not get to me. From now on, if you used that old address simply use steve@ncsa.uiuc.edu instead. Steve Christensen MathGroup From stevec Wed Mar 15 10:56:58 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA02626; Wed, 15 Mar 89 10:55:30 CST Date: Wed, 15 Mar 89 10:55:30 CST From: stevec (Steve Christensen) Message-Id: <8903151655.AA02626@yoda.ncsa.uiuc.edu> To: mathgroup Status: RO >From att!twitch!rvk@uxc.cso.uiuc.edu Subject: Mathematica and libm? The following item was seen in a netnews group, and might be of some interest to people in your area. I coded the program, and get essentially the same results. while I don't know whether the explanation supplied is correct or not, I am wondering how something like this might affect packages like Mathematica. ------------------------------------------------------------ If you use libm (especially trancendental functions sin(), cos(), ln(), exp() etc..) you can get nearly a 10* speedup by using the clumsy code inlining facility provided by Sun's C complier. For example (on Sun 3/60, SunOS 4.0.1) The following code: #include main() { register int i; register double x, y; for(i = 0, x = 0; i < 100000; i++, x += 2*M_PI/100000.0) y = cos(x); } Compiled with: cc -O -f68881 -o cos cos.c -lm Runs in: real 0m30.16s user 0m24.56s sys 0m0.58s Compiled with (but how incredibly *UGLY*): cc -O -f68881 -o cos cos.c /usr/lib/f68881/libm.il Runs in: real 0m4.33s user 0m3.65s sys 0m0.20s REASON: Although Sun went to the trouble of making the assembly inline file /usr/lib/f68881/libm.il, and a 68881 version of the maths library, they *DID NOT* make assembly versions of the maths functions to put into the maths library! (and similarly for the FPA) From stevec Wed Mar 15 11:12:04 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA02663; Wed, 15 Mar 89 11:00:29 CST Date: Wed, 15 Mar 89 11:00:29 CST Message-Id: <8903151700.AA02663@yoda.ncsa.uiuc.edu> To: mathgroup Subject: Re: Archives From: zolliker%math.ethz.ch@RELAY.CS.NET Status: RO [I would like to know from the European list members who has had success in ftp'ing to the US and how they do it. --- smc] > ... [Some of you - especially in > Europe - have problems getting to this machine using its name, > try ftp 128.174.20.50 instead.] ... Do you really think this works? Is there any internet connection between Europe and the United States at all? Urs From stevec Wed Mar 15 22:53:24 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA03204; Wed, 15 Mar 89 22:50:18 CST Date: Wed, 15 Mar 89 22:50:18 CST From: stevec (Steve Christensen) Message-Id: <8903160450.AA03204@yoda.ncsa.uiuc.edu> To: mathgroup Subject: Dirac trace package Status: RO [From sci.math.symbolic - smc] brooks Dirac traces 12:27 pm Mar 2, 1989 (at maddog.llnl.gov) (From News system) Does anyone have a Dirac trace package for Mathematica? brooks@maddog.llnl.gov, brooks@maddog.uucp, uunet!maddog.llnl.gov!brooks From stevec Mon Mar 20 13:50:43 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA07498; Mon, 20 Mar 89 13:49:01 CST Date: Mon, 20 Mar 89 13:49:01 CST From: stevec (Steve Christensen) Message-Id: <8903201949.AA07498@yoda.ncsa.uiuc.edu> To: mathgroup Subject: Mathematica and Matrices (From sci.math.symbolic) Status: RO gmk Mathematica and matrices 9:25 pm Mar 16, 1989(at wjh12.harvard.edu) (From News system) I have a Mathematica question. I did the following: In[1]:= y x . b - E[x . b] x.b Out[1]:= -E + yx.b In[2]:= D[%,b] x.b Out[2]:= -(E (0.b + x.1)) + y(0.b + x.1) Of course, this answer is right, but I would prefer if Mathematica knew that 0.b=0 and x.1=1, so that the above equation would be written as follows: x.b -x E + yx Does anyone know how to get Mathematica to do this? Thanks in advance Gary King ........... : Gary King, Department of Government, Harvard University, Cambridge, MA 02138 harvard.edu, BITnet: gmk@harvunxw, Phone: 617-495-2027 From stevec Mon Mar 20 14:50:27 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA07571; Mon, 20 Mar 89 14:48:56 CST Date: Mon, 20 Mar 89 14:48:56 CST Message-Id: <8903202048.AA07571@yoda.ncsa.uiuc.edu> To: mathgroup Subject: Fourier Transforms? From: skankman@ux1.lbl.gov Status: RO I would be very interested in a symbolic fourier and inverse fourier transform package. Such a package is strangely absent from the Sun Mathematica version to which I have access. Nor could I find one on the Mac. David Schurig Lawrence Berkeley Lab Bldg 70-157 1 Cyclotron Rd. Berkeley, CA 94720 skankman@ux1.lbl.gov From stevec Mon Mar 20 14:53:19 1989 To: mathgroup Subject: Asymptotia Status: RO I am sure that M'ica does its sums in a very clever way, but it seems to take some chances at the margin. Consider the classical case of a divergent series, the asymptotic expansion for the exponential integral (Whittaker and Watson, chapter VIII): n! (-x)^n. M'ica (running on a Mac IIx, local kernel, default settings) returns a finite result without warning for surprisingly large values of x: x = 0.04934 Sum[n! (-x)^n, {n, 0, Infinity}] //N 0.954923 though, to be entirely fair, it does spot trouble for larger values: x = 0.05 Sum[n! (-x)^n, {n, 0, Infinity}] //N NLimit::dubious: The result from NLimit may be completely wrong. 0.954371 If the results of the ratio test are looked at properly (i.e. nth ratio = (n+1) x, grows indefinitely large with n), this series is seen to be divergent even at the smallest values of x. This sort of test picks out the divergent series that most frequently occur in asymptotic expansions, and I wonder why it has not been implemented. From stevec Mon Mar 20 14:58:49 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA07601; Mon, 20 Mar 89 14:55:40 CST Date: Mon, 20 Mar 89 14:55:40 CST Message-Id: <8903202055.AA07601@yoda.ncsa.uiuc.edu> To: mathgroup Subject: Mathematica bugs From: knutm@ifi.uio.no Status: RO There is a simple bug in the Chebychev polynomial function which I imagine others have also found. Mathematica (version 1.1 on a Mac II) will tell you that the first degree Chebychev polynomial of the first kind is the constant zero, i.e., ChebychevT[1,x] = 0 if I remember the syntax correctly. This bug has already been reported to Wolfram Research. A much more serious bug that I found was in the integer factorization routine FactorInteger. According to Shawn Sheridan who is Manager of Technical Support this bug has now been fixed in Wolfram Research's development version and the fix will be included in the next release. Below is an extract of the message I received from Dr. Sheridan (dated March 18) >Thank you for your bug report on Mathematica v1.1. As you can see below, >the large integer bug has been fixed in our development version. You >should be receiving this version in the spring. >SunMathematica (sun3.fpa) 1.2-development (March 7, 1989) [With pre-loaded data] >by S. Wolfram, D. Grayson, R. Maeder, H. Cejtin, > S. Omohundro, D. Ballman and J. Keiper >with I. Rivin and D. Withoff >Copyright 1988 Wolfram Research Inc. >-- Terminal graphics initialized -- >In[1]:= 536903681 107367629 >Out[1]= 57646075230342349 >In[2]:= PrimeQ[%] >Out[2]= False >In[3]:= FactorInteger[%1] >Out[3]= {{107367629, 1}, {536903681, 1}} In version 1.1, Mathematica claims that the product of the two integers is prime. Knut Morken Institute of Informatics University of Oslo Norway (knutm@ifi.uio.no) From stevec Mon Mar 20 15:00:06 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA07605; Mon, 20 Mar 89 14:57:06 CST Date: Mon, 20 Mar 89 14:57:06 CST Message-Id: <8903202057.AA07605@yoda.ncsa.uiuc.edu> To: mathgroup Subject: control-c and modified Bessel function bugs From: perry@pacific.mps.ohio-state.EDU Status: RO I wanted to report two bugs I've found in version 1.1 of Mathematica running on a SUN 4/110. During runaway calculations, if I use ^C and then try to abort my calculation, my SUN crashes with a "watchdog reset" message. It is possible that this problem is related to our local configuration of SUN's. The second bug also exists in the Mac version of Mathematica. Try: In[1]:= Plot[BesselK[1/2,x],{x,20,25}] The resultant output looks like noise. The problem exists for other values of l, but I have not thoroughly tested other special functions. The problem does not seem to occur outside of a special region, making me suspect that a poor marriage between different numerical algorithms has been made. I'm probably naive, but it would seem worthwhile for Wolfram Research to compile a series of tests which use tabulated results from Abromowitz and Stegun and other sources. Some things Mathematica can't do that I would like to see: Limit[eps Gamma[eps],eps -> 0] Limit[E^(-.2 x+1),x -> Infinity] for Integrate[E^(1-0.2x),{x,0,Infinity}] Integrate[x/(a+b x^2+c x^4),x] --macsyma will do this Integrate[x^2/(a+b x^2+c x^4),x] -Gradshteyn & Ryzhik 2.161 Integrate[1/x^3/(a+b x)^(1/3),x] -G&R 2.236 Integrate[1/Sqrt[a+b E^(m x)],x] -G&R 2.315 Integrate[Sinh[a x+b] Sinh[c x+d],x] G&R 2.425 Integrate[Sinh[a x] Sinh[b x] Cosh[c x],x] G&R 2.426 Macsyma will do most of the above, but it is usually slower than Mathematica. There are many times when I want to find a Series about Infinity, but am forced to introduce 1 over the original variable and take a series about zero instead. It is extremely unfortunate that the SUN version of Mathematica does not contain a NOTEBOOK facility. This cripples Mathematica to some extent. It would also be great if the graphics windows on the SUN had some walking menus that allowed the user to alter options, instead of having to use Show. How about using the mouse to set light sources and rotate surfaces? CPU speed isn't there yet, but I can dream. Having finished bitching, let me say I love this program. It's good enough that it's constantly got me thinking about what the "perfect" package would be. Robert Perry Dept. of Physics The Ohio State University perry@public.mps.ohio-state.edu bitnet: perry@ohstpy 614-292-6506 From stevec Tue Mar 21 12:43:11 1989 To: mathgroup Subject: Splicing into tex docs Status: RO I'm having touble using Splice["texdoc.mtex"] in that the expression that I want is automatically converted to "short form" (many terms left out and replaced by <> which is then inserted into my document in TeXForm! My not-so-elegant solution is to type the expression within Mathematica, set a variable to it's TeXForm, Save the variable and then manually edit it into my tex document. Hmmmm Has anybody figured this one out? Also, has anybody written a package that produces graphs in TeX notation? OK, lonce lwyse@bucasb.BU.EDU From stevec Tue Mar 21 13:50:28 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA09421; Tue, 21 Mar 89 13:47:09 CST Date: Tue, 21 Mar 89 13:47:09 CST From: stevec (Steve Christensen) Message-Id: <8903211947.AA09421@yoda.ncsa.uiuc.edu> To: mathgroup Status: RO >From Jim_Wendel@ub.cc.umich.edu Tue Mar 21 06:19:52 1989 Subject: Re: Chebyshev "bug" My Mac II version 1.04 of Mathematica gives the correct answer x for ChebyshevT[1,x]. Your message referred to Chebychev... Note slight difference in spelling! My 1.04 version of Mathematica, running on a Mac II, thinks that the product of your two large integers (9 digits each) is a prime. Consistently then it factors it as itself to the 1 power. Plot[BesselK[1/2,x],{x,20,25}] came out beautifully, values from 0 down to -0.0000175 on the vertical axis. [It appears that there are some bugs in 1.1 that were not in 1.04 on all machines. I will try to report on these problems when 1.2 comes out. If you do report bugs, please indicate always which version of the software you are using and on what machine. --- smc] From stevec Tue Mar 21 16:04:51 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA10039; Tue, 21 Mar 89 16:01:31 CST Date: Tue, 21 Mar 89 16:01:31 CST Message-Id: <8903212201.AA10039@yoda.ncsa.uiuc.edu> To: mathgroup Subject: Re: Mathematica and Matrices (From sci.math.symbolic) From: maeder@symcom.math.uiuc.edu Tue Mar 21 13:54:43 1989 Status: RO > I have a Mathematica question. I did the following: > > In[1]:= y x . b - E[x . b] > > x.b > Out[1]:= -E + yx.b I don't understand how you got that output from your input. E[expr] gives just that, E[expr]. Didn't you mean E^expr or Exp[expr] ? Is your example a verbatim copy of the session? Roman Maeder maeder@symcom.math.uiuc.edu From stevec Wed Mar 22 14:26:58 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA12288; Wed, 22 Mar 89 14:23:16 CST Date: Wed, 22 Mar 89 14:23:16 CST Message-Id: <8903222023.AA12288@yoda.ncsa.uiuc.edu> To: mathgroup Subject: RE: BesselK[1/2,x] From: Mike Monagan Status: RO > >From Jim_Wendel@ub.cc.umich.edu Tue Mar 21 06:19:52 1989 > Subject: Re: Chebyshev "bug" > ... > Plot[BesselK[1/2,x],{x,20,25}] came out beautifully, values from 0 down to > -0.0000175 on the vertical axis. ================================================= Except that BesselK[1/2,x] is positive for x > 0. Abramowitz & Stegun, pp. 444, give a formula for BesselK[1/2,x] in terms of Exp[-x] namely 10.2.17. sqrt(Pi/2/x) K(1/2,x) = Pi/2/x exp(-x) from which you can deduce this. I tried the Plot on our Mac II (version 1.1 of Mathematica) and it gives random noise beyond x = 21. Mike mbmonagan@watcauchy.waterloo.edu From norman@fermi Wed Mar 22 14:25:37 1989 Received: from fermi.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA12316; Wed, 22 Mar 89 14:25:36 CST Return-Path: Received: by fermi.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA10381; Wed, 22 Mar 89 14:17:37 CST Date: Wed, 22 Mar 89 14:17:37 CST From: norman@fermi (Mike Norman) Message-Id: <8903222017.AA10381@fermi.ncsa.uiuc.edu> To: maper@fermi Subject: ethernet card for Steve Christensen Cc: sc@fermi Status: RO Please take the ethernet card out of my Mac IIx and put it in Steve Christensen's machine. Thanks, Mike From stevec Wed Mar 22 14:32:34 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA12328; Wed, 22 Mar 89 14:30:38 CST Date: Wed, 22 Mar 89 14:30:38 CST Message-Id: <8903222030.AA12328@yoda.ncsa.uiuc.edu> To: mathgroup Subject: Re: Mathematica and Matrices (From sci.math.symbolic) From: Jim_Wendel@ub.cc.umich.edu Status: RO Yes, the exponential forms don't e-mail very well. E[...] is intended to be E^[...] or, equivalently, Exp[...]. I thought the differentiation in the other part of this example was strange. The user wanted to differentiate with respect to b, but the dot-product notation suggests that b is a vector, and then differentiation makes no sense. The answers obtained appear to assume that b is a number after all. But then the notation is peculiar to say the least. Jim_Wendel@ub.cc.umich.edu From stevec Wed Mar 22 14:45:41 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA12344; Wed, 22 Mar 89 14:37:22 CST Date: Wed, 22 Mar 89 14:37:22 CST Message-Id: <8903222037.AA12344@yoda.ncsa.uiuc.edu> To: mathgroup Subject: Orthogonal Polynomials From: CLARK@ENH.NBS.GOV Status: RO Regarding your response to an apparent bug in Tschebischeff (that's the way I like it!) polynomial evaluation: I discovered problems with several of the orthogonal polynomial packages in M'ica Beta Release 0.1 f31 of 6/1/88 (enhanced vers.) on a Mac II with the System and Finder current at the time (early June 1988). These were reported to WRI in the beta tester notebook format, sent on a floppy. I regret that I do not seem to have retained a copy of the corespondence, nor have I tried to reproduce the problems in version 1.1. The problems became manifest in the evaluation of standard recurrence formulae, in which sums of polynomials of different orders must vanish. 0.1 f31 did OK when evaluating these numerically, but would screw up at some values of the argument, such as 1/2, where it did its arithmetic in the clever way. I seem to recall that the Hermite, Jacobi, and Laguerre polynomials exhibited this difficulty. Regards, Charles Clark CLARK@ENH.NBS.GOV From stevec Wed Mar 22 15:33:14 1989 To: mathgroup Subject: please note Status: RO Plot[BesselK[1/2,x],{x,20,25}] came out beautifully, values from 0 down to ^^^^^^^^^^^ -0.0000175 on the vertical axis. ==================================== sounds funny, people may be reading this with a chuckle, as the K function is positive in that range. (Actually positive for all x). Gaston H Gonnet From stevec@yoda Thu Mar 23 11:31:22 1989 Received: from spock.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA14217; Thu, 23 Mar 89 11:31:20 CST Received: from yoda.ncsa.uiuc.edu by spock.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA00157; Thu, 23 Mar 89 11:25:49 CST Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA12344; Wed, 22 Mar 89 14:37:22 CST Date: Wed, 22 Mar 89 14:37:22 CST Message-Id: <8903222037.AA12344@yoda.ncsa.uiuc.edu> To: mathgroup@yoda Subject: Orthogonal Polynomials From: CLARK@ENH.NBS.GOV Status: RO Regarding your response to an apparent bug in Tschebischeff (that's the way I like it!) polynomial evaluation: I discovered problems with several of the orthogonal polynomial packages in M'ica Beta Release 0.1 f31 of 6/1/88 (enhanced vers.) on a Mac II with the System and Finder current at the time (early June 1988). These were reported to WRI in the beta tester notebook format, sent on a floppy. I regret that I do not seem to have retained a copy of the corespondence, nor have I tried to reproduce the problems in version 1.1. The problems became manifest in the evaluation of standard recurrence formulae, in which sums of polynomials of different orders must vanish. 0.1 f31 did OK when evaluating these numerically, but would screw up at some values of the argument, such as 1/2, where it did its arithmetic in the clever way. I seem to recall that the Hermite, Jacobi, and Laguerre polynomials exhibited this difficulty. Regards, Charles Clark CLARK@ENH.NBS.GOV From stevec@yoda Thu Mar 23 11:31:25 1989 Received: from spock.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA14221; Thu, 23 Mar 89 11:31:23 CST Received: from yoda.ncsa.uiuc.edu by spock.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA00160; Thu, 23 Mar 89 11:25:51 CST Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA12460; Wed, 22 Mar 89 15:24:43 CST Date: Wed, 22 Mar 89 15:24:43 CST Message-Id: <8903222124.AA12460@yoda.ncsa.uiuc.edu> To: mathgroup@yoda Subject: please note From: Gaston H Gonnet Status: RO Plot[BesselK[1/2,x],{x,20,25}] came out beautifully, values from 0 down to ^^^^^^^^^^^ -0.0000175 on the vertical axis. ==================================== sounds funny, people may be reading this with a chuckle, as the K function is positive in that range. (Actually positive for all x). Gaston H Gonnet ----- End Included Message ----- From stevec@yoda Thu Mar 23 11:31:26 1989 Received: from spock.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA14223; Thu, 23 Mar 89 11:31:25 CST Received: from yoda.ncsa.uiuc.edu by spock.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA00163; Thu, 23 Mar 89 11:25:54 CST Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA12328; Wed, 22 Mar 89 14:30:38 CST Date: Wed, 22 Mar 89 14:30:38 CST Message-Id: <8903222030.AA12328@yoda.ncsa.uiuc.edu> To: mathgroup@yoda Subject: Re: Mathematica and Matrices (From sci.math.symbolic) From: Jim_Wendel@ub.cc.umich.edu Status: RO Yes, the exponential forms don't e-mail very well. E[...] is intended to be E^[...] or, equivalently, Exp[...]. I thought the differentiation in the other part of this example was strange. The user wanted to differentiate with respect to b, but the dot-product notation suggests that b is a vector, and then differentiation makes no sense. The answers obtained appear to assume that b is a number after all. But then the notation is peculiar to say the least. Jim_Wendel@ub.cc.umich.edu From stevec@yoda Thu Mar 23 11:31:30 1989 Received: from spock.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA14230; Thu, 23 Mar 89 11:31:28 CST Received: from yoda.ncsa.uiuc.edu by spock.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA00166; Thu, 23 Mar 89 11:25:57 CST Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA10039; Tue, 21 Mar 89 16:01:31 CST Date: Tue, 21 Mar 89 16:01:31 CST Message-Id: <8903212201.AA10039@yoda.ncsa.uiuc.edu> To: mathgroup@yoda Subject: Re: Mathematica and Matrices (From sci.math.symbolic) From: maeder@symcom.math.uiuc.edu, Tue@yoda, Mar@yoda, 21@yoda, 54:43@13, 1989@yoda Status: RO > I have a Mathematica question. I did the following: > > In[1]:= y x . b - E[x . b] > > x.b > Out[1]:= -E + yx.b I don't understand how you got that output from your input. E[expr] gives just that, E[expr]. Didn't you mean E^expr or Exp[expr] ? Is your example a verbatim copy of the session? Roman Maeder maeder@symcom.math.uiuc.edu From stevec@yoda Thu Mar 23 11:31:32 1989 Received: from spock.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA14234; Thu, 23 Mar 89 11:31:31 CST Received: from yoda.ncsa.uiuc.edu by spock.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA00169; Thu, 23 Mar 89 11:26:00 CST Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA09421; Tue, 21 Mar 89 13:47:09 CST Date: Tue, 21 Mar 89 13:47:09 CST From: stevec@yoda (Steve Christensen) Message-Id: <8903211947.AA09421@yoda.ncsa.uiuc.edu> To: mathgroup@yoda Status: RO >From Jim_Wendel@ub.cc.umich.edu Tue Mar 21 06:19:52 1989 Subject: Re: Chebyshev "bug" My Mac II version 1.04 of Mathematica gives the correct answer x for ChebyshevT[1,x]. Your message referred to Chebychev... Note slight difference in spelling! My 1.04 version of Mathematica, running on a Mac II, thinks that the product of your two large integers (9 digits each) is a prime. Consistently then it factors it as itself to the 1 power. Plot[BesselK[1/2,x],{x,20,25}] came out beautifully, values from 0 down to -0.0000175 on the vertical axis. [It appears that there are some bugs in 1.1 that were not in 1.04 on all machines. I will try to report on these problems when 1.2 comes out. If you do report bugs, please indicate always which version of the software you are using and on what machine. --- smc] From stevec@yoda Thu Mar 23 11:31:34 1989 Received: from spock.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA14238; Thu, 23 Mar 89 11:31:33 CST Received: from yoda.ncsa.uiuc.edu by spock.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA00172; Thu, 23 Mar 89 11:26:02 CST Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA07587; Mon, 20 Mar 89 14:51:48 CST Date: Mon, 20 Mar 89 14:51:48 CST Message-Id: <8903202051.AA07587@yoda.ncsa.uiuc.edu> To: mathgroup@yoda Subject: Asymptotia From: "Charles W. Clark, NIST, (301) 975-3738" Status: RO I am sure that M'ica does its sums in a very clever way, but it seems to take some chances at the margin. Consider the classical case of a divergent series, the asymptotic expansion for the exponential integral (Whittaker and Watson, chapter VIII): n! (-x)^n. M'ica (running on a Mac IIx , local kernel, default settings) returns a finite result without warning for surprisingly large values of x: x = 0.04934 Sum[n! (-x)^n, {n, 0, Infinity}] //N 0.954923 though, to be entirely fair, it does spot trouble for larger values: x = 0.05 Sum[n! (-x)^n, {n, 0, Infinity}] //N NLimit::dubious: The result from NLimit may be completely wrong. 0.954371 If the results of the ratio test are looked at properly (i.e. nth ratio = (n+1) x, grows indefinitely large with n), this series is seen to be divergent even at the smallest values of x. This sort of test picks out the divergent series that most frequently occur in asymptotic expansions, and I wonder why it has not been implemented. From stevec@yoda Thu Mar 23 11:31:36 1989 Received: from spock.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA14242; Thu, 23 Mar 89 11:31:35 CST Received: from yoda.ncsa.uiuc.edu by spock.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA00175; Thu, 23 Mar 89 11:26:04 CST Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA07601; Mon, 20 Mar 89 14:55:40 CST Date: Mon, 20 Mar 89 14:55:40 CST Message-Id: <8903202055.AA07601@yoda.ncsa.uiuc.edu> To: mathgroup@yoda Subject: Mathematica bugs From: knutm@ifi.uio.no Status: RO There is a simple bug in the Chebychev polynomial function which I imagine others have also found. Mathematica (version 1.1 on a Mac II) will tell you that the first degree Chebychev polynomial of the first kind is the constant zero, i.e., ChebychevT[1,x] = 0 if I remember the syntax correctly. This bug has already been reported to Wolfram Research. A much more serious bug that I found was in the integer factorization routine FactorInteger. According to Shawn Sheridan who is Manager of Technical Support this bug has now been fixed in Wolfram Research's development version and the fix will be included in the next release. Below is an extract of the message I received from Dr. Sheridan (dated March 18) >Thank you for your bug report on Mathematica v1.1. As you can see below, >the large integer bug has been fixed in our development version. You >should be receiving this version in the spring. >SunMathematica (sun3.fpa) 1.2-development (March 7, 1989) [With pre-loaded data] >by S. Wolfram, D. Grayson, R. Maeder, H. Cejtin, > S. Omohundro, D. Ballman and J. Keiper >with I. Rivin and D. Withoff >Copyright 1988 Wolfram Research Inc. >-- Terminal graphics initialized -- >In[1]:= 536903681 107367629 >Out[1]= 57646075230342349 >In[2]:= PrimeQ[%] >Out[2]= False >In[3]:= FactorInteger[%1] >Out[3]= {{107367629, 1}, {536903681, 1}} In version 1.1, Mathematica claims that the product of the two integers is prime. Knut Morken Institute of Informatics University of Oslo Norway (knutm@ifi.uio.no) From stevec@yoda Thu Mar 23 11:31:38 1989 Received: from spock.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA14246; Thu, 23 Mar 89 11:31:37 CST Received: from yoda.ncsa.uiuc.edu by spock.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA00178; Thu, 23 Mar 89 11:26:06 CST Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA07498; Mon, 20 Mar 89 13:49:01 CST Date: Mon, 20 Mar 89 13:49:01 CST From: stevec@yoda (Steve Christensen) Message-Id: <8903201949.AA07498@yoda.ncsa.uiuc.edu> To: mathgroup@yoda Subject: Mathematica and Matrices (From sci.math.symbolic) Status: RO gmk Mathematica and matrices 9:25 pm Mar 16, 1989(at wjh12.harvard.edu) (From News system) I have a Mathematica question. I did the following: In[1]:= y x . b - E[x . b] x.b Out[1]:= -E + yx.b In[2]:= D[%,b] x.b Out[2]:= -(E (0.b + x.1)) + y(0.b + x.1) Of course, this answer is right, but I would prefer if Mathematica knew that 0.b=0 and x.1=1, so that the above equation would be written as follows: x.b -x E + yx Does anyone know how to get Mathematica to do this? Thanks in advance Gary King ........... : Gary King, Department of Government, Harvard University, Cambridge, MA 02138 harvard.edu, BITnet: gmk@harvunxw, Phone: 617-495-2027 From stevec Thu Mar 23 12:06:26 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA14278; Thu, 23 Mar 89 12:02:53 CST Date: Thu, 23 Mar 89 12:02:53 CST From: stevec (Steve Christensen) Message-Id: <8903231802.AA14278@yoda.ncsa.uiuc.edu> To: mathgroup Subject: Laplace Transforms on Mathematica Status: RO >From sci.math.symbolic: [Note that some people who post to sci.math.symbolic are not members of this mailing list. So, in addition to sending replies to messages to me to forward to the mailing list, you may want to reply in sci.math.symbolic or directly to the author. I am posting sci.math.symbolic messages here as a service to those of you who do not have access to that newsgroup. -smc] tca Laplace Transforms on Mathematica 12:21 pm Mar 22, 1989(at ut-emx.UUCP) (From News system) Before I went ahead and created my own functions, I would like to see if anyone else has created additional functions in the Laplace.m file in Mathematica which handle more complicated transforms such as hyperbolic and trigonometric functions. The Mathematica release for the Macintosh handles polynomials and exponential functions but that's about all. Any additions to InverseLaplace.m would be welcome as well. -------------------- Tobin C. Anthony Department of Aerospace Engineering and Engineering Mechanics University of Texas at Austin e-mail : tca@gunaco.ae.utexas.edu Office : 512-471-3681 From stevec@yoda Thu Mar 23 12:24:40 1989 Received: from spock.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA14534; Thu, 23 Mar 89 12:24:39 CST Received: from yoda.ncsa.uiuc.edu by spock.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA00206; Thu, 23 Mar 89 12:19:08 CST Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA14278; Thu, 23 Mar 89 12:02:53 CST Date: Thu, 23 Mar 89 12:02:53 CST From: stevec@yoda (Steve Christensen) Message-Id: <8903231802.AA14278@yoda.ncsa.uiuc.edu> To: mathgroup@yoda Subject: Laplace Transforms on Mathematica Status: RO >From sci.math.symbolic: [Note that some people who post to sci.math.symbolic are not members of this mailing list. So, in addition to sending replies to messages to me to forward to the mailing list, you may want to reply in sci.math.symbolic or directly to the author. I am posting sci.math.symbolic messages here as a service to those of you who do not have access to that newsgroup. -smc] tca Laplace Transforms on Mathematica 12:21 pm Mar 22, 1989(at ut-emx.UUCP) (From News system) Before I went ahead and created my own functions, I would like to see if anyone else has created additional functions in the Laplace.m file in Mathematica which handle more complicated transforms such as hyperbolic and trigonometric functions. The Mathematica release for the Macintosh handles polynomials and exponential functions but that's about all. Any additions to InverseLaplace.m would be welcome as well. -------------------- Tobin C. Anthony Department of Aerospace Engineering and Engineering Mechanics University of Texas at Austin e-mail : tca@gunaco.ae.utexas.edu Office : 512-471-3681 From stevec Fri Mar 24 15:50:24 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA16271; Fri, 24 Mar 89 15:48:08 CST Date: Fri, 24 Mar 89 15:48:08 CST Message-Id: <8903242148.AA16271@yoda.ncsa.uiuc.edu> To: mathgroup Subject: Need help Solv[]ing equations From: sdoyle@fed.frb.gov Status: RO Hi: I am trying to solve a system of four equations using Mathematica, and Solve[] (and/or Reduce[]) are running out of memory. It is possible that the equations have no solution. I'm using SunMathematica (sun3.68881) 1.1 on a Sun 3/60. I'd like to understand why Mathematica has difficulty with this problem (it probably isn't Mathematica's fault.) This set of equations is from two economists that don't have access to Mathematica. They would like a solution, but I'm more interested in how the algorithms work. Any hints/solutions/truth&beauty appreciated. Part 1:How to create the out-of-memory error: I've attached the file SolveProblem.m below. After you read the file in (e.g. < In[2]:= Solve[eqns,{w,x,y,z}] > Out of memory. Also about half an hour (different session) > In[2]:= Reduce[Share[eqns], {w,x,y,z}] > Out of memory. Share seems to simply to delay out-of-memory message. As an aside, Mathematica doesn't seem to respond to Control-C after either Solve[] or Reduce[] has been running a while (I did wait a few minutes to respond before killing the process). (******************* File SolveProblem.m ************************) (* Small model that Solve[] has problems solving. Solve[eqns, {w,x,y,z}] *) eqns = { w x y z == 1/b^2, w x (y + z) + y z (w + x) == - (c a + f g)/(a q b^2 (f c + p d)), w (x + z) + y (w + x) + z (x + y) == (1 + 2 b a q (f c + p d))/ (a q b^2 (f c + p d)), w + x + y + z == -(f q + c a)/(b q a (f c + p d)) } (****************** End of file SolveProblem.m ************************) Part 2: Various questions: 1. Why is this problem hard? 2. Solve[] and Reduce[] are (to me) black boxes. If this were *my* problem I'd start by reducing the dimensions to three, and create some plots. Can others suggest a better search procedure? 3. Are there ways of posing problems to Solve[] and Reduce[] that are easier for them to solve? Since I don't know what the algorithms are doing internally, I don't know if the failure to find a solution is because a) The problem has no solution b) The algorithm doesn't deal with this class of problems, so I'm abusing the software c) I haven't RTFM closely enough Thanks! Sean Doyle Board of Governors of the Federal Reserve System 20 and Constitution, NW Mail Stop 76 Washington, DC 20551 (202) 452-2352 uucp: uunet!fed!m1swd00 , internet: sdoyle@fed.frb.gov From stevec Fri Mar 24 16:02:27 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA16300; Fri, 24 Mar 89 15:54:54 CST Date: Fri, 24 Mar 89 15:54:54 CST Message-Id: <8903242154.AA16300@yoda.ncsa.uiuc.edu> To: mathgroup Subject: Some questions on Mac II version 1.1 From: munnari!merlin.bhpmrl.oz.au!tim@uunet.UU.NET (Tim Monks) Status: RO Steve, I have a couple of questions about the Mathematica, (Mac II version 1.1) which I hope either you or someone on the Mathematica mailing list can answer - Australia is rather isolated & there aren't any Mathematica experts here (yet !!) 1. Our copy of version 1.1 does not have the ODE.m package for solving differential equations. Is this package available yet, or is it to be released in a later version ? 2. How do we go about getting future updates to Mathematica ? News of any upgrades takes a bit of time to filter out to Oz, we have got electronic mail and a hook into Usenet news, but not a Portal account. Do you know if the Portal system is functional in Australia so we can get access to Mathematica on-line services ? 3. We have a network of Apollo's and a Silicon Graphics Iris at the labs as well as Macs. Once Apollo get their act together and release Mathematica we would like to run it on our DN10000. We have got both serial and ethernet links between the Mac and the Apollo - will future versions of Mathematica on the Mac support ethernet comms protocol or will it be limited to serial links ? Would there be any advantage in high speed communication between a remote kernel and the front end ? 4. I read a review in the 16th. Feb. edition of Nature for MathReader - a program for viewing Mathematica notebooks. Is this just a utility for those unfortunate sods who have not got Mathematica or does it do more tricks ? I hope you can provide a few answers. Many thanks for your time, From stevec Fri Mar 24 16:03:55 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA16296; Fri, 24 Mar 89 15:53:33 CST Date: Fri, 24 Mar 89 15:53:33 CST Message-Id: <8903242153.AA16296@yoda.ncsa.uiuc.edu> To: mathgroup Subject: bug in cross product From: mrk@athena.Princeton.EDU Status: RO There is a bug in the Mathematica Package CrossProduct.m. Following is a sample session illustrating the problem: In[1]:= < Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA16271; Fri, 24 Mar 89 15:48:08 CST Date: Fri, 24 Mar 89 15:48:08 CST Message-Id: <8903242148.AA16271@yoda.ncsa.uiuc.edu> To: mathgroup@yoda Subject: Need help Solv[]ing equations From: sdoyle@fed.frb.gov Status: RO Hi: I am trying to solve a system of four equations using Mathematica, and Solve[] (and/or Reduce[]) are running out of memory. It is possible that the equations have no solution. I'm using SunMathematica (sun3.68881) 1.1 on a Sun 3/60. I'd like to understand why Mathematica has difficulty with this problem (it probably isn't Mathematica's fault.) This set of equations is from two economists that don't have access to Mathematica. They would like a solution, but I'm more interested in how the algorithms work. Any hints/solutions/truth&beauty appreciated. Part 1:How to create the out-of-memory error: I've attached the file SolveProblem.m below. After you read the file in (e.g. < In[2]:= Solve[eqns,{w,x,y,z}] > Out of memory. Also about half an hour (different session) > In[2]:= Reduce[Share[eqns], {w,x,y,z}] > Out of memory. Share seems to simply to delay out-of-memory message. As an aside, Mathematica doesn't seem to respond to Control-C after either Solve[] or Reduce[] has been running a while (I did wait a few minutes to respond before killing the process). (******************* File SolveProblem.m ************************) (* Small model that Solve[] has problems solving. Solve[eqns, {w,x,y,z}] *) eqns = { w x y z == 1/b^2, w x (y + z) + y z (w + x) == - (c a + f g)/(a q b^2 (f c + p d)), w (x + z) + y (w + x) + z (x + y) == (1 + 2 b a q (f c + p d))/ (a q b^2 (f c + p d)), w + x + y + z == -(f q + c a)/(b q a (f c + p d)) } (****************** End of file SolveProblem.m ************************) Part 2: Various questions: 1. Why is this problem hard? 2. Solve[] and Reduce[] are (to me) black boxes. If this were *my* problem I'd start by reducing the dimensions to three, and create some plots. Can others suggest a better search procedure? 3. Are there ways of posing problems to Solve[] and Reduce[] that are easier for them to solve? Since I don't know what the algorithms are doing internally, I don't know if the failure to find a solution is because a) The problem has no solution b) The algorithm doesn't deal with this class of problems, so I'm abusing the software c) I haven't RTFM closely enough Thanks! Sean Doyle Board of Governors of the Federal Reserve System 20 and Constitution, NW Mail Stop 76 Washington, DC 20551 (202) 452-2352 uucp: uunet!fed!m1swd00 , internet: sdoyle@fed.frb.gov From stevec@yoda Fri Mar 24 17:33:16 1989 Received: from spock.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA16394; Fri, 24 Mar 89 17:33:15 CST Received: from yoda.ncsa.uiuc.edu by spock.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA00779; Fri, 24 Mar 89 17:27:43 CST Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA16300; Fri, 24 Mar 89 15:54:54 CST Date: Fri, 24 Mar 89 15:54:54 CST Message-Id: <8903242154.AA16300@yoda.ncsa.uiuc.edu> To: mathgroup@yoda Subject: Some questions on Mac II version 1.1 From: munnari!merlin.bhpmrl.oz.au!tim@uunet.UU.NET (Tim Monks) Status: RO Steve, I have a couple of questions about the Mathematica, (Mac II version 1.1) which I hope either you or someone on the Mathematica mailing list can answer - Australia is rather isolated & there aren't any Mathematica experts here (yet !!) 1. Our copy of version 1.1 does not have the ODE.m package for solving differential equations. Is this package available yet, or is it to be released in a later version ? 2. How do we go about getting future updates to Mathematica ? News of any upgrades takes a bit of time to filter out to Oz, we have got electronic mail and a hook into Usenet news, but not a Portal account. Do you know if the Portal system is functional in Australia so we can get access to Mathematica on-line services ? 3. We have a network of Apollo's and a Silicon Graphics Iris at the labs as well as Macs. Once Apollo get their act together and release Mathematica we would like to run it on our DN10000. We have got both serial and ethernet links between the Mac and the Apollo - will future versions of Mathematica on the Mac support ethernet comms protocol or will it be limited to serial links ? Would there be any advantage in high speed communication between a remote kernel and the front end ? 4. I read a review in the 16th. Feb. edition of Nature for MathReader - a program for viewing Mathematica notebooks. Is this just a utility for those unfortunate sods who have not got Mathematica or does it do more tricks ? I hope you can provide a few answers. Many thanks for your time, From stevec Wed Mar 29 13:12:53 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA20547; Wed, 29 Mar 89 13:06:44 CST Date: Wed, 29 Mar 89 13:06:44 CST Message-Id: <8903291906.AA20547@yoda.ncsa.uiuc.edu> To: mathgroup Subject: Re: Splicing into tex docs From: dooley@ernie.berkeley.edu Status: RO Apparently the Splice command uses the PageWidth option to control how to use the Short form. So you can try: Splice[ "test.mtex", PageWidth -> Infinity ] to stop Splice from using the Short form at all. The option, and others, are listed, but not fully explained, on page 688 of the Mathematica manual. Sam Dooley dooley@ernie.berkeley.edu From stevec Wed Mar 29 13:14:27 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA20543; Wed, 29 Mar 89 13:05:11 CST Date: Wed, 29 Mar 89 13:05:11 CST Message-Id: <8903291905.AA20543@yoda.ncsa.uiuc.edu> To: mathgroup Subject: Jobs at Wolfram Reseearch, Inc. From: sueann@wri.com Status: RO Positions Available at WOLFRAM RESEARCH, INC. Wolfram Research, Inc. is seeking top-quality individuals in a number of areas. We are the developer of Mathematica, a system for doing mathematics, which runs on a range of computers from Macintosh and MS-DOS 386 systems to workstations and supercomputers. We are based in Champaign, Illinois, and currently have about 55 employees, some of whom work from remote locations. SOFTWARE ENGINEERING Work on implementation of Mathematica on a variety of computers. There are openings for experts in several different environments. At present, the highest priorities are MacOS, VAX VMS, IBM mainframe systems and supercomputer systems. Requirements: At least two years of systems programming experience; good problem-solving skills and attention to detail. MATHEMATICAL DEVELOPMENT Develop and implement mathematical algorithms, both in C and in the Mathematica language. Current priorities include: numerical analysis, differential equations, and nonlinear optimization. Requirements: Ph.D. in mathematical sciences or equivalent; ability to develop original mathematical algorithms; extensive programming experience. Preferred: Experience with C and very high-level languages. STATISTICS DEVELOPMENT Develop and implement statistical algorithms, primarily in the Mathematica language. Requirements: Ph.D. in statistics or related area; broad knowledge of statistics and its applications; ability to develop original ideas and algorithms in statistics; extensive programming experience. Preferred: Experience with Mathematica or other very high-level languages. GRAPHICS DEVELOPMENT Develop and implement graphics algorithms in both hardware-independent and hardware-dependent code. Special code for real-time graphics on various high-end graphics workstations is needed. Requirements: Extensive experience with graphics programming on a variety of computer systems; ability to interact effectively with hardware vendors; availability for travel. Preferred: Documentation and graphic design skills. SYSTEM ADMINISTRATION Administer a network that includes at least one of nearly every personal computer and workstation on the market. Requirements: At least two years of UNIX systems programming experience; good organizational skills. USER SUPPORT Provide support to Mathematica users, primarily by electronic mail and telephone. Requirments: B.S. or equivalent; good mathematical skills; experience with a variety of computer software and hardware systems; good problem-solving, verbal and written communication skills. Preferred: Experience with Mathematica. Part-time applicants will be considered. SOFTWARE QUALITY ASSURANCE Identify, document and track bugs. Coordinate software testing activities. (Reports to Manager of User Support.) Requirements: B.S. or equivalent; good organizational skills and attention to detail; mathematical knowledge; experience with UNIX systems. SOFTWARE PROJECT COORDINATION Schedule and coordinate major software projects and releases. Involves extensive interaction with company management, technical, and manufacturing staff, as well as computer manufacturers. Requirements: B.S. or equivalent; significant experience with UNIX; familiarity with a wide range of computer systems from personal computers to supercomputers; two years of programming experience; a balance of technical and administrative ability; good interpersonal skills. Preferred: Experience with a large software project. TECHNICAL SALES Present Mathematica sales programs, both by telephone and at customer sites, to corporate and university customers. Requirements: B.S. or equivalent; knowledge of applied mathematics; familiarity with a wide range of computer systems; excellent verbal, written, and interpersonal skills; availability for travel. Preferred: Two years of work experience in computer industry; two years of sales experience. TECHNICAL SALES SUPPORT Explain aspects of Mathematica to potential customers, primarily by telephone. Requirements: B.S. or equivalent; knowledge of applied mathematics; experience with a variety of computer systems; excellent verbal skills. Preferred: Sales experience. Send resume to: Amy Visentin Wolfram Research, Inc. 201 W. Springfield Ave., 5th floor P.O. Box 6059 Champaign, IL 61826 217-398-0700 fax: 217-398-0747 or send Email to: resumes@wri.com or resumes%wri.com@uunet 3/24/89 From stevec@yoda Wed Mar 29 13:27:50 1989 Received: from spock.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA20553; Wed, 29 Mar 89 13:27:49 CST Received: from yoda.ncsa.uiuc.edu by spock.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA03600; Wed, 29 Mar 89 13:22:10 CST Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA20547; Wed, 29 Mar 89 13:06:44 CST Date: Wed, 29 Mar 89 13:06:44 CST Message-Id: <8903291906.AA20547@yoda.ncsa.uiuc.edu> To: mathgroup@yoda Subject: Re: Splicing into tex docs From: dooley@ernie.berkeley.edu Status: RO Apparently the Splice command uses the PageWidth option to control how to use the Short form. So you can try: Splice[ "test.mtex", PageWidth -> Infinity ] to stop Splice from using the Short form at all. The option, and others, are listed, but not fully explained, on page 688 of the Mathematica manual. Sam Dooley dooley@ernie.berkeley.edu From stevec@yoda Wed Mar 29 13:28:01 1989 Received: from spock.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA20561; Wed, 29 Mar 89 13:27:59 CST Received: from yoda.ncsa.uiuc.edu by spock.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA03603; Wed, 29 Mar 89 13:22:19 CST Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA20543; Wed, 29 Mar 89 13:05:11 CST Date: Wed, 29 Mar 89 13:05:11 CST Message-Id: <8903291905.AA20543@yoda.ncsa.uiuc.edu> To: mathgroup@yoda Subject: Jobs at Wolfram Reseearch, Inc. From: sueann@wri.com Status: RO Positions Available at WOLFRAM RESEARCH, INC. Wolfram Research, Inc. is seeking top-quality individuals in a number of areas. We are the developer of Mathematica, a system for doing mathematics, which runs on a range of computers from Macintosh and MS-DOS 386 systems to workstations and supercomputers. We are based in Champaign, Illinois, and currently have about 55 employees, some of whom work from remote locations. SOFTWARE ENGINEERING Work on implementation of Mathematica on a variety of computers. There are openings for experts in several different environments. At present, the highest priorities are MacOS, VAX VMS, IBM mainframe systems and supercomputer systems. Requirements: At least two years of systems programming experience; good problem-solving skills and attention to detail. MATHEMATICAL DEVELOPMENT Develop and implement mathematical algorithms, both in C and in the Mathematica language. Current priorities include: numerical analysis, differential equations, and nonlinear optimization. Requirements: Ph.D. in mathematical sciences or equivalent; ability to develop original mathematical algorithms; extensive programming experience. Preferred: Experience with C and very high-level languages. STATISTICS DEVELOPMENT Develop and implement statistical algorithms, primarily in the Mathematica language. Requirements: Ph.D. in statistics or related area; broad knowledge of statistics and its applications; ability to develop original ideas and algorithms in statistics; extensive programming experience. Preferred: Experience with Mathematica or other very high-level languages. GRAPHICS DEVELOPMENT Develop and implement graphics algorithms in both hardware-independent and hardware-dependent code. Special code for real-time graphics on various high-end graphics workstations is needed. Requirements: Extensive experience with graphics programming on a variety of computer systems; ability to interact effectively with hardware vendors; availability for travel. Preferred: Documentation and graphic design skills. SYSTEM ADMINISTRATION Administer a network that includes at least one of nearly every personal computer and workstation on the market. Requirements: At least two years of UNIX systems programming experience; good organizational skills. USER SUPPORT Provide support to Mathematica users, primarily by electronic mail and telephone. Requirments: B.S. or equivalent; good mathematical skills; experience with a variety of computer software and hardware systems; good problem-solving, verbal and written communication skills. Preferred: Experience with Mathematica. Part-time applicants will be considered. SOFTWARE QUALITY ASSURANCE Identify, document and track bugs. Coordinate software testing activities. (Reports to Manager of User Support.) Requirements: B.S. or equivalent; good organizational skills and attention to detail; mathematical knowledge; experience with UNIX systems. SOFTWARE PROJECT COORDINATION Schedule and coordinate major software projects and releases. Involves extensive interaction with company management, technical, and manufacturing staff, as well as computer manufacturers. Requirements: B.S. or equivalent; significant experience with UNIX; familiarity with a wide range of computer systems from personal computers to supercomputers; two years of programming experience; a balance of technical and administrative ability; good interpersonal skills. Preferred: Experience with a large software project. TECHNICAL SALES Present Mathematica sales programs, both by telephone and at customer sites, to corporate and university customers. Requirements: B.S. or equivalent; knowledge of applied mathematics; familiarity with a wide range of computer systems; excellent verbal, written, and interpersonal skills; availability for travel. Preferred: Two years of work experience in computer industry; two years of sales experience. TECHNICAL SALES SUPPORT Explain aspects of Mathematica to potential customers, primarily by telephone. Requirements: B.S. or equivalent; knowledge of applied mathematics; experience with a variety of computer systems; excellent verbal skills. Preferred: Sales experience. Send resume to: Amy Visentin Wolfram Research, Inc. 201 W. Springfield Ave., 5th floor P.O. Box 6059 Champaign, IL 61826 217-398-0700 fax: 217-398-0747 or send Email to: resumes@wri.com or resumes%wri.com@uunet 3/24/89 From stevec@yoda Fri Mar 31 22:06:43 1989 Received: from spock.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA22782; Fri, 31 Mar 89 22:06:42 CST Received: from yoda.ncsa.uiuc.edu by spock.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA04762; Fri, 31 Mar 89 22:00:59 CST Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA22756; Fri, 31 Mar 89 20:59:21 CST Date: Fri, 31 Mar 89 20:59:21 CST Message-Id: <8904010259.AA22756@yoda.ncsa.uiuc.edu> To: mathgroup@yoda Subject: ftp in Europe From: knutm@ifi.uio.no Status: RO [For those of you in Europe who have asked how some users there can ftp to the Mathematica archive, here is one answer. I will try to provide an alternative for those of you who cannot arrange something like this. --smc] As you mentioned in your letter I have ftp'ed successfully to the MathGroup archive. According to our local net guru this is possible since we are connected to the NSF-net in the States (at the John von Neumann Computing Center or something like that). At the moment, the only European countries with this facility is Finland, Sweden, Denmark and Norway. These countries share this connection. Apparently, Holland will soon establish a similar link, and possibly also France. Hope this helps. Knut Morken knutm@ifi.uio.no ----- End Included Message ----- From stevec Mon Apr 3 16:51:27 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA25226; Mon, 3 Apr 89 16:39:53 CDT Date: Mon, 3 Apr 89 16:39:53 CDT From: stevec (Steve Christensen) Message-Id: <8904032139.AA25226@yoda.ncsa.uiuc.edu> To: mathgroup Subject: Dirac Algebra? Status: RO [I have heard from a number of users who want to know if anyone has done a Dirac Algebra package in Mathematica. Anyone out there know of one? -smc] >From RDC@vms.cis.pittsburgh.edu Mon Apr 3 15:50:58 1989 >Subject: RE: Dirac Algegra >To: stevec@ncsa.uiuc.edu >X-Vms-To: IN%"stevec%ncsa.uiuc.EDU@unix.cis.pittsburgh.edu" >Dear Steve, >Earlier this year we discussed the question of Dirac algebra macros for >Mathematica. I am reaching the point of doing some more calculations >which will require this sort of thing. Has anything happened on this >front? I know there are other people who are interested in this, but >I haven't been following the latest developments. Could you please >fill me in. >Thanks, >Bob Carlitz From stevec@yoda Mon Apr 3 17:20:43 1989 Received: from spock.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA25307; Mon, 3 Apr 89 17:20:42 CDT Received: from yoda.ncsa.uiuc.edu by spock.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA06431; Mon, 3 Apr 89 17:18:00 CDT Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA25226; Mon, 3 Apr 89 16:39:53 CDT Date: Mon, 3 Apr 89 16:39:53 CDT From: stevec@yoda (Steve Christensen) Message-Id: <8904032139.AA25226@yoda.ncsa.uiuc.edu> To: mathgroup@yoda Subject: Dirac Algebra? Status: RO [I have heard from a number of users who want to know if anyone has done a Dirac Algebra package in Mathematica. Anyone out there know of one? -smc] >From RDC@vms.cis.pittsburgh.edu Mon Apr 3 15:50:58 1989 >Subject: RE: Dirac Algegra >To: stevec@ncsa.uiuc.edu >X-Vms-To: IN%"stevec%ncsa.uiuc.EDU@unix.cis.pittsburgh.edu" >Dear Steve, >Earlier this year we discussed the question of Dirac algebra macros for >Mathematica. I am reaching the point of doing some more calculations >which will require this sort of thing. Has anything happened on this >front? I know there are other people who are interested in this, but >I haven't been following the latest developments. Could you please >fill me in. >Thanks, >Bob Carlitz From stevec Mon Apr 17 12:53:39 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA11214; Mon, 17 Apr 89 12:35:26 CDT Date: Mon, 17 Apr 89 12:35:26 CDT Message-Id: <8904171735.AA11214@yoda.ncsa.uiuc.edu> To: mathgroup Subject: Fourier Transform Package From: Victor Sparrow Status: RO [Here is a contributed package. As with all future packages, please report any problems you may have to the author first so that the author may submit corrections. Authors should give credit to the persons locating problems. Disagreements over the workings of a package can be posted to the mailing list freely. This package will be placed in the archive. -smc] April 13, 1989 Dear Steve, Here is the symbolic Fourier transform package as promised. Please post to the appropriate notesfiles and archives. You are getting a shar(1) archive of two files: Ft.m and Ft.doc. I have developed this on a MacII using Mathematica release 1.1. Please contact me if you have any questions or suggestions. Best wishes, Vic Sparrow sparrow@osiris.cso.uiuc.edu -----------Cut Here---------- #! /bin/sh # This is a shell archive, meaning: # 1. Remove everything above the #! /bin/sh line. # 2. Save the resulting text in a file. # 3. Execute the file with /bin/sh (not csh) to create: # Ft.m # Ft.doc # This archive created: Thu Apr 13 15:43:43 1989 export PATH; PATH=/bin:/usr/bin:$PATH if test -f 'Ft.m' then echo shar: "will not over-write existing file 'Ft.m'" else cat << \SHAR_EOF > 'Ft.m' (* Ft.m copyright 1989 by Victor W. Sparrow *) (* Permission is granted to copy the file provided that the copyright notice is left intact and the copies are not distributed commercially. *) (* The author wishes to thank Roman Maeder, George Swenson, and Mike White, who helped in the development of this package. Dr. Maeder for his help in the treatment of complex numbers in pattern matching, and Drs. Swenson and White for their encouragement and suggestions. *) BeginPackage["Ft`"] (* Version 9: added Fta[], Ftb[], iFta[], iFtb[], conversion functions for alternate transform definitions. 04/10/89 *) (* Version 8: fixed delay with optional scaling for forward transforms. Also some other rearrangements. 04/04/89 *) (* Version 7: fixed differentiation transforms and some other things on 03/27/89 *) (* Version 6: more inverse transforms and many improvements to forward ones 03/23/89 *) (* Version 5: started adding inverse transforms on 03/22/89 *) (* Version 4: more usage statements, and additional improvements to many functions. 03/20/89 *) (* Version 3: more forward transforms 03/03/89 *) (* In version 2 Vic Sparrow, the author of this package, had a little help on complex numbers from Roman Maeder. 02/28/89 *) Ft::usage = "Ft[expr,t,omega] gives the symbolic Fourier transform of expr in t space to omega space." iFt::usage = "iFt[expr,t,omega] gives the symbolic inverse Fourier transform of expr in omega space to t space." Fta::usage = "Fta[expr,t,omega] gives the symbolic Fourier transform of expr in t space to omega space. In this transform the 2 Pi appears in the exponent of the exponential function." iFta::usage = "iFta[expr,t,omega] gives the symbolic inverse Fourier transform of expr in omega space to t space. In this transform the 2 Pi appears in the exponent of the exponential function." Ftb::usage = "Ftb[expr,t,omega] gives the symbolic Fourier transform of expr in t space to omega space. This transform includes Sqrt[2 Pi] as a scaling factor" iFtb::usage = "iFtb[expr,t,omega] gives the symbolic inverse Fourier transform of expr in omega space to t space. This transform includes Sqrt[2 Pi] as a scaling factor." convolution::usage = "convolution[a,b] is the convolution integral of a and b." delta::usage = "delta[t] is the dirac delta function of t." u::usage = "u[t] is the unit step function of t, u[t]=0 for t<0 and u[t]=1 for t>0." rect::usage = "rect[t] is the rectagular function of t, rect[t]=1 for Abs[t]<1/2 and rect[t]=0 otherwise." sinc::usage = "sinc[t] is the function Sin[t]/t." triangle::usage = "triangle[t] is the triangular function of t, triangle[t]=1-Abs[t] for Abs[t]<1 and triangle[t]=0 otherwise." Begin["`private`"] (* Fourier Transform Section: *) (* constants *) Ft[c_,t_,om_]:= 2 Pi c delta[om] /; FreeQ[c,t] (* linearity *) Ft[a_ + b_,t_,om_]:= Ft[a,t,om] + Ft[b,t,om] (* pick off constants *) Ft[c_ a_,t_,om_]:= c Ft[a,t,om] /; FreeQ[c,t] (* frequency translation *) Ft[a_ Exp[c_Complex omn_. t_],t_,om_]:= Ft[a,t,om-Im[c]omn] /; (FreeQ[omn,t] && Re[c]==0) (* amplitude modulation *) Ft[a_ Cos[omn_. t_],t_,om_]:= Ft[a,t,om+omn]/2 + Ft[a,t,om-omn]/2 /; FreeQ[omn,t] (* time differentiation *) Unprotect[Derivative] Derivative/: Ft[Derivative[n_Integer?Positive][a_][t_],t_,om_]:= (I om)^n Ft[a[t],t,om] Protect[Derivative] (* time convolution *) Ft[convolution[a_,b_],t_,om_]:= Ft[a,t,om] Ft[b,t,om] (* complex conjugate *) Ft[Conjugate[a_],t_,om_]:= Conjugate[Ft[a,t,-om]] (* sign function *) Ft[Sign[t_],t_,om_]:= 2 / (I om) (* delta function *) Ft[delta[t_],t_,om_]:= 1 (* step function *) Ft[u[t_],t_,om_]:= Pi delta[om] - I/om (* complex exponential *) Ft[Exp[c_Complex omn_. t_],t_,om_]:= 2 Pi delta[om - Im[c]omn] /; (FreeQ[omn,t] && Re[c]==0) (* cosine *) Ft[Cos[omn_. t_],t_,om_]:= Pi(delta[om -omn] + delta[om+omn]) /; FreeQ[omn,t] (* sine *) Ft[Sin[omn_. t_],t_,om_]:= -I Pi(delta[om - omn] - delta[om+omn]) /; FreeQ[omn,t] (* step exponential *) Ft[Exp[c_?NumberQ con_. t_] u[t_],t_,om_]:= 1/(-c con + I om) /; (FreeQ[con,t] && c<0 && Im[c]==0) (* step exponential 2 *) Ft[t_ Exp[c_?NumberQ con_. t_] u[t_],t_,om_]:= 1/(-c con + I om)^2 /; (FreeQ[con,t] && c<0 && Im[c]==0) (* double sided exponential *) Ft[Exp[c_?NumberQ con_. Abs[t_]],t_,om_]:= -2 c con/((- c con)^2 + om^2) /; (FreeQ[con,t] && c<0 && Im[c]==0) (* Gaussian: c=-1/(2 sigma^2) sigma=Sqrt[-1/2c] assume c<0 and sigma>0 *) Ft[Exp[c_?NumberQ ccon_. t_^2],t_,om_]:= Sqrt[- Pi/(c ccon)] Exp[om^2/( 4 c ccon)] /; (FreeQ[ccon,t] && c<0 && Im[c]==0) (* Sign in freq. domain. *) Ft[Power[t_,-1],t_,om_]:= -I Pi Sign[om] /; FreeQ[c,t] (* Rectangular fn. *) Ft[rect[t_],t_,om_]:= sinc[om/2] (* sinc fn. *) Ft[sinc[t_],t_,om_]:= Pi rect[om/2] (* Triangle fn. *) Ft[triangle[t_],t_,om_]:=(sinc[om/2])^2 (* Very general rules should be last. *) (* frequency differentiation *) Ft[t_^n_. a_,t_,om_]:= I^n Derivative[n][ Ft[a,t,om] ][om] /; FreeQ[n,t] && n>0 (* multiplication by delta function *) Ft[a_ delta[t_ + tnot_.],t_,om_]:= Limit[a Exp[-I om t],t->-tnot] /; FreeQ[tnot,t] (* scaling *) Ft[a_[alph_ t_],t_,om_]:= (1/Abs[alph] Ft[a[t],t,om/alph] /; FreeQ[alph,t] ) (* delay with optional scaling *) Ft[a_[alph_. t_ + tnot_],t_,om_]:= (1/Abs[alph] Ft[a[t],t,om/alph] Exp[I tnot om / alph] /; FreeQ[alph,t] && FreeQ[tnot,t]) (* frequency convolution for 2 *) Ft[a_[t_] b_[t_],t_,om_]:= convolution[Ft[a[t],t,om],Ft[b[t],t,om]]/(2 Pi) (* Inverse Fourier Transform Section: *) (* constants *) iFt[c_,t_,om_]:= c delta[t] /; FreeQ[c,om] (* linearity *) iFt[a_ + b_,t_,om_]:= iFt[a,t,om] + iFt[b,t,om] (* pick off constants *) iFt[c_ a_,t_,om_]:= c iFt[a,t,om] /; FreeQ[c,om] (* one sided exponential *) iFt[1/(c_ + I om_),t_,om_]:= Exp[-c t] u[t] /; FreeQ[c,om] (* t and one sided exponential *) iFt[1/(c_ + I om_)^2,t_,om_]:= t Exp[-c t] u[t] /; FreeQ[c,om] (* double sided exponential *) iFt[1/(c_ + om_^2),t_,om_]:= ( Exp[-Sqrt[c] Abs[t]] /(2 Sqrt[c]) /; FreeQ[c,om] ) (* Gaussian *) (* c=-sigma^2/2) sigma=Sqrt[-2c] assume c<0 and sigma>0 *) iFt[Exp[c_?NumberQ ccon_. om_^2],t_,om_]:= Exp[t^2/(4 c ccon)]/(2 Sqrt[-Pi c ccon]) /; (FreeQ[ccon,om] && c<0 && Im[c]==0) (* Sign[] in time *) iFt[1/om_,t_,om_]:= I Sign[t]/2 (* Sign[] for frequency *) iFt[Sign[om_],t_,om_]:= I/(Pi t) (* delta function *) iFt[delta[om_],t_,om_]:= 1/( 2 Pi) (* sine: this could be improved *) iFt[delta[om_-omnot_]-delta[om_+omnot_],t_,om_]:= I Sin[omnot t]/Pi /; FreeQ[omnot,om] (* cosine: this could be improved *) iFt[delta[om_-omnot_]+delta[om_+omnot_],t_,om_]:= Cos[omnot t]/Pi /; FreeQ[omnot,om] (* sinc function *) iFt[sinc[om_],t_,om_]:= rect[t/2]/2 (* rect function *) iFt[rect[om_],t_,om_]:= sinc[t/2]/(2 Pi) (* sinc squared *) iFt[sinc[om_ tau_.]^2,t_,om_]:= triangle[t/(2 tau)]/(2 tau) /; FreeQ[tau,om] (* time differentiation *) iFt[om_^n_. a_,t_,om_]:= (-I)^n Derivative[n][ iFt[a,t,om] ][t] /; FreeQ[n,om] && n>0 (* frequency differentiation *) Unprotect[Derivative] Derivative/: iFt[Derivative[n_Integer?Positive][a_][om_],t_,om_]:= (t/I)^n iFt[a[om],t,om] Protect[Derivative] (* general rules last *) (* multiplication by delta function *) iFt[a_ delta[om_ + omnot_.],t_,om_]:= Limit[a Exp[I om t]/(2 Pi),om->-omnot] /; FreeQ[omnot,om] (* scaling *) iFt[a_[alph_ om_],t_,om_]:= ( iFt[a[om],t/alph,om]/Abs[alph] /; FreeQ[alph,om] ) (* frequency translation *) iFt[a_[om_ + omnot_],t_,om_]:= iFt[a[om],t,om] Exp[-I omnot t]/; FreeQ[omnot,om] (* time translation *) iFt[a_[om_] Exp[c_Complex tnot_. om_],t_,om_]:= iFt[a[om],t + Im[c] tnot, om] /; FreeQ[tnot,om] && Re[c]==0 (* frequency multiplication *) iFt[a_[om_] b_[om_],t_,om_]:= convolution[iFt[a[om],t,om],iFt[b[om],t,om]] (* Alternative definition transform section. *) (* Alternative a: 2Pi only in exponent of expoentials. *) Fta[a_,t_,om_]:=Ft[a,t,2 Pi om] iFta[a_,t_,om_]:=iFt[2 Pi a, 2 Pi t, om] (* Alternative b: Sqrt[2 Pi] appears in both forward and inverse trasforms. *) Ftb[a_,t_,om_]:=Ft[a,t,om]/Sqrt[2 Pi] iFtb[a_,t_,om_]:=Sqrt[2 Pi] iFt[a,t,om] End[] EndPackage[] SHAR_EOF fi if test -f 'Ft.doc' then echo shar: "will not over-write existing file 'Ft.doc'" else cat << \SHAR_EOF > 'Ft.doc' Ft: a symbolic Fourier transform package for Mathematica by Victor W. Sparrow Dept. of Electrical and Computer Engineering, University of Illinois, Urbana-Champaign and USA-CERL Acoustics Team, Champaign, IL April 13, 1989 Ft is a Mathematica package written to perform symbolic forward and inverse Fourier transforms. To load this package into Mathematica, type the following at a Mathematica prompt: <0 u[t]=0 for t<0 delta[t], the Dirac delta function rect[t], the rectangular function: rect[t]=1 for Abs[t] < (1/2) rect[t]=0 otherwise sinc[t], the Sin[t]/t function, and triangle[t], the triangular function: triangle[t] = 1 - Abs[t] for Abs[t] < 1 triangle[t] = 0 otherwise Ft.m, however, does not know the properties of these functions if they are not used in Fourier transforms. In addition, Ft.m knows about certain mathematical operations such as convolution. Ft[convolution[a[t],b[t]],t,omega] gives the Fourier transform of the convolution of the functions of a[t] and b[t]. The Fourier transform pair Infinity / -I omega t F[omega]= | f[t] e dt / -Infinity Infinity 1 / I omega t f[t]= ____ | F[omega] e d omega 2 Pi / -Infinity is implicitly used in this package. The way the package is written, however, the integral forms of these expressions are never referred to in Ft.m. Ft.m will not help Mathematica in evaluating expressions like Integral[f[t] Exp[-I omega t],{t,-Infinity,Infinity}] which Mathematica cannot handle alone. All of the calculations in Ft.m use the above Fourier transform pair. If one prefers the pair Infinity / -I 2 Pi nu t F[nu]= | f[t] e dt / -Infinity Infinity / I 2 Pi nu t f[t]= | F[nu] e d nu / -Infinity he can use Fta[expression in domain 1, domain 1 variable, domain 2 variable] and iFta[expression in domain 2, domain 1 variable, domain 2 variable] . This usage merely converts the expressions to the Ft[] and iFt[] format and evaluates the expressions. Note: the way this is implemented means that if one takes the Fta[] of some complicated expression, the answer may be in terms of the Ft[] of simple expressions. Similarly one can use the Fourier transform pair Infinity 1 / -I omega t F[omega]=__________ | f[t] e dt Sqrt[2 Pi] / -Infinity Infinity 1 / I omega t f[t]=__________ | F[omega] e d omega Sqrt[2 Pi] / -Infinity using the general forms Ftb[expression in domain 1, domain 1 variable, domain 2 variable] and iFtb[expression in domain 2, domain 1 variable, domain 2 variable] although again the resultant expressions may be in terms of Ft[] and iFt[]. Often to get the inverse Fourier transform of a complicated expression in the frequency domain, the user will need to do some processing in Mathematica outside of Ft.m. For instance Apart[] is useful for breaking ratios of polynomials into sums of terms with simple denominators. (Partial fraction expansion.) Comments on this package from users would be helpful. Please contact Victor W. Sparrow at sparrow@osiris.cso.uiuc.edu via E-mail. SHAR_EOF fi exit 0 # End of shell archive ----- End Included Message ----- From stevec Tue Apr 18 14:05:37 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA01484; Wed, 5 Apr 89 12:04:41 CDT Date: Wed, 5 Apr 89 12:04:41 CDT Message-Id: <8904051704.AA01484@yoda.ncsa.uiuc.edu> To: mathgroup Subject: Re: Dirac Algebra In Mathematica From: petti@ALLEGHENY.SCRC.Symbolics.COM Status: RO >From RDC@vms.cis.pittsburgh.edu Mon Apr 3 15:50:58 1989 >Subject: RE: Dirac Algegra >To: stevec@ncsa.uiuc.edu >X-Vms-To: IN%"stevec%ncsa.uiuc.EDU@unix.cis.pittsburgh.edu" >Dear Steve, >Earlier this year we discussed the question of Dirac algebra macros for >Mathematica. I am reaching the point of doing some more calculations >which will require this sort of thing. Has anything happened on this >front? I know there are other people who are interested in this, but >I haven't been following the latest developments. Could you please >fill me in. >Thanks, >Bob Carlitz I am just finishing a general tensor package to do universal, Clifford, symplectic, Grassmann, and enveloping Lie algebras in MACSYMA. Dirac is a special case of Clifford at this level, but this package operates without choosing a matrix representation. The matrix version is another job. What do you want in the package? I assume a matrix representation with the basic operations, such as hermitian conjugation, particle conjugation etc.? Dick Petti petti@symbolics.com petti@scrc-stony-brook.arpa ----- End Included Message ----- From stevec Tue Apr 18 15:05:05 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA05961; Tue, 11 Apr 89 19:43:51 CDT Date: Tue, 11 Apr 89 19:43:51 CDT From: stevec (Steve Christensen) Message-Id: <8904120043.AA05961@yoda.ncsa.uiuc.edu> To: mathgroup Subject: Mathematica and the complex plane Status: RO >From @VMD.CSO.UIUC.EDU:zaccone@sol.bucknell.edu Tue Apr 11 16:04:44 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA05896; Tue, 11 Apr 89 16:04:42 CDT Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA24390; Tue, 11 Apr 89 16:02:06 CDT Received: from VMD.CSO.UIUC.EDU by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA12119; Tue, 11 Apr 89 16:02:02 CDT Received: from BKNLVMS.BITNET by VMD.CSO.UIUC.EDU (IBM VM SMTP R1.2) with BSMTP id 2679; Tue, 11 Apr 89 16:02:03 CDT Return-Path: zaccone%sol.bucknell.edu@VMD.CSO.UIUC.EDU Received: from rigel.bucknell.edu by BKNLVMS.BITNET; Tue, 11 Apr 89 16:57 EDT Received: by rigel.bucknell.edu (4.0/SMI-3.2) id AA04064; Tue, 11 Apr 89 16:56:03 EDT Date: Tue, 11 Apr 89 16:56:03 EDT From: Rick Zaccone Subject: Mathematica and the complex plane To: steve@ncsa.uiuc.edu Message-Id: <8904112056.AA04064@rigel.bucknell.edu> Status: R Could you please forward this to sci.math.symbolic and anywhere else that seems appropriate? I would like to know how to get Mathematica to produce plots in the complex plane. For example, if x is complex, how do I graph the following on the complex plane? Abs[ 1 + x + x^2/2] == 1 Rick Zaccone zaccone@bknlvms.bitnet zaccone@rigel.bucknell.edu From stevec Tue Apr 18 16:01:53 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA06041; Tue, 11 Apr 89 22:08:46 CDT Date: Tue, 11 Apr 89 22:08:46 CDT From: stevec (Steve Christensen) Message-Id: <8904120308.AA06041@yoda.ncsa.uiuc.edu> To: mathgroup Subject: Mathematica machines and prices Status: RO Here is the latest list I have received: >From wri!leslie@uxc.cso.uiuc.edu Tue Apr 11 11:47:54 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA05855; Tue, 11 Apr 89 11:47:52 CDT Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA23575; Tue, 11 Apr 89 11:45:17 CDT Return-Path: Received: from uxc.cso.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA07426; Tue, 11 Apr 89 11:45:13 CDT Received: from wri.UUCP by uxc.cso.uiuc.edu with UUCP (5.61+/IDA-1.2.8) id AA21753; Tue, 11 Apr 89 10:10:47 -0500 From: wri!leslie@uxc.cso.uiuc.edu Received: by WRI.com (3.2/SMI-3.0DEV3) id AA21610; Tue, 11 Apr 89 09:51:40 CDT Message-Id: <8904111451.AA21610@WRI.com> Date: Tue, 11 Apr 89 09:51:37 CDT To: steve@ncsa.uiuc.edu Status: R EDUCATIONAL MATHEMATICA PRICE LIST April, 1989 Prices subject to change without notice SYSTEM STANDARD EDUCATIONAL SPECIFICATIONS VERSION PRICE PRICE Apollo ====== DN 3000, 3500, $2,400 $1,600 Runs under SR9.7 or 4000 & 4500 SR10. Supports Display Manager window system. Distributed on 1/4" tape. Cray ==== Cray X-MP $160,000 $96,000 Runs under UNICOS. Cray Y-MP $240,000 $144,000 Available Q3 1989. Cray 2 $240,000 $144,000 DEC === VAXstation, MICROVAX 2000 $2,400 $1,600 VMS and ULTRIX versions MICROVAX II, 730 $4,800 $2,900 available for all VAX 750, 78X, 82XX $8,600 $5,200 systems. Runs under 8300, 8350, 6210 ULTRIX on DECstation MICROVAX 3500, 3600 $12,600 $7,600 3100. Distributed on 8530, 8550, 86XX, 8700, 9 track tape. 8810, 6200, 6230 $18,000 $11,000 8800, 8820, 8830, 8840, 8842, 8974, 6240 $42,000 $25,000 DECstation 3100 $2,800 $1,800 Hewlett-Packard =============== HP 9000/300 Series $2,400 $1,600 Supports X Windows. For HP 9000/825 & 835 $6,200 $3,700 Series 300, requires HP HP 9000/840, 850 & 855 $11,800 $7,100 ID module. Distributed on HP 16 TRACK 1/4" tape. MIPS ==== M/120 $5,200 $3,100 Requires operating system M/1000 & M/2000 $8,600 $5,200 3.1 or higher. Includes X Windows driver. Distributed on 1/4" tape. Silicon Graphics ================ Personal Iris $2,800 $1,800 Runs under operating Iris-4D/50 through 80GT $6,200 $3,700 system release 3.5 Iris-4D/120S through 240GTX $7,800 $4,700 or 4. Runs under X and 4Sight network window systems. Includes real-time 3D graphics rendering package. Distributed on 1/4" tape. Sony ==== NEWS 700, 800, 1700, 1800 $2,400 $1,600 Runs under X Windows. NEWS 1900 $3,400 $2,200 Distributed on 3 1/2" diskettes. Sun === Sun-3 *$1,800 $995 Runs under SunView, Sun-4 and compatibles $2,400 $1,600 NeWS and X Windows Sun386i $2,400 $1,600 network window systems. On Sun-3, supports 68881 and FPA numeric coprocessors. For Sun-3 and Sun-4: distributed on 1/4" cartridge tape. For Sun-386i: distributed on DSDD diskettes. *Special introductory price; expires July 1, 1989. Regular price $2250/$1395. ================================================================== Apple ===== Macintosh Standard Version $495 2.5 megabytes memory required; 4 megabytes Macintosh Enhanced Version recommended. (numeric coprocessor required) $795 2 megabytes suffice if a virtual memory system is used. Supports Mathematica Notebook user interface. Supports connectivity to remote Mathematica kernel. MS-DOS Systems ====== ======= 386 Version $695 640k memory & 1 megabyte extended memory required. 386/7 Version Supports CGA, EGA, VGA and (287 or 387 coprocessor required) $995 Hercules graphics standards, Postscript, Laserjet, 386/Weitek Epson FX and (Weitek coprocessor required) $1,295 Toshiba P3 compatible printers. ================================================================ General Information ======= =========== All versions include a hardbound copy of the book, "Mathematica: A System for Doing Mathematics by Computer," together with version-specific documentation. All workstation versions include T4010 and character-based graphics support, as well as support for PostScript-based printers. Prices are inclusive of shipping within the U.S. Shipping charges will be added for destinations outside the U.S. All prices are in U.S. dollars. Credit terms are subject to approval. Volume discounts are available on selected workstations for quantities of 10 and above. Educational discounts are available for accredited universities and colleges. Upgrade contracts are available. Wolfram Research, Inc. P.O. Box 6059 Champaign, IL 61826 Telephone: 217-398-0700 Fax: 217-398-0747 Orders only: 800-441-MATH Mathematica is a trademark of Wolfram Research, Inc. All other trademarks are trademarks of their respective companies. From stevec Thu Apr 20 10:06:35 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA04358; Thu, 20 Apr 89 09:48:49 CDT Date: Thu, 20 Apr 89 09:48:49 CDT Message-Id: <8904201448.AA04358@yoda.ncsa.uiuc.edu> To: mathgroup Subject: Remote kernel via Ethernet from a Macintosh From: Stein Arild Stromme Status: RO Is there a way to run the Mac Mathematica front end and a remote kernel over an Ethernet? The options given in the communications window don't seem to support this. Also: can the Mac front end be purchased separately? My Mac II version front end crashes on a Mac Plus, even though I make no attempt to load any kernel at all. Why is there a difference in the front ends between the two Mac versions? As a matter of curiosity, I would like to know how many Cray versions have been sold, educational discount or not! Stein Arild Stromme Mathematics Bergen University From stevec Thu Apr 20 12:07:54 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA04677; Thu, 20 Apr 89 11:40:15 CDT Date: Thu, 20 Apr 89 11:40:15 CDT Message-Id: <8904201640.AA04677@yoda.ncsa.uiuc.edu> To: mathgroup Subject: Bug reports From: wadej@Sun.COM Status: RO [Here are some bug reported by: James F. Wade wadej@sun.com at Sun Microsystems. Many of these may already be fixed in the 1.2 release. -smc] Here is a summary of the SunMathematica bugs that we know about at Sun: Bug Id SUMMARY 1014637: Shading does not work on a monochrome 386i. 1014657: Segmentation violation on large calulation on 3/60. Large calculations using large amounts of memory may fail with a Segmentation violation. 1014678: Prompt displayed at the wrong time on a regular terminal. When a plot is done on a regular terminal, the prompt for the next equation is displayed before the plot is made on the screen. 1014679: There are drawing problems when dispaying a Torus. Some "glitches" appear in the inside, lower part of a Torus graph. This appears on both Sunview and NeWS. 1014680: When running "suntools -i", most plots are invisible. 1014681: NeWS will freeze on very high resolution Mathematica graphs. This is a known NeWS problem. 1017088: The Gosper.m summation example does not work The following may serve as a work-around for SOME cases only: qn = Expand[ Numerator[rat]]; <<<<<< Add Expand here rn = Expand[ Denominator[rat]]; <<<<<< Add Expand here 1017089: ODE.m and Fourier.m are documented but files are missing. 1017090: 'foption' used in 'math' script, but it only under 4.0 The main script 'math' uses 'foption' which only is available under 4.0 and NOT under 3.5. So the script can fail. Work around: Copy 'foption' from the 'common' directory under the main mathematica directory into some directory that is on the path. 1018441: No X11 postscript driver for Sun4 running 4.0 If a Sun4 driver for x11 is used, the Mathematica output must be piped through ../math/common/Utilities/psfix to expand the WRI macros to standard postscript. 1018450: Interface between C language and Mathematica is ackward. Calling mathematica from a C main is ackward. Arguments must be passed through a pipe in text form. 101845******* exit Mathematica or exit sunview to restore windows. The unix Kernal can be reconfigured to allow more windows. 1018470: mathlink.c does not work for more than 2 arguments. Routines provided to call C from Mathematica only work for Functions with exactly 1 or 2 arguments. 1018536: Simplify fails dby0: Division by zero on complex expressions. Description: eq1 = Times[vt, Power[Plus[1, Times[-1, ut]], -1], Power[Plus[1, Times[-1, Plus[1, Times[-1, Power[Plus[1, Times[-1, ut]], m]]]]], m]] eq1s = Simplify[eq1 ] (* Fails General::dby0: Division by zero. *) Work around: The simplification can be done using /. command to reduce complexity of expression. In[5]:= eq2 = Simplify[ eq1 /. 1-ut -> mu] /. mu -> 1-ut 2 -1 + m Out[5]= vt (1 - ut) 1018541: Chop does not work with two arguments. Work around: Define for Two arguments In[12]:= ClearAttributes[Chop,Protected] In[13]:= Chop[x_,d_] = If[Abs[x] .00001] 1018605: on the sun4 multiple application of Transformation fails Description: In[1]:= f/: f[x_] f[y_] := f[x y] In[2]:= f[x] f[y] f[1] Out[2]= f[x] <<<< WRONG should be f[x y] In[3]:= f[x] f[y] f[z] Segmentation fault 1018740: PlotLabel fails in Plot3d, SurfaceGraphics, Display. 1018783: Hypergeometric2F1 fails by looping Description: N[Hypergeometric2F1[2,1/2,3,2/3]] recures indefinitely. condition may be: first arg is integer, 2nd is 1/2 integer, third is integer > first and fourth anything. May cause Beta to fail, as well as any other function that call Hypergeometric2F1 . 1019507: Plot3D Gives poor results on rlogin. Description: Plot3D[x^y,{x,0,1},{y,1,2},Shading->False] appears to give same results as: Plot3D[x^y,{x,0,1},{y,1,2}]. Actually this is due to default: PlotPoints -> 15 . Work around: Use: SetOptions[Plot3D, PlotPoints -> 4] or some other small value. Terminal.m may be modified to SetOptions for Plot3D to be more appropriate for terminal output. 1019660: FindMinimum fails with some arguments. FindMinimum[ f(a,b), {a,1}, {b,0}] fails for some functions f when it must calculate derivitives to get gradient. Use the alternate form FindMinimum[ f(a,b), {a,{.9,1}}, {b,{0,.1}}] that uses approximations to calculate gradient. additional notes: Linear Algebra Zero Test Linear algebra functions such as LinearSolve, RowReduce, NullSpace and Eigenvectors use the ZeroTest argument. The default setting for this is ZeroTest -> (Together[#1] == 0 & ). This does not work well for numerical or symbolic arrays. For symbolic arrays you may need: ZeroTest -> (Simplify[#1] == 0 & ) or the more expensive: ZeroTest -> (Reduce[#1==0] & ) For approximate numeric arrays you may need: ZeroTest -> (Chop[#1] == 0 & ) or ZeroTest -> (Chop[#1,dx] == 0 & ) with dx apropriate for the precision you are using. For general use, a combination of the two may work fairly well: RowReduce[A,ZeroTest -> (Reduce[Chop[#1]==0] &)] SetOptions can be used to change the default ZeroTest for each function. Packages Must Be Loaded Before Use The Mathematica text does not always mention that you need to load a package before using it. They are usually in /usr/math/common/Packages and may be loaded by with the << command. If you have a color display you should load Colors.m with command < Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA01274; Tue, 14 Mar 89 13:13:42 CST Date: Tue, 14 Mar 89 13:13:42 CST Message-Id: <8903141913.AA01274@yoda.ncsa.uiuc.edu> To: mathgroup@yoda Subject: mathematica/TeX question for mathgroup From: lwyse@bucasb.BU.EDU Status: RO I am having trouble "Splice"ing TeXForms into a Tex document. Mathematica automatically converts even not-so-long expressions into "short" form (abbreviating by elliding out middle terms and replacing them with a count of them between angle brackets.) This short form is then spliced into my TeX document in beautiful TeX notation. Has anybody foung an elegant solution to this? thanx, lonce ----- End Included Message ----- From stevec Tue Apr 25 10:39:31 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA01044; Tue, 25 Apr 89 09:58:32 CDT Date: Tue, 25 Apr 89 09:58:32 CDT Message-Id: <8904251458.AA01044@yoda.ncsa.uiuc.edu> To: mathgroup Subject: Bug in Solve/Reduce? From: sdoyle@fed.frb.gov Status: RO I've run into a problem with Solve and Reduce where it appears to be `creating' null variables that only contain the name of the Context where the manipulations are taking place. To re-create the problem, just read in the file `SolveBug.m' (included below) in the normal way. This defines a symbol poly with a fourth degree polynomial in X and sets the Cubics option of Roots to False. When you enter Solve[poly==0, X] an answer is returned that contains a variable Global` (the Context name with no symbol appended). I've included sample session following SolveBug.m. The FullForm of the value returned by Reduce also contains this null variable. Any Ideas? Or... Did I make a mistake? Is it an error to turn off the Cubics option but not the Quartics? Any help appreciated! Sean Doyle Board of Governors of the Federal Reserve System Washington, DC 20551 (202) 452-2352 uucp: uunet!fed!m1swd00 , internet: sdoyle@fed.frb.gov (* ****************** Start of SolveBug.m ****************** *) (* Bug in Solve/Reduce *) (* Set options for Roots *) SetOptions[Roots, Cubics->False] (* Define polynomial in X *) poly = (d e + f g) a c b^2 X^4 + (a e + c d) b X^3 + (1 + 2 (d e + f g) a b c) X^2 + (a e + c d) X + (d e + f g) a c Print["Input Polynomial: ", poly] Print["Solve[poly==0, X]",Solve[poly==0, X]]; (* **************** End of SolveBug.m ************************* *) **** Session: Part 1. Notice that the solution contains the **** variable Global`. If I bury this in a Package, the name of **** the package is there instead. Why should there be a package **** name in the middle of an expression with no variable attached? mqws2(14)% math SunMathematica (sun3.68881) 1.1 (September 14, 1988) [With pre-loaded data] by S. Wolfram, D. Grayson, R. Maeder, H. Cejtin, S. Omohundro, D. Ballman and J. Keiper Copyright 1988 Wolfram Research Inc. -- SunView graphics initialized -- In[1]:= < X b (c d + a e) + a c (d e + f g) + X a b c (d e + f g) Solve[poly==0, X]{{X -> -(b (c d + a e)) > (--------------------------- + 2 2 2 (a b c d e + a b c f g) Global` > Sqrt[-4 (------- - 2 <<< And so on.... the output goes on for a while with many Global` variables appearing... >> In[2]:= **** Now let's look at the FullForm of this expression. It still contains **** the Global` context string with no variable attached. Out[4]//FullForm= > List[List[Rule[X, Times[Rational[1, 2], > Plus[Times[Rational[-1, 2], b, > Plus[Times[c, d], Times[a, e]], > Power[Plus[Times[a, Power[b, 2], c, d, e], > Times[a, Power[b, 2], c, f, g]], -1]], > Power[Plus[Times[-4, > Plus[Times[Rational[1, 2], Global`], > Times[-1, <<< And so on. The expression goes on for a number of lines...>>> **** The Global` variables appear in output from Reduce as well. From stevec Tue May 2 10:47:42 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA15802; Tue, 2 May 89 09:46:39 CDT Date: Tue, 2 May 89 09:46:39 CDT Message-Id: <8905021446.AA15802@yoda.ncsa.uiuc.edu> To: mathgroup Subject: Question about Check[] From: sdoyle@fed.frb.gov Status: RO [This is the first of a series of messages between Sean and me which basically discuss some differences between version 1.1 of Mathematica and a 1.2 beta release I am testing. I do not know the release date of 1.2 non-beta. -smc] I'm having some trouble getting Check[] to work with messages that I've defined. This would make error trapping much easier! When I enter the example from the manual (page 261), things work fine. Below is a similar example with a user-defined Message that doesn't work. This might be something I've missed in the manual, although examples of messages (such as for Convert on page 539) don't work with Check[] either. The desired result would be for the symbol `y' in Out[8] to have the value meaningless instead of `Null'. I've also tried using On[test::tosmall] without any difference in results. So... how can I create messages that Check[] will trap? Thanks! Sean Doyle Board of Governors of the Federal Reserve System 20 and Constitution, NW Mail Stop 76 Washington, DC 20551 (202) 452-2352 uucp: uunet!fed!m1swd00 , internet: sdoyle@fed.frb.gov ********************* Session below ************************ mqws2(115)% math SunMathematica (sun3.68881) 1.1 (September 14, 1988) [With pre-loaded data] by S. Wolfram, D. Grayson, R. Maeder, H. Cejtin, S. Omohundro, D. Ballman and J. Keiper Copyright 1988 Wolfram Research Inc. -- SunView graphics initialized -- In[1]:= test[x_]:= x /; x>0 In[2]:= test::toosmall = "The input to test is too small" Out[2]= The input to test is too small In[3]:= test[x_] := Message[test::toosmall] In[4]:= ??test test test/: test[x_] := x /; x > 0 test/: test[x_] := Message[test::toosmall] In[4]:= Messages[test] Out[4]= test::toosmall -> The input to test is too small In[5]:= test[5] Out[5]= 5 In[6]:= test[-4] test::toosmall: The input to test is too small In[7]:= y = Check[test[7],meaningless] Out[7]= 7 In[8]:= y = Check[test[-7],meaningless] test::toosmall: The input to test is too small In[9]:= y In[10]:= FullForm[y] Out[10]//FullForm= Null In[11]:= From stevec Tue May 2 10:51:07 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA15818; Tue, 2 May 89 09:52:32 CDT Date: Tue, 2 May 89 09:52:32 CDT Message-Id: <8905021452.AA15818@yoda.ncsa.uiuc.edu> To: mathgroup Subject: Re: Question about Check[] From: sdoyle@fed.frb.gov Status: RO [Third in the series on Check[]. -smc] Steve: Do you have any information on when 1.2 is coming out? I don't want to ask you anything for which you would have to break a non-disclosure agreement, but I'm leaving here June 1 and I'd like to know if 1.2 for the Sun might be here before then... You can forward the problem below to the list if you want. If it is fixed in 1.2 please let me know. The two most serious problems (for me) in 1.1 are that CForm[] wasn't working correctly with user-defined objects and that I get segmentation violations when performing assigments " := " nested deeply within large programs. While I can't pin down the latter for a simple example (yet), the formatting problem is reproduced below. The basic problems are: (a) When CForm distributes down the list, it doesn't apply the CForm rule that I defined. (Out[5]) (b) If I use rules to replace the objects, the resulting output doesn't completely evaluate. While Out[6] appears as I desire, FullForm[] shows that the SequenceForm[] expressions have not evaluated. (c) The problem in (b) becomes serious if (for example) I have exponents in the expression. Then I have to evaluate the expression once for my objects, and then once again for the operators surrounding the objects. A workaround for the problem of (c) is to use the function ToString[] in the user-specified CForm rules. This forces these sub-expressions to evaluate the SequenceForm[] function. After CForm is applied to the entire expression there may be embedded quotation (") characters... so I convert the entire statement to a string and then strip out all of the quotation characters. This is slow, and it won't work if one wants to generate C expressions that contain quotation characters..... I'm also curious.... the evaluation problem mentioned in (b) seems to be a violation of the rule that evaluation takes place until there is no change in the expression... but the *Form[] commands operate by different rules than other functions. If this is fixed in 1.2, or if there is a better workaround, please let me know. Thanks! Sean Doyle Board of Governors of the Federal Reserve System 20 and Constitution, NW Mail Stop 76 Washington, DC 20551 (202) 452-2352 uucp: uunet!fed!m1swd00 , internet: sdoyle@fed.frb.gov *************** Session below. *************************** SunMathematica (sun4) 1.1 (September 17, 1988) [With pre-loaded data] by S. Wolfram, D. Grayson, R. Maeder, H. Cejtin, S. Omohundro, D. Ballman and J. Keiper Copyright 1988 Wolfram Research Inc. -- Terminal graphics initialized -- In[1]:= foo/: CForm[foo[x_,y_]]:= SequenceForm[ "readdata( foo,", x , ",", y,")"] In[2]:= foo[1,2] Out[2]= foo[1, 2] In[3]:= CForm[%] Out[3]= readdata( foo,1,2) In[4]:= temp = foo[1,2] + foo[2,3] + foo[3,4] Out[4]= foo[1, 2] + foo[2, 3] + foo[3, 4] In[5]:= CForm[temp] Out[5]//CForm= foo(1,2) + foo(2,3) + foo(3,4) In[6]:= temp /. {foo[x___] -> CForm[foo[x]]} Out[6]= readdata( foo,1,2) + readdata( foo,2,3) + readdata( foo,3,4) In[7]:= FullForm[%] Out[7]//FullForm= > Plus[SequenceForm[readdata( foo,, 1, ,, 2, )], > SequenceForm[readdata( foo,, 2, ,, 3, )], > SequenceForm[readdata( foo,, 3, ,, 4, )]] (* Here's the `fix' to force the SequenceForm[] statements to evaluate *) In[8]:= foo/: CForm[foo[x_,y_]]:= ToString[SequenceForm[ "readdata( foo,", x , ",", y,")"]] From stevec Wed May 3 14:31:09 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA15810; Tue, 2 May 89 09:48:12 CDT Date: Tue, 2 May 89 09:48:12 CDT Message-Id: <8905021448.AA15810@yoda.ncsa.uiuc.edu> To: mathgroup Subject: Re: Question about Check[] From: stevec@ncsa.uiuc.edu Status: RO [The second messsage in the series about Check[]. -smc] I have run your program through version 1.2 (beta) and do not get the same results. The session is below. Is there still a bug you want reported to Wolfram Research or the mailing list? ===================================================================== In[1]:= test[x_]:= x /; x>0 In[2]:= test::toosmall = "The input to test is too small" Out[2]= The input to test is too small In[3]:= test[x_] := Message[test::toosmall] In[4]:= Messages[test] Out[4]= test::toosmall -> The input to test is too small In[5]:= test[5] Out[5]= 5 In[6]:= test[-4] In[7]:= y = Check[test[7],meaningless] Out[7]= 7 In[8]:= y = Check[test[-7],meaningless] Out[8]= meaningless In[9]:= y Out[9]= meaningless In[10]:= FullForm[y] Out[10]//FullForm= meaningless In[11]:= Quit[] From stevec Wed May 3 16:41:23 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA15864; Tue, 2 May 89 10:08:57 CDT Date: Tue, 2 May 89 10:08:57 CDT From: stevec (Steve Christensen) Message-Id: <8905021508.AA15864@yoda.ncsa.uiuc.edu> To: mathgroup Subject: mathgroup email addresses Status: RO There has been some confusion regarding how to send messages to the Mathematica mailing list or to reply to a message you receive. DO NOT send message to mathgroup@yoda.ncsa.uiuc.edu. While this will work to get to the mailing list, it will also mean that any reflected messages will get sent back to you. On some days when the mailer machines on the net get weird, this may mean that you will get a lot of returns. So, please send messages and replies to: steve@ncsa.uiuc.edu or stevec@ncsa.uiuc.edu or 14008@ncsavmsa.bitnet. If you want to say mathgroup, you can send to mathgroup@wri.com which is aliases to me. Steve Christensen NCSA & Beckman Institute University of Illinois at Urbana-Champaign From stevec Fri May 5 10:16:46 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA03467; Fri, 5 May 89 09:10:53 CDT Date: Fri, 5 May 89 09:10:53 CDT Message-Id: <8905051410.AA03467@yoda.ncsa.uiuc.edu> To: mathgroup Subject: Mathematica bug on Sun4 From: sdoyle@fed.frb.gov Reply-To: steve@ncsa.uiuc.edu Status: RO [See the follow up note to this one regarding the fix of this problem in 1.2 beta. - smc] A tale of two Suns ( 3/60 and a 4/260) It was the best of Suns, it was the worst of Suns. I've been having some trouble with segmentation violations and/or bus errors on a Sun4 that do not occur on a Sun3. Both machines are running version 1.1. As is true of most memory type bugs, they are hard to program around if one doesn't know the underlying algorithms. If I use On[] or Debug[] to attempt to isolate the problem, usually it `goes away'. However, if the Sun4 does return an answer, it is sometimes incorrect. I can't replicate the segmentation violations with the test file (appended below), but I can replicate the incorrect answers. Hopefully these problems have a common root. Before I get to the code, it might help to explain what its purpose is. In economic models one often has variables that have a time subscript, such as GNP[T], where T represents the current time. Lag operators are used to increment (or decrement) the time index. If we represent the lag operator as L, we have the following relationships: L GNP[T] = GNP[T-1] L^2 GNP[T] = L GNP[T-1] = GNP[T-2] One can even have polynomials in the lag operators: (1 + L) GNP[T] = GNP[T] + GNP[T-1] (1 - L) GNP[T] = GNP[T] - GNP[T-1] The lag operator L has been implemented in Mathmatica as the operator LagOperator[n]. Delta[n] expands to (Identity - LagOperator[n]). The code treats Identity and LagOperator[n] as scalar expressions in polynomials until they are applied to expressions that have time indexes. Then they are converted to Function[]s and applied using Through[] and MapAt[]. This is done because Mathematica's built-in rules handle scalar value polynomials much better than function-valued polynomials. Now... the bottom line(s): (1) Could someone see if this is a problem under 1.2? Or... is there an obvious problem with the code (even though it works on the 3/60?) (2) Can I get 1.2 here (even in beta release?). Normally I would try to be patient, but I'm leaving here June 1 for another job, and I'll only have limited Mathematica access in the future (sigh...) In return for getting 1.2, I promise to beat on it very hard before I go. So far I've built a slot-and-filler database for storing model files, tools for manipulating models algebraically, and formatting out TeX and C versions... and more! The database is very general and is has nothing to do with economic models. Once one has defined the attributes of a `class', all of the database commands for storing or retrieving information are defined. I'll have something to post before I `retire'. (3) FOR WRI (!!!) (Please) (a) Any hints on debugging 1.1 applications? There is another nasty memory bug lurking in my code that I can't seem to isolate. On[] and Debug[] both have side effects on the environment... often I will get a `segmentation violation' or `bus error' while running a program which works fine when On[] or Debug[] are used. I'm not doing anything weird in the code (e.g., Raw[]). (b) Is there any way of figuring out where I'm straining Mathematica? I have about 4500 lines of code (including comments!). I don't know anything about how many rules Mathematica can handle, nor what the tradeoffs are in how complex conditions are for controlling the application of rules (I tend to build a lot of predicate functions to make the code easier to read)... (c) What should I avoid using in 1.1? (If I can't get 1.2 here, perhaps at least I can leave behind robust code). Most of the problems I've had are with assignment in programs that are deeply nested, or with Match[]/Select[] on lists which are nested within my database procedures... I'm sorry I can't be more specific, but I'm having trouble isolating the problems (small programs tend to work fine). The rest of this message is three parts: (1) Sun4 segmentation violation (2) Sun4 incorrect answer (3) A file for replicating the problem Thanks in advance! Sean Doyle *************** PART 1: Sun 4 segmentation violation *********************** Sun4: os4cs1(25)% math SunMathematica (sun4) 1.1 (September 17, 1988) [With pre-loaded data] by S. Wolfram, D. Grayson, R. Maeder, H. Cejtin, S. Omohundro, D. Ballman and J. Keiper Copyright 1988 Wolfram Research Inc. -- Terminal graphics initialized -- In[1]:= < LagOperator[4] - Identity LagOperator[100] + LagOperator[101] + > LagOperator[103] - LagOperator[104]] We also see that the answer it correct, since it is just expanding a polynomial. Delta[n] expands to to the polynomial (1-LagOperator[n]), and LagOperator[n]^x becomes LagOperator[n*x], so we can simulate this below using the scalar L: In[3]:= (1-L)(1-L^100)(1-L^3) 0. 3 100 Out[3]= (1 - L) (1 - L ) (1 - L ) In[4]:= ExpandAll[%] 0.166667 Second 3 4 100 101 103 104 Out[4]= 1 - L - L + L - L + L + L - L The `Identity^n' terms in Out[2] are simplified (in the rules for ApplyLag) before they applied as operators to an expression. *************** PART 2: Sun 4, wrong answer *********************** If I use On[] with the Sun 4, it will generate an incorrect answer instead of a segmentation violation. Here is the last part of the trace: ShowTime::trace: ShowTime[Delta[1] Delta[100] Delta[3]] --> 3 2 ApplyLag[Identity - LagOperator[1] - Identity LagOperator[1] + LagOperator[2] - LagOperator[3] + 2 LagOperator[4] - LagOperator[5]]. 3 2 Out[3]= ApplyLag[Identity - LagOperator[1] - Identity LagOperator[1] + > LagOperator[2] - LagOperator[3] + 2 LagOperator[4] - LagOperator[5]] This is clearly the wrong polynomial. To try to isolate the problem I created a file `lagbug.m' that had most of the lag-operator related code (it excludes the Format[] rules). While I don't get a segmentation violation, I do get the same (wrong) answer on the Sun 4 as when I used On[]: os4cs1(55)% math SunMathematica (sun4) 1.1 (September 17, 1988) [With pre-loaded data] by S. Wolfram, D. Grayson, R. Maeder, H. Cejtin, S. Omohundro, D. Ballman and J. Keiper Copyright 1988 Wolfram Research Inc. -- Terminal graphics initialized -- In[1]:= < LagOperator[2] - LagOperator[3] + 2 LagOperator[4] - LagOperator[5]] On the 3/60 the correct answer is returned. *************** PART 3: lagbug.m file ********************** (* L a g O p e r a t o r The LagOperator package contains several definitions and tools for manipulating Lag operators in EconoMod objects and expressions. [Note: some of these comments refer to other parts of the package. I could have deleted them, but then I thought people might be interested in what other users are up to... One of the main excluded portions here are the objects that the lag operators are applied to. When this all works [ :-) ] I'll post that to the net. ] *) BeginPackage["LagOperator`"] ApplyLag::usage= "ApplyLag[lagpoly][expr] applies the lag polynomial to expr. ApplyLag[lagpoly1]*ApplyLag[lagpoly2] will multiply the polynomial expressions in the normal Mathematica fashion." LagOperator::usage= "LagOperator[n] is the internal representation of the Lag operator \"L\". LagOperator[n][expr] applies the lag operator to expr." Delta::usage= "Delta[n][expr] applies the lag polynomial (1-L^n) to the expression." MovingAverage::usage= "MovingAverage[n][expr] applies the lag polynomial\n \t ((1/n) (1 + L + L^2 + ... + L^(n-1) )) \n to the expression." MovingTotal::usage= "MovingTotal[n][expr] applies the lag polynomial\n \t (1 + L + L^2 + ... + L^(n-1) ) \n to the expression." LagPolynomial Begin["`Private`"] (* Initialize functions *) (* ******************************************************************** LagOperator functions and utilities ******************************************************************** *) (* **** Evaluation **** ApplyLag is a Mathematica object that performs two functions: (1) It `holds' lag polynomials in an unevaluated form. These polynomials can be further manipulated (i.e., raised to a power, etc..) (2) When ApplyLag is followed by an expression, a rule is fired (LagFunction) that transforms the lag polynomial to a Function[] and then uses Through to distribute the lag operators through the expression. Digression: These two steps are necessary. Once the lag polynomial is in Function[] form, one can't use any of the Expand[] or other polynomial manipulation tools on it. So, if we defer tranforming the polynomial into a Function[] until we are ready to apply the lag operators, we can keep some flexibility about nesting lag polynomials such as Delta[x] Delta[y] expr Delta[x]^2 expr *) ApplyLag[lagopts_][expr_]:=Through[LagFunction[lagopts] [expr],Plus] ApplyLag/: ApplyLag[x_] ApplyLag[y_]:= ApplyLag[ExpandAll[(x)(y)]] ApplyLag/: Power[ApplyLag[x_],n_]:= ApplyLag[ExpandAll[Power[x,n]]] (* LagFunction[] maps the lag polynomial into a Function[] object. Note the slight kludge of mapping Identity^n to Identity. This is necessary because Identity may have been raised to a power in some polynomial transformation. While a rule could have been specified elsewhere for this, Identity is a Mathematica entity and I didn't want to mess it up with a rule. *) LagFunction[lagpoly_]:= (lagpoly /. { Identity^n_->Identity[#], Identity->Identity[#], LagOperator[lag_]->LagOperator[lag][#] })& (* ********** Algebra of lag operators ************ *) (* Higher level lag operators *) Delta/: Delta[lag_]:= ApplyLag[(Identity - LagOperator[lag])] MovingTotal/: MovingTotal[lag_]:= ApplyLag[Sum[LagOperator[i],{i,0,lag-1}]] MovingAverage/: MovingAverage[lag_]:= ApplyLag[(1/lag)*Sum[LagOperator[i],{i,0,lag-1}]] LagPolynomial[CoefPlaceHolder[name_,{}],degree_]:= ApplyLag[Sum[CoefPlaceHolder[name,i] LagOperator[i],{i,0,degree-1}]] (* ************ LagOperator algebra *********** *) (* Simplification rules *) LagOperator/: LagOperator[n_]*Identity := LagOperator[n] (* Product of two LagOperators *) LagOperator/: LagOperator[n1_] * LagOperator[n2_]:= LagOperator[n1+n2] (* Powers of LagOperators *) LagOperator/: LagOperator[n_]^exp_ := LagOperator[n*exp] (* L^0 is the Identity function *) LagOperator[0]:= Identity (* ****** Application of lag operators to objects ******* *) (* Case #1: Application of LagOperator to ANY class containing a LagOffset. If future class types (TimeVaryingCoef, for example) have the same general form as DiscreteVariable/ContinuousVariable, this rule will work for them as well. *) LagOperator[lag_][class_[Name[x_],LagOffset[n_]]]:= class[Name[x],LagOffset[n-lag]] (* Case #2: Application of LagOperator to all other EconoMod classes *) LagOperator[lag_][class_[Name[x_],contents_]]:= class[Name[x],contents] (* Case #3: Primitive Mathematica objects *) LagOperator[lag_][x_Symbol]:= x LagOperator[lag_][x_?NumberQ]:= x LagOperator[lag_][x_String]:= x (* Case #4: Application of LagOperator to an expression. The positions of the time-varying objects are located using Position[], and then only those objects have the lag applied.*) LagOperator[lag_][x_]:=Block[{positions}, positions = Position[x,class_[name_,LagOffset[xxx___]]]; If[SameQ[positions,{}], Return[x], Return[MapAt[LagOperator[lag][#] &, x, positions]] ]] End[] EndPackage[] ********************* End of lagbug.m ********************** Sean Doyle Board of Governors of the Federal Reserve System 20 and Constitution, NW Mail Stop 76 Washington, DC 20551 (202) 452-2352 uucp: uunet!fed!m1swd00 , internet: sdoyle@fed.frb.gov ----- End Included Message ----- From stevec Fri May 5 11:49:48 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA03758; Fri, 5 May 89 11:21:40 CDT Date: Fri, 5 May 89 11:21:40 CDT Message-Id: <8905051621.AA03758@yoda.ncsa.uiuc.edu> To: mathgroup Subject: Re: Mathematica bug on Sun4 From: fateman@renoir.Berkeley.EDU (Richard Fateman) Reply-To: stevec@ncsa.uiuc.edu Status: RO [Richard, in his message below brings up a number of good points. I would like to hear from members of this mailing list about what bug reports they would like me to send to the list and what others to keep to myself and WRI. My initial thoughts were that users might like to be aware of changes between 1.1 and 1.2 and that a number of bugs have been fixed. I realize it is difficult to know for sure if a bug is in Mathematica itself, in the operating system, compiler of the hardware or in the user's code. I can try to limit bug reports to Mathematica bugs only or to help with bugs in a user's code, but I am not sure I can always judge what kind of a bug exists. Comments please. - smc] I don't know what to make of all of this stuff comparing 1.1 to 1.2, memory violations, etc. It obviously is not in the best interests of anyone (other than WRI, and I'm not sure of that either) to have a whole mailing-list of individuals, almost all of whom are relatively naive, look at (perhaps buggy) code that runs differently on different machines. In dealing with Macsyma, I generally view any discrepancy between (say) VAX and Sun or Sun 2/3/4/ ... operations as a bug in either the operating system, the lisp system, or (rarely) a hardware bug. It is NOT a bug in Macsyma, and I expect whoever is responsible for support of the substructure to fix it. If Mathematica has different SOURCE code for Sun 3 and 4, etc. then its problem is different. But since only WRI has access to source, what point is there to telling us all about such bugs? Regards, Richard From stevec Mon May 8 12:26:50 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA09012; Mon, 8 May 89 12:00:08 CDT Date: Mon, 8 May 89 12:00:08 CDT Message-Id: <8905081700.AA09012@yoda.ncsa.uiuc.edu> To: mathgroup Subject: Re: Bug reports on MathGroup (long) From: sdoyle@fed.frb.gov Relpy-To: stevec@ncsa.uiuc.edu Status: RO I've sent several bug/feature reports to Steve Christensen, who in turn has forwarded these to the MathGroup list. Some of these problems appear only on a particular version of Mathematica or a particular machine. This led Richard Fateman to ask: > [...] since only WRI has access to source, > what point is there to telling us all about such bugs? Well, I think that the current policy of posting differences between 1.1 and 1.2 or between different machines is a good one, although I also partially agree with Richard. Many of the people on this list are more interested in computer algebra or algorithm design, and not difficulties of specific implementations of those algorithms. Even if they were (as Richard points out), the non-WRI members of the group don't have access to the source code, so their advice might be of limited use. Finally, some (perhaps naive) readers of MathGroup might interpret a bug report as a signal that Mathematica was not a good software package (and it IS a very good package!). Since Richard made a good case for limiting the types of bugs posted to MathGroup, I'll present some reasons for the other side: (1) Users may have encountered some of the same problems and have figured out some work-arounds. From my point of view, it doesn't matter if the problem is Sun's or WRI's... but if someone on MathGroup can describe the problem in a consisent way then we are all better off. (2) I like to know the limits of the programming environment that I'm working in. Sometimes these limits are specific to an implementation, sometimes not. I assume that others might share this interest. (3) I tried to explain in my posting the point of what the function of the program was (polynomials used as operators), and this seemed like a generic enough problem that I was sure that someone else had already solved it in a clean way. I often learn a great deal by watching these sort of conversations on the net... (4) I usually interpret bug reports/problems with packages as a positive signal. It means that people are really using the package and pushing it into areas where the designers might not have anticipated it being applied. (Of course, others could have interpreted my posting in a different light. If so, I apologize to WRI. ) These are my reasons for keeping MathGroup's posting policy in its present form. But... I've been wrong before. :-) Sean Doyle Board of Governors of the Federal Reserve System 20 and Constitution, NW Mail Stop 76 Washington, DC 20551 (202) 452-2352 uucp: uunet!fed!m1swd00 , internet: sdoyle@fed.frb.gov ----- End Included Message ----- From stevec Fri May 12 16:39:10 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA17305; Fri, 12 May 89 15:42:19 CDT Date: Fri, 12 May 89 15:42:19 CDT Message-Id: <8905122042.AA17305@yoda.ncsa.uiuc.edu> To: mathgroup Subject: bug reports.. From: LFEAGIN@CALSTATE.BITNET Reply-To: stevec@ncsa.uiuc.edu Status: RO Steve, I vote to keep the bug reports coming. It's easy enough to sift thru them. Users in the group are bound to be able to provide suggestions, at least some of the time. This should also help "naive" users come up to speed, and should certainly help make Mathematica a better tool. Some apparent bugs in version 1.1 for the MacII: Limit[ x/Sqrt[x^2], x->-Infinity ] returns +1. This error seems to mess up the integrator on some functions when integrated on {x,-Infinity,a}, as e.g. 1/(x^2+1)^(3/2). Integral[ x b^(a x), x ] then Together[ D[ %, x ] ] doesn't return x b^(a x). Jim LFEAGIN@CALSTATE.BITNET From stevec Mon May 15 11:30:40 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA22198; Mon, 15 May 89 10:51:19 CDT Date: Mon, 15 May 89 10:51:19 CDT Message-Id: <8905151551.AA22198@yoda.ncsa.uiuc.edu> To: mathgroup Subject: Mathematica Programming Position From: sdoyle@fed.frb.gov Reply-To: stevec@ncsa.uiuc.edu Status: RO Steve: I don't know if this is appropriate for this group. If it isn't, could you let me know what might be a good place? We'd love to find someone with Mathematica programming experience. We have already posted this to misc.jobs.offered, but we'd like to consider more candidates. Thanks! Sean Doyle Board of Governors of the Federal Reserve System 20 and Constitution, NW Mail Stop 76 Washington, DC 20551 (202) 452-2352 uucp: uunet!fed!m1swd00 , internet: sdoyle@fed.frb.gov Posting follows: JOB OPENING: RESEARCH PROGRAMMER Board of Governors of the Federal Reserve System Division of Research and Statistics MAQS Section Description: Work with economists and programmers on a large network of Sun workstations (120+) used for theoretical and applied economic analysis. Responsibilities would include: ; Software development for estimation and simulation of macroeconomic models. ; Identification and evaluation of new Unix software (such as editors, mathematical/statistical software, utilities, etc.) that may be useful for staff work on the network. Education/Training: Required: Bachelors degree or equivalent experience in computer science, economics, mathematics, or statistics; Familiarity with both traditional (e.g. C or FORTRAN) and non-traditional (e.g. LISP, SMALLTALK or MATHEMATICA) programming languages; Familiarity with UNIX or a UNIX-like operating system; Knowledge of a windowing environment (preferably X or SunView) or design of user interfaces. Desirable:Interest/familiarity with object-oriented programming, symbolic computing, numerical analysis and optimization, parallel processing, computer networks, and SUN workstations. The best candidates will have demonstrated evidence of self-motivation and creativity. From stevec Tue May 16 09:43:01 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA23971; Tue, 16 May 89 09:25:26 CDT Date: Tue, 16 May 89 09:25:26 CDT Message-Id: <8905161425.AA23971@yoda.ncsa.uiuc.edu> To: mathgroup Subject: Notebooks.... From: wri!windsor@uxc.cso.uiuc.edu (Eric Blankenburg) Reply-To: wri!windsor@uxc.cso.uiuc.edu Status: RO [Please reply directly to Eric on this. - smc] Steve, Rob Wolff, of Apple, is looking for 100 Megs of science notebooks for distribution on a CD-ROM during SIGGRAPH 89. He is looking for general science notebooks that cover general science issues. Any help on this would be greatly appreciated. If you can put this across to MathGroup, Wolfram Research, Inc and Apple would appreciate it. Eric Blankenburg PS: By the way, we have a deadline of about 10 days on this little project. From stevec Wed May 17 10:38:50 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA15840; Tue, 2 May 89 09:59:00 CDT Date: Tue, 2 May 89 09:59:00 CDT Message-Id: <8905021459.AA15840@yoda.ncsa.uiuc.edu> To: mathgroup Subject: Re: Question about Check[] From: stevec@ncsa.uiuc.edu Status: RO [Fourth in the series on Check and other things. -smc] Here is a 1.2 session: Comments? ==================================================================== In[57]:= foo/: CForm[foo[x_,y_]]:= SequenceForm[ "readdata( foo,", x , ",", y,")"] log: SING error In[58]:= foo[1,2] Out[58]= foo[1, 2] In[59]:= CForm[%] Out[59]= readdata( foo,1,2) In[60]:= temp = foo[1,2] + foo[2,3] + foo[3,4] Out[60]= foo[1, 2] + foo[2, 3] + foo[3, 4] In[61]:= CForm[temp] Out[61]//CForm= foo(1,2) + foo(2,3) + foo(3,4) In[62]:= temp /. {foo[x___] -> CForm[foo[x]]} Out[62]= readdata( foo,1,2) + readdata( foo,2,3) + readdata( foo,3,4) In[63]:= FullForm[%] Out[63]//FullForm= > Plus[SequenceForm["readdata( foo,", 1, ",", 2, ")"], > SequenceForm["readdata( foo,", 2, ",", 3, ")"], > SequenceForm["readdata( foo,", 3, ",", 4, ")"]] From stevec Wed May 17 11:08:27 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA15846; Tue, 2 May 89 10:00:22 CDT Date: Tue, 2 May 89 10:00:22 CDT Message-Id: <8905021500.AA15846@yoda.ncsa.uiuc.edu> To: mathgroup Subject: Re: Question about Check[] From: sdoyle@fed.frb.gov Status: RO [Last in the series on Check[] -smc] Thanks for the 1.2 session. I think that CForm[] isn't working the way that a user would want it to. If a user has particular CForm rules defined for an object, a CForm on an expression containing those objects should use the user's rules... and as your Out[60] shows, it doesn't use the user's rules. It is slow and awkward have a rule for each object that maps it into a string and then parses the string.... so if someone at WRI (or on the list) has better ideas I'd love to hear them. So... could you forward either your session or mine to WRI? Or... I could send it if you would rather. Thanks! Sean Doyle Board of Governors of the Federal Reserve System 20 and Constitution, NW Mail Stop 76 Washington, DC 20551 (202) 452-2352 uucp: uunet!fed!m1swd00 , internet: sdoyle@fed.frb.gov P.S. By the way, TeXForm[] works pretty much as one would hope, so if WRI could make CForm[] more like TeXForm my programs would have less kludgey code.... From stevec Wed May 17 11:36:23 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA03472; Fri, 5 May 89 09:13:05 CDT Date: Fri, 5 May 89 09:13:05 CDT Message-Id: <8905051413.AA03472@yoda.ncsa.uiuc.edu> To: mathgroup Subject: lagbug.m From: stevec@ncsa.uiuc.edu Reply-To: stevec@ncsa.uiuc.edu Status: RO [Response to previous message on Sun-4 "bug" by Sean Doyle. -smc] Here is a session on my Sun-4/110 running 1.2 beta: Mathematica (sun4) 1.2.beta (April 2, 1989) [With pre-loaded data] by S. Wolfram, D. Grayson, R. Maeder, H. Cejtin, S. Omohundro, D. Ballman and J. Keiper with I. Rivin and D. Withoff Copyright 1988,1989 Wolfram Research Inc. -- SunView graphics initialized -- In[1]:= < LagOperator[4] - Identity LagOperator[100] + LagOperator[101] + > LagOperator[103] - LagOperator[104]] In[3]:= Which appears to agree with your 1.1 3/60 answer. So, something seems better. I will be getting the official non-beta 1.2 today. I will ship you message and this one to the mailing list also. Steve Christensen ----- End Included Message ----- From stevec Thu May 18 13:18:46 1989 Return-Path: Received: by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA17313; Fri, 12 May 89 15:46:50 CDT Date: Fri, 12 May 89 15:46:50 CDT Message-Id: <8905122046.AA17313@yoda.ncsa.uiuc.edu> To: mathgroup Subject: Re: bug reports.. From: stevec@ncsa.uiuc.edu Reply-To: stevec@ncsa.uiuc.edu Status: RO For your bugs (from LFEAGIN@CALSTATE.BITNET), I get (run in Sun verison 1.2): In[1]:= Limit[ x/Sqrt[x^2], x->-Infinity ] Out[1]= 1 In[2]:= Integrate[x b^(a x), x ] a x Log[b] 1 x Out[2]= E (-(----------) + --------) 2 2 a Log[b] a Log[b] In[3]:= D[%,x] a x Log[b] E a x Log[b] 1 x Out[3]= ----------- + E a (-(----------) + --------) Log[b] a Log[b] 2 2 a Log[b] a Log[b] In[4]:= Expand[%] a x Log[b] Out[4]= E When you ask Mathematica to Plot the function x/Sqrt[x] say from -1 to 1, you get the step function with jump at 0, but the Limit function does not give -1 as it probably should. In the second example, it is clear that the rules for E and Log's are not automatic, but could easily be programmed in. I note that Maple also gives 1 for In[1], But does simplify Out[4] back to the x b^(a x). Macsyma gives -1 for the limit, but does not simplify the exponential automatically. Steve ------------------------------------------------------------------------- Steven M. Christensen Senior Research Scientist (Theoretical Physics) National Center for Supercomputing Applications Beckman Institute for Advanced Science and Technology University of Illinois at Urbana-Champaign Urbana, Illinios 61801 USA Phone: (217) 244-0544 (with answering machine) Phone: (217) 244-0072 (main NCSA number for messages to a human being) FAX: (217) 244-2909 Email: stevec@ncsa.uiuc.edu (Internet) Email: 14008@ncsavmsa.bitnet (Bitnet) ------------------------------------------------------------------------- From mathgroup-adm@yoda.ncsa.uiuc.edu Mon May 22 15:21:42 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA10350; Mon, 22 May 89 15:21:41 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA02671; Mon, 22 May 89 15:21:51 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA22333; Mon, 22 May 89 15:21:47 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA10268; Mon, 22 May 89 14:12:50 -0500 Date: Mon, 22 May 89 14:12:50 -0500 From: mathgroup-adm@yoda.ncsa.uiuc.edu Message-Id: <8905221912.AA10268@yoda.ncsa.uiuc.edu> Apparently-To: mathgroup-out@yoda.ncsa.uiuc.edu Status: RO Mathematica Mailing List Modifications: First, to all mailing list members, my apologies. The mailing list broke down seriously and many messages not ment for wide distribution, especially requests to be added or removed from the list, were sent and got out of control. Further, many people were mailing to an address that got sent immediately to everyone on the list without a chance for me to filter it first. In addition, bug reports which I thought might be of interest turned out not to be. Finally, some mail machines between my Sun-4 and your machines got overwhelmed by the size of the mailing list (over 300 people and despite the number of people asking to be removed, there are more asking to be added). This caused many machines to stop somewhere in the middle of a mailing, go down and then come back up and start the mailings over again. This ment that messages were often sent to some people many times. After having to deal with irate mail list members and literally hundreds of messages of all kinds, I called in a consultant. He spent this weekend fixing the problems. He moved much of the responsibility for handling the mail to my machine so that mail can avoid going through the sick intermediate machines when possible. Now when anyone mails to the mailing list the mail will go to me first and will not go out to the whole list. This will avoid repeated messages and add and remove requests. This should reduce the junk mail you will get from the mailing list to almost zero if all goes well. The vote about bug reports was heavily against having them unless they are very significant bugs that could affect all users. In any case, I will try to label bug reports I do send out with the word BUG in the Subject heading. If you are not interested you can delete it immediately. However, so that those interested in bug reports are not left out, I will archive bug reports on the archive server under the directory Bugs. In a lot of cases, I can answer the question about the bug, so it is not necessary to sent it to the list. I have also been asked to provide a mechanism for Bitnet users to get the archives. Periodically, I will send a table of contents to the mailing list. If you are a user who wants to receive a file via email, send me a message and I will see to it. Otherwise, I still prefer that you use anonymous ftp when possible. ============================================================================= So, here are the new addresses: You may now mail to: mathgroup@yoda.ncsa.uiuc.edu or stevec@ncsa.uiuc.edu yoda is a Sun-4 with internet address: 128.174.222.70 Requests to be added or removed or other administrative things go to: mathgroup-request@yoda.ncsa.uiuc.edu. Bitnet users can mail to me at 14008@ncsavmsa.bitnet ----------------------------------------------------------------------------- The ftp server is ftp.ncsa.uiuc.edu and has internet address: 128.174.20.50 The current contents are: /usr6/ftp/Symbolic/Mathematica (main directory) MathGroup_Mail_Archive (subdirectory) MathGroupMail1 (file) Packages (subdirectory) Cochlear_Model ShowTime.m fourier.sh Complex.m VecCalc.m mdefs.h (individual files) Sci.Math.Symbolic (subdirectory) Archive1 Archive2 Archive3 (files) Bugs (subdirectory) (empty right now) ============================================================================ If you have any problems sending to me, if you are getting duplicate or seriously unwanted messages or have any other problem, please email me at the mathgroup address above. This is the first message sent out under the new mechanism so I hope it works. I also hope that the problems are taken care of and that you get some use out of this list in the future. Please contribute to make it work. Thanks for your patience and sorry for the junk mail. [One final note. It is possible that there is still some junk left in the system. I would like to know if you get any mail dated before this message. I want to isolate the sick machines in the mail network.] Steve Christensen ------------------------------------------------------------------------- Steven M. Christensen Senior Research Scientist (Theoretical Physics) National Center for Supercomputing Applications Beckman Institute for Advanced Science and Technology University of Illinois at Urbana-Champaign Urbana, Illinios 61801 USA Phone: (217) 244-0544 (with answering machine) Phone: (217) 244-0072 (main NCSA number for messages to a human being) FAX: (217) 244-2909 Email: stevec@ncsa.uiuc.edu (Internet) Email: 14008@ncsavmsa.bitnet (Bitnet) MathGroup: mathgroup@yoda.ncsa.uiuc.edu Mathgroup-request: mathgroup-request@yoda.ncsa.uiuc.edu ------------------------------------------------------------------------- From mathgroup-adm@yoda.ncsa.uiuc.edu Mon May 22 19:11:08 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA10622; Mon, 22 May 89 19:11:07 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA03287; Mon, 22 May 89 19:11:13 CDT Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA24990; Mon, 22 May 89 19:11:11 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA10569; Mon, 22 May 89 17:46:35 -0500 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA02106; Thu, 18 May 89 10:31:42 CDT Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA15526; Thu, 18 May 89 10:29:13 CDT Return-Path: Received: from lakisis.umd.edu ([128.8.134.19]) by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA04426; Thu, 18 May 89 10:29:10 CDT Date: Thu, 18 May 89 11:24:50 EDT From: "Mark Phillips" Message-Id: <8905181524.AA17012@lakisis.umd.edu> Received: by lakisis.umd.edu; Thu, 18 May 89 11:24:50 EDT To: stevec@ncsa.uiuc.edu Subject: Complex.m --- a package for calculations with complex expressions Status: RO Hello MathGroupers, Guess what!? This is not a bug report or a request to be removed from this list! [[ applause here ]] It's a package for dealing with complex expressions. Have you ever noticed that Mathematica doesn't evaluate Re[x], Conjugate[x], etc, unless x is a number? There are many situations, however, in which it is nice to be able to delcare a symbol to represent a real quantity, so that complex expressions involving that symbol and Re, Im, Conjugate, and so on can be simplified. This package defines the function DeclareReal which does just this. It also defines several other functions which are useful in the context of calculations with complex expressions. I would be interested in hearing what people think of it, plus suggestions for how to improve it. One thing that I have not been able to work out satisfactorily is how to tell Mathematica that Sqrt[x] is real when x is real an nonnegative. The package currently just checks for N[x]>=0, which works if x is a real number but not otherwise. Similar problems exist for other functions, most notably Power, of which Sqrt is just a special case. Any ideas? Mark Phillips mbp@lakisis.umd.edu (arpanet) Department of Mathematics (301) 454-2693 University of Maryland College Park, Maryland 20742 ---------snip snip------snip snip------snip snip------snip snip--------- (* * Complex.m: * Allows symbols to be declared to represent real numbers. * Expressions involving these symbols and Re,Im,Conjugate, etc, * then simplify nicely. Also defines some useful functions for * manipulating complex expressions. * * Author: Mark B. Phillips (mbp@lakisis.umd.edu) * Dept. of Mathematics * University of Maryland * May 18, 1989 * * Typical usage: * * In[1]:= <0 Im[x_Integer ^ n_Rational] := 0 /; OddQ[Denominator[n]] || x>0 Re[(-1) ^ n_Rational] := Cos[n Pi] Im[(-1) ^ n_Rational] := Sin[n Pi] Re[Sin[x_]] := Sin[Re[x]] Cosh[Im[x]] Im[Sin[x_]] := Cos[Re[x]] Sinh[Im[x]] Re[Cos[x_]] := Cos[Re[x]] Cosh[Im[x]] Im[Cos[x_]] := -Sin[Re[x]] Sinh[Im[x]] Re[Tan[x_]] := Re[Sin[x]/Cos[x]] Im[Tan[x_]] := Im[Sin[x]/Cos[x]] Protect[Re,Im] (* End of ReIm.m *) (*----------------------------------------------------------------------*) RealQ[f_[x_]] := True /; RealValuedQ[f] RealValuedQ[Re] := True RealValuedQ[Im] := True RealValuedQ[Abs] := True RealValuedQ[Arg] := True (* NOTE: RealQ should have an option to specify how it does comparisons for <, >, ==, etc. Right now we just use N[#]. *) RealQ[Sqrt[x_]] := True /; (RealQ[x] && (N[x] >= 0)) RealQ[x_?RealQ + y_?RealQ] := True RealQ[x_?RealQ * y_?RealQ] := True RealQ[x_?RealQ ^ -1] := True Unprotect[Conjugate] Conjugate[x_] := x /; Re[x] == x Conjugate[x_ + y_] := Conjugate[x] + Conjugate[y] Conjugate[x_ * y_] := Conjugate[x] * Conjugate[y] Conjugate[Conjugate[x_]] := x Conjugate[Exp[y_]] := Exp[-y] /; Re[y] == 0 Protect[Conjugate] Unprotect[Arg] Arg[x_] := 0 /; (Im[x]==0 && N[x]>0) Arg[x_] := Pi /; (Im[x]==0 && N[x]<0) Arg[0] = 0 Protect[Arg] SetAttributes[DeclareReal, Listable] DeclareReal[x_,y__] := (DeclareReal[{x,y}] ; Null) DeclareReal[x_] := (x/: RealQ[x] = True ; Null) SetAttributes[DeclareRealValued, Listable] DeclareRealValued[f_,g__] := (DeclareRealValued[{f,g}] ; Null) DeclareRealValued[f_] := (f/: RealValuedQ[f] = True ; Null) ComplexNormSquared[z_] := Expand[ z Conjugate[z] ] ComplexNorm[z_] := Sqrt[ComplexNormSquared[z]] AbsReduce[e_] := e //. Abs[z_] -> Sqrt[ Re[z]^2 + Im[z]^2 ] ComplexParametricPlot[f_, args__] := ParametricPlot[ {Re[f],Im[f]}, args ] ComplexCanonify[z_] := Together[Expand[Re[z]]] + I Together[Expand[Im[z]]] End[] EndPackage[] From mathgroup-adm@yoda.ncsa.uiuc.edu Tue May 30 14:22:17 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA18579; Tue, 30 May 89 14:22:16 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA23914; Tue, 30 May 89 14:22:05 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA16378; Tue, 30 May 89 14:22:02 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA18491; Tue, 30 May 89 11:35:37 -0500 Date: Tue, 30 May 89 11:35:37 -0500 From: mathgroup-adm@yoda.ncsa.uiuc.edu Message-Id: <8905301635.AA18491@yoda.ncsa.uiuc.edu> Apparently-To: mathgroup-out@yoda.ncsa.uiuc.edu Status: RO GASPARD@HROEUR5.BITNET Sun May 21 15:32:08 1989 Subject: Colour output in Mathematica? I use 386-Mathematica 1.1 with a VGA colour monitor. Other than simple lines, I somehow cannot get Mathematica to display colour graphics on the screen. Most of the time I get an empty frame. The Mathematica book says it is complicated but provides little clarification. Could someone please post a complete example of a 3D colour graphic, e.g. the one on the cover of the book. Gaspard A. de Jong Erasmus University Computing Center =================================================================== [Here is my response. -smc] The commands to produce the graphic similar to the one on the front of the Mathematica book are: <{0,6},ViewPoint->{-0.8,-2,1.2}, BoxRatios->{1.2,1,0.7},PlotPoints->40] I have not tested this on a 386 machine but it works on a Macintosh and on a Sun. If it doesn't work on your machine you might check to make sure your installation was done to tell Mathematica you have a VGA system. Steve Christensen ======================================================================= [Gaspard's response.] Steve, When your example (thanks for the quick reply by the way) didn't work, I decided to look again at some other parameters. Minstall correctly recognizes VGA 16 col. and creates DISPLAY.BAT accordingly. The cause of the problem turned out to be that the software makes my Paradise VGA Prof. card default to MCGA mode (black & white). The problem was solved by including a line in DISPLAY.BAT which explicitly puts the card in VGA mode. This is a strange problem because VGA-mode is the card's default setting and none of the other graphics programs I use has ever given me problems in generating colour output. It might be worthwhile checking the 386-version of the Mathematica display modules for a possible problem here. I have a request for a future release of the display software. The Paradise card, like many VGA cards on the market, is capable of displaying 256 colours in 640x480 resolution. It would be very nice to be able to use this feature in Mathematica. At present only the expensive 8514 option offers this number of colours. I expect it shouldn't be very difficult to add a few extended VGA or extended EGA modes to the program. Thank you again for your help. Gaspard A. de Jong ============================================================================ From mathgroup-adm@yoda.ncsa.uiuc.edu Tue May 30 15:27:12 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA18645; Tue, 30 May 89 15:27:10 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA24113; Tue, 30 May 89 15:26:55 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA17278; Tue, 30 May 89 15:26:51 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA18563; Tue, 30 May 89 12:48:45 -0500 Date: Tue, 30 May 89 12:48:45 -0500 Message-Id: <8905301748.AA18563@yoda.ncsa.uiuc.edu> From: sen@danny.math.unc.edu, Fri@yoda.ncsa.uiuc.edu, May@yoda.ncsa.uiuc.edu, 19@yoda.ncsa.uiuc.edu, 15:17:48@yoda.ncsa.uiuc.edu, 1989@yoda.ncsa.uiuc.edu Subject: Plotting in Mathematica [4 messages] Apparently-To: mathgroup-out@yoda.ncsa.uiuc.edu Status: RO Steve, Here is a question about plotting in Mathematica. 1. Can one plot in a small part of the screen? For instance, suppose one wants to issue the command: Plot[x^2,{x,-1,1}] and then one would like to have this plot restricted to the upper left quarter, i.e. 2nd quadrant of the graphics window. 2. Can one use greek letters as text on plots? Any help is appreciated. Sheldon Newhouse ========================================================================= [I asked for clarification. This is Sheldon's response. -smc] Yes, I would like to plot in a quadrant of a window sometimes. For instance, I would like to make a page with a window at the top and text at the bottom, or perhaps a window on one wide and text on another side. If they cannot yet do this (or the greek letters), perhaps they would consider adding these options. I think many users would like them, and it would not be too hard to do it. Sheldon =========================================================================== Steve, I am certain that one can set up procedures in mathematica to plot on parts of a window as I asked you. For instance, g1 = Graphics[Line[{{0,0},{1,1}}]]; g2 = Graphics[{GrayLevel[1.],Point[{2,0}]}]; Show[g1,g2]; plots a line in the left half of the window. Similarly, g1 = Graphics[Line[{{0,0},{1,1}}]]; g3 = Graphics[{GrayLevel[1.],Point[{2,-1}]}]; Show[g1,g3]; plots the line in the upper left-hand quarter of the window. Of course, routines could be written to do this with any plot, but one good thing about mathematica is that it has many useful procedures which don't require programming. What about asking the people at Wolfram & Assoc. to add an option to Plot, ParametricPlot, ListPlot, Graphics3D, etc , say of the form ViewPort -> {x,y,z,w} where x,y,z,w are real numbers in [0,1] with 0 <= x < y <= 1 and 0 <= z < w <= 1 and this option means: do the plot in the subwindow whose horizontal coordinates go from x to y ( with 0 to 1 meaning the whole horizontal extent of the window), and whose vertical coordinates go from z to w ( again with 0 to 1 meaning the whole vertical extent of the window). Thus, ViewPort -> {0,.5,.5,1} would mean the upper left-hand quarter of the window, ViewPort -> {.5,1,.5,1} would mean the upper right-handquarter of the window,etc. - Sheldon =========================================================================== Steve, Of course in my last message, 3D graphics would require a ViewPort setting which is a six-tuple, say {x,y,z,w,u,v} -sheldon ============================================================================ From mathgroup-adm@yoda.ncsa.uiuc.edu Mon Jun 5 16:53:45 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA02910; Mon, 5 Jun 89 16:53:44 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA19414; Mon, 5 Jun 89 16:52:18 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA29844; Mon, 5 Jun 89 16:52:16 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA02884; Mon, 5 Jun 89 16:04:57 -0500 Date: Mon, 5 Jun 89 16:04:57 -0500 Message-Id: <8906052104.AA02884@yoda.ncsa.uiuc.edu> From: rhs@flash.bellcore.com Subject: MathExec() bug (?) Apparently-To: mathgroup-out@yoda.ncsa.uiuc.edu Status: RO On p. 586 of the manual, it is claimed that MathExec("expr") evaluate[s] expr as Mathematica input, and return[s] the result as a string. On the sun 4 1.1 version (though mathlink.c is in common so I expect this is true everywhere), there is no mechanism for returning the result to the user program that I can see. And it doesn't seem to work. (I can get MathExec to work, it just doesn't return anything) I haven't seen anything anywhere about this. Ideas? More generally, how does one pump a lot of numbers efficiently into the user program, i.e. suppose one wants to send a 50 by 50 matrix from Mathematica to the user program. I don't see how the mechanism of Section B.7.6 allows this except through MathExec() as above (which looks kludgy but doable if it worked). rhs@flash.bellcore.com From fischer@slothrop.math.ufl.edu Tue Jun 6 10:19:01 1989 Received: from slothrop.math.ufl.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA03889; Tue, 6 Jun 89 10:18:53 -0500 From: fischer@slothrop.math.ufl.edu Received: by slothrop.math.ufl.edu (5.61ufl/4.03) id AA10565; Tue, 6 Jun 89 11:18:50 -0400 Date: Tue, 6 Jun 89 11:18:50 -0400 Message-Id: <8906061518.AA10565@slothrop.math.ufl.edu> To: mathgroup@yoda.ncsa.uiuc.edu Subject: endless loop in TrigExpand? Reply-To: jde@mathlab.math.ufl.edu Status: RO Please reply to jde@mathlab.math.ufl.edu (James D English). Problem: When, using Mathematica, the following command is entered: TrigExpand[ Cos[t1] Sin[t2] + Cos[t2] Sin[t1]] the following, expected result is displayed (almost immediately) : Sin[t1 + t2] However, a problem arises when the following is entered: TrigExpand[Cos[t1] Sin[t2] Sin[t3] + Cos[t2] Sin[t1] Sin[t3]] rather than the expected Sin[t1 +t2] Sin[t3], the program goes into what appears to be an endless loop. Nor does it work when the function is entered in the following form: TrigExpand[(Cos[t1] Sin[t2] + Cos[t2] Sin[t1])Sin[t3]] From mathgroup-adm@yoda.ncsa.uiuc.edu Sat Jun 17 01:40:48 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA16367; Sat, 17 Jun 89 01:40:47 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA18129; Sat, 17 Jun 89 01:40:36 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA21859; Sat, 17 Jun 89 01:40:35 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA16355; Sat, 17 Jun 89 01:07:00 -0500 Date: Sat, 17 Jun 89 01:07:00 -0500 Message-Id: <8906170607.AA16355@yoda.ncsa.uiuc.edu> From: leon@extro.ucc.su.oz.au Subject: Postscript macros in Mathematica Apparently-To: mathgroup-out@yoda.ncsa.uiuc.edu Status: RO Mathematica users, I would like to incorporate the postscript graphics generated by Mathematica in other documents (and on other computers), however the postscript text generated contains a number of macros (Mpstart, Mscale, Msboxa, Mshowa, Mistroke, MfstrokeMpend and perhaps others I haven't come across yet). Is there anyway of finding out what these commands do in terms of standard postscript commands. Any help is appreciated. Leon Poladian leon@extro.ucc.su.OZ.AU From mathgroup-adm@yoda.ncsa.uiuc.edu Mon Jun 19 17:29:59 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA18381; Mon, 19 Jun 89 17:29:57 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA27361; Mon, 19 Jun 89 17:29:39 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA18866; Mon, 19 Jun 89 16:08:18 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA18240; Mon, 19 Jun 89 12:31:49 -0500 Date: Mon, 19 Jun 89 12:31:49 -0500 Message-Id: <8906191731.AA18240@yoda.ncsa.uiuc.edu> From: dhj@rice.edu Subject: Mathematica Postscript Macros Apparently-To: mathgroup-out@yoda.ncsa.uiuc.edu Status: RO The PostScript file can be intercepted on its way to the printer on any Macintosh. When you print, you acknowledge the dialog box which says what printer you are accessing, the number of copies, etc. Now comes the new part: after clicking OK, hold down command-f. Rather than messages appearing about searching for printer, starting job, etc., you obtain the message "Creating PostScript File". Nothing is printed, but a file is created in the directory from which Mathematica was launched named PostScript0. This file is pure text and contains Mathematica's macro definitions and the description of what you wanted to print. By the way, this procedure will NOT work if you are running under MultiFinder and are using the PrintMonitor. For those who find this inconvenient or don't have a Mac, here is what my version of Mathematica has for its PostScript macro definitions. Don H. Johnson Elec. & Comp. Eng. Dept. Rice University dhj@rice.edu /Mnodistort true def /Mpstart { MathPictureStart } bind def /Mpend { MathPictureEnd } bind def /Mscale { 0 1 0 1 5 -1 roll MathScale } bind def /Plain /Courier findfont def /Bold /Courier-Bold findfont def /Italic /Courier-Oblique findfont def /MathPictureStart { gsave newpath Mleft Mbottom translate 1 -1 scale /Mtmatrix matrix currentmatrix def Plain Mfontsize scalefont setfont 0 setgray 0 setlinewidth } bind def /MathPictureEnd { grestore } bind def /Mdot { moveto 0 0 rlineto stroke } bind def /Mtetra { moveto lineto lineto lineto fill } bind def /Metetra { moveto lineto lineto lineto closepath gsave fill grestore 0 setgray stroke } bind def /Mistroke { flattenpath 0 0 0 { 4 2 roll pop pop } { 4 -1 roll 2 index sub dup mul 4 -1 roll 2 index sub dup mul add sqrt 4 -1 roll add 3 1 roll } { stop } { stop } pathforall pop pop currentpoint stroke moveto currentdash 3 -1 roll add setdash } bind def /Mfstroke { stroke currentdash pop 0 setdash } bind def /Msboxa { newpath 5 -1 roll Mvboxa pop 6 -1 roll 5 -1 roll 4 -1 roll Msboxa1 5 -3 roll Msboxa1 [ 7 -2 roll [ 2 index 2 index 10 -1 roll 9 -1 roll ] 6 1 roll 5 -2 roll ] } bind def /Msboxa1 { sub 2 div dup 2 index 1 add mul 3 -1 roll -1 add 3 -1 roll mul } bind def /Mvboxa { gsave newpath [ true 3 -1 roll { Mbbox 5 -1 roll { 0 5 1 roll } { 7 -1 roll exch sub (m) stringwidth pop .3 mul sub 7 1 roll 6 -1 roll 4 -1 roll Mmin 3 -1 roll 5 index add 5 -1 roll 4 -1 roll Mmax 4 -1 roll } ifelse false } forall { stop } if counttomark 1 add 4 roll ] grestore } bind def /Mbbox { 0 0 moveto false charpath flattenpath pathbbox newpath } bind def /Mmin { 2 copy gt { exch } if pop } bind def /Mmax { 2 copy lt { exch } if popSERT \ } bind def /Mshowa { 4 -2 roll moveto 2 index Mtmatrix setmatrix Mvboxa 7 1 roll 6 -1 roll 5 -1 roll 4 -1 roll Mshowa1 4 1 roll Mshowa1 rmoveto currentpoint 0 1 4 index length -1 add { 2 index 4 index 2 index get 3 index add moveto 4 index exch get show } for pop pop pop pop Mgmatrix setmatrix } bind def /Mshowa1 { 2 copy add 4 1 roll sub mul sub -2 div } bind def /MathScale { Mwidth Mheight Mlp translate scale pop pop pop pop /Mgmatrix matrix currentmatrix def } bind def /Mlp { 3 copy Mlpfirst { Mnodistort { Mmin dup } if 4 index 2 index 2 index Mlprun 11 index 11 -1 roll 10 -4 roll Mlp1 8 index 9 -5 roll Mlp1 4 -1 roll and { exit } if 3 -1 roll pop pop } loop exch 3 1 roll 7 -3 roll pop pop pop } bind def /Mlpfirst { 3 -1 roll dup length 2 copy -2 add get aload pop pop pop 4 -2 roll -1 add get aload pop pop pop 6 -1 roll 3 -1 roll 5 -1 roll sub div 4 1 roll exch sub div } bind def /Mlprun { 2 copy 4 index 0 get dup 4 1 roll Mlprun1 3 copy 8 -2 roll 9 -1 roll { 3 copy Mlprun1 3 copy 11 -3 roll /gt Mlpminmax 8 3 roll 11 -3 roll /lt Mlpminmax 8 3 roll } forall pop pop pop pop 3 1 roll pop pop aload pop 5 -1 roll aload pop exch 6 -1 roll Mlprun2 8 2 roll 4 -1 roll Mlprun2 6 2 roll 3 -1 roll Mlprun2 4 2 roll exch Mlprun2 6 2 roll } bind def /Mlprun1 { aload pop exch 6 -1 roll 5 -1 roll mul add 4 -2 roll mul 3 -1 roll add } bind def /Mlprun2 { 2 copy add 2 div 3 1 roll exch sub } bind def /Mlpminmax { cvx 2 index 6 index 2 index exec { 7 -3 roll 4 -1 roll } if 1 index 5 index 3 -1 roll exec { 4 1 roll pop 5 -1 roll aload pop pop 4 -1 roll aload pop [ 8 -2 roll pop 5 -2 roll pop 6 -2 roll pop 5 -1 roll ] 4 1 roll pop } { pop pop pop } ifelse } bind def /Mlp1 { 5 index 3 index sub 5 index 2 index mul 1 index le 1 index 0 le or dup not { 1 index 3 index div .99999 mul 8 -1 roll pop 7 1 roll } if 8 -1 roll 2 div 7 -2 roll pop sub 5 index 6 -3 roll pop pop mul sub exch } bind def From mathgroup-adm@yoda.ncsa.uiuc.edu Mon Jun 19 18:15:33 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA18468; Mon, 19 Jun 89 18:15:32 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA27478; Mon, 19 Jun 89 18:15:25 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA19940; Mon, 19 Jun 89 18:15:24 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA18286; Mon, 19 Jun 89 14:51:49 -0500 Date: Mon, 19 Jun 89 14:51:49 -0500 Message-Id: <8906191951.AA18286@yoda.ncsa.uiuc.edu> From: jack@sun.acs.udel.edu Subject: Mathematica Problem Apparently-To: mathgroup-out@yoda.ncsa.uiuc.edu Status: RO Perhaps someone can help solve the following Mathematica problem: Given y' = y, solve using a series solution and prove that the result is E[x]. It is proving that the result is E[x] that I have not been able to do. Here is a sample session: In[1]:= Derivative[n_][y][x_]:=Derivative[n-1][y][x] In[2]:= Series[y[x],{x,0,5}] 2 3 4 5 y[0] x y[0] x y[0] x y[0] x 6 Out[2]= y[0] + y[0] x + ------- + ------- + ------- + ------- + O[x] 2 6 24 120 In[3]:= seriesbyy0[x_,n_]:=Normal[Expand[Cancel[Series[y[x],{x,0,n}]/y[0]]]] In[4]:= expseries[x_,n_]:=Sum[x^i/i!,{i,0,n}] In[5]:= seriesbyy0[x,6] 2 3 4 5 6 x x x x x Out[5]= 1 + x + -- + -- + -- + --- + --- 2 6 24 120 720 In[6]:= expseries[x,6] 2 3 4 5 6 x x x x x Out[6]= 1 + x + -- + -- + -- + --- + --- 2 6 24 120 720 In[7]:= seriesbyy0[x,100]-expseries[x,100] Out[7]= 0 As shown, I can prove the results are identical for a constant value of the argument "n", but not for general n. I realize that the identity is proven by visual inspection, but I would like to prove it by showing the identity seriesbyy0[x,n] == expseries[x,n] evaluates to true. I have tried LogicalExpand, but to no avail. Jack Seltzer jack@sun.acs.udel.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Jun 20 01:38:49 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA19297; Tue, 20 Jun 89 01:38:48 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA29363; Tue, 20 Jun 89 01:38:43 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA23238; Tue, 20 Jun 89 01:38:41 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA18677; Mon, 19 Jun 89 23:22:16 -0500 Date: Mon, 19 Jun 89 23:22:16 -0500 Message-Id: <8906200422.AA18677@yoda.ncsa.uiuc.edu> From: dooley@ernie.Berkeley.EDU Subject: Re: Mathematica Problem Apparently-To: mathgroup-out@yoda.ncsa.uiuc.edu Status: RO Considering the following result proven by Mathematica, I wonder exactly how useful a proof like the one you describe would be. Mathematica (as well as any other of the popular computer algebra systems) is not a proof system; it merely answers your questions. Sam Dooley dooley@ernie.Berkeley.EDU IBM RT PC AIX Mathematica 1.1 (September 29, 1988) [With pre-loaded data] by S. Wolfram, D. Grayson, R. Maeder, H. Cejtin, S. Omohundro, D. Ballman and J. Keiper Copyright 1988 Wolfram Research Inc. -- Terminal graphics initialized -- In[1]:= Sin[x] ^ 2 == 1 - Cos[x] ^ 2 2 2 Out[1]= Sin[x] == 1 - Cos[x] In[2]:= Series[%, {x, 0, 5}] 4 2 2 False x 6 Out[2]= True + 2 False x - ---------- + O[x] 3 From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Jun 21 01:40:29 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA20558; Wed, 21 Jun 89 01:40:27 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA04128; Wed, 21 Jun 89 01:40:19 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA08920; Wed, 21 Jun 89 01:40:18 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA20469; Wed, 21 Jun 89 00:35:34 -0500 Date: Wed, 21 Jun 89 00:35:34 -0500 Message-Id: <8906210535.AA20469@yoda.ncsa.uiuc.edu> From: Dallas_Burtraw@um.cc.umich.edu Subject: Two problems Apparently-To: mathgroup-out@yoda.ncsa.uiuc.edu Status: RO Greetings. I am in the Economics Dept at Michigan and have been using Mathematica for a little while. Two questions have surfaced that we have not been able to resolve. Can you help? First, I want to attach a penalty in a function within a program, so for example, I always want x > xo. The number x is a real. I want to write ((x - xo)^2)^(.5) - (x - xo) which is 0 for x nonnegative and greater than 0 for x negative. The problem is Mathematica automatically simplifies this algebra. Is there a way to prevent that? The second, more substantial question is the reason the first came up. It seems Mathematica can not use its problem solving techniques, either Solve or FindRoot, over conditional statements. For example, f(x) = x if .... f(x) = x^2 otherwise. Writing such a conditional with If or Which, then FindRoot can not solve because it can not compute the derivatives. Is there a way around this other than calculating maximization conditions separately and then rewriting a new conditional? It seems like an easy fix within the program if it truly is a bug. The real issue on this second question is the construction of a constrained maximization or Lagrangian problem. It seems clumsy, but I have had to solve each f(x) = x, etc. and then test the "if" statement. This wastes time and I lose any numerical value for the Lagrangian weight on the constraint. Do you have suggestions? Regards, Dallas Burtraw Dallas_Burtraw@um.cc.umich.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Jun 22 14:46:30 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA21955; Thu, 22 Jun 89 14:46:29 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA10793; Thu, 22 Jun 89 14:46:24 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA00662; Thu, 22 Jun 89 14:46:21 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA21916; Thu, 22 Jun 89 13:48:20 -0500 Date: Thu, 22 Jun 89 13:48:20 -0500 Message-Id: <8906221848.AA21916@yoda.ncsa.uiuc.edu> From: mike@imager.mit.edu Subject: Quaternions in Mathematica? Apparently-To: mathgroup-out@yoda.ncsa.uiuc.edu Status: RO I'm interested in MathGroup. My particular interest is in quaternion mathematics. I've been trying to develop a package around a Quaternion data type and have been having trouble when it comes to defining multiplication. If anyone else is taking a stab at this I'm interested. My address is : mike@imager.mit.edu Thanks. From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Jun 22 15:55:06 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA21999; Thu, 22 Jun 89 15:55:05 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA11297; Thu, 22 Jun 89 15:55:00 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA01640; Thu, 22 Jun 89 15:54:57 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA21919; Thu, 22 Jun 89 13:51:01 -0500 Date: Thu, 22 Jun 89 13:51:01 -0500 Message-Id: <8906221851.AA21919@yoda.ncsa.uiuc.edu> From: Richard Petti Subject: Two problems Apparently-To: mathgroup-out@yoda.ncsa.uiuc.edu Status: RO Date: Wed, 21 Jun 89 00:35:34 -0500 From: Dallas_Burtraw@um.cc.umich.edu Greetings. I am in the Economics Dept at Michigan and have been using Mathematica for a little while. Two questions have surfaced that we have not been able to resolve. Can you help? First, I want to attach a penalty in a function within a program, so for example, I always want x > xo. The number x is a real. I want to write ((x - xo)^2)^(.5) - (x - xo) which is 0 for x nonnegative and greater than 0 for x negative. The problem is Mathematica automatically simplifies this algebra. Is there a way to prevent that? I can only suggest how these problems are solved using MACSYMA. Perhaps Mathematica has similar features. MACSYMA is quite careful about assumptions like SQRT(X^2) -> ABS(X), and has a data base for storing facts about symbolic variables. It helps in this case: (C1) F1:SQRT((X-X0)^2)-(X-X0); (D1) ABS(X0 - X) + X0 - X (C2) ASSUME(X-X0 > 0); (D2) [X > X0] (C3) F2:SQRT((X-X0)^2)-(X-X0); (D3) 0 (C4) FORGET(X-X0 > 0); (D4) [X > X0] (C5) F3:SQRT((X-X0)^2)-(X-X0); (D5) ABS(X0 - X) + X0 - X (C6) ASSUME(X-X0 < 0); (D6) [X0 > X] (C7) F4:SQRT((X-X0)^2)-(X-X0); (D7) 2 X0 - 2 X (C8) FORGET(X-X0 < 0); (D8) [X0 > X] The MACSYMA data base can store many other types of properties and use them in calculuations. For example consider the greatest integer function ENTIER: (C16) ENTIER(3/2); (D16) 1 (C17) ENTIER(Y); (D17) ENTIER(Y) (C18) DECLARE(Y,INTEGER); (D18) DONE (C19) ENTIER(Y); (D19) Y ------------------------- The second, more substantial question is the reason the first came up. It seems Mathematica can not use its problem solving techniques, either Solve or FindRoot, over conditional statements. For example, f(x) = x if .... f(x) = x^2 otherwise. Writing such a conditional with If or Which, then FindRoot can not solve because it can not compute the derivatives. Is there a way around this other than calculating maximization conditions separately and then rewriting a new conditional? It seems like an easy fix within the program if it truly is a bug. The real issue on this second question is the construction of a constrained maximization or Lagrangian problem. It seems clumsy, but I have had to solve each f(x) = x, etc. and then test the "if" statement. This wastes time and I lose any numerical value for the Lagrangian weight on the constraint. Do you have suggestions? Regards, Dallas Burtraw Dallas_Burtraw@um.cc.umich.edu MACSYMA's ROOT_BY_BISECTION command handles functions, including compiled user-defined functions. The functions can include logical operations like conditional branching (if-then) statements. Example: (C1) F(X):=IF X > 0 THEN 2*(X-3) ELSE 3*(X-3); (D1) F(X) := IF X > 0 THEN 2 (X - 3) ELSE 3 (X - 3) (C2) COMPILE(F); (D2) [F] (C3) ROOT_BY_BISECTION(F,0.0,10.0); (D3) 3.0 Dick Petti Director, Computer Aided Mathematics Group Symbolics, Inc. email: petti@symbolics.com From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Jul 26 19:01:12 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA01531; Wed, 26 Jul 89 19:01:11 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA18277; Wed, 26 Jul 89 19:01:42 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA12107; Wed, 26 Jul 89 19:01:40 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA01500; Wed, 26 Jul 89 17:28:34 -0500 Date: Wed, 26 Jul 89 17:28:34 -0500 Message-Id: <8907262228.AA01500@yoda.ncsa.uiuc.edu> From: wang-samuel@YALE.EDU Subject: Mathematica graphics in X11 Apparently-To: mathgroup-out@yoda.ncsa.uiuc.edu Status: RO Does any one know whether Mathematica graphics works in X11. I got the following error message when I tried the following simple graphics command. SunMathematica (sun3.68881) 1.1 (September 14, 1988) [With pre-loaded data] by S. Wolfram, D. Grayson, R. Maeder, H. Cejtin, S. Omohundro, D. Ballman and J. Keiper Copyright 1988 Wolfram Research Inc. -- X11 windows graphics initialized -- In[1]:= Plot[x, {x, 0, 1}] 0.383333 Second Out[1]= -Graphics- In[2]:= %%[ Error: setup_fonts: can't load font; OffendingCommand: (null) ]%% It seems that Mathematica cannot handle the font names in the latest release of the X window system. I would appreciate it very much if anyone has any suggestions for solving this problem. Sam Wang From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Jul 27 00:05:15 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA02245; Thu, 27 Jul 89 00:05:13 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA19683; Thu, 27 Jul 89 00:05:37 CDT Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA15717; Thu, 27 Jul 89 00:05:33 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA01644; Wed, 26 Jul 89 23:06:59 -0500 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA01603; Wed, 26 Jul 89 22:37:30 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA18668; Wed, 26 Jul 89 22:38:13 CDT Return-Path: Received: from cu-arpa.cs.cornell.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA13856; Wed, 26 Jul 89 22:38:10 CDT Received: from ARTEMIS.TN.CORNELL.EDU by cu-arpa.cs.cornell.edu (5.61+2/1.91d) id AA07966; Wed, 26 Jul 89 23:36:40 -0400 Received: from localhost by artemis.TN.CORNELL.EDU (3.2/1.1nn-Cornell-LASSP) id AA01877; Wed, 26 Jul 89 23:34:13 EDT Message-Id: <8907270334.AA01877@artemis.TN.CORNELL.EDU> To: steve@ncsa.uiuc.edu Subject: Mathematica graphics in X11 Date: Wed, 26 Jul 89 23:34:11 -0400 From: myers@helios.TN.cornell.edu Status: RO This is in response to Sam Wang's question about getting Mathematica graphics in X11R3. (I presume he meant R3, although he never said so explicitly.) The secret lies in setting the shell environment variable XPSFONT to something that exists under X11R3. We have used setenv XPSFONT 9x15 and this does the trick. (Just set it in .cshrc). There may be other fonts that work too. Chris Myers myers@helios.tn.cornell.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Sat Jul 29 14:07:02 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA04721; Sat, 29 Jul 89 14:07:01 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA05203; Sat, 29 Jul 89 14:07:36 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA28422; Sat, 29 Jul 89 14:07:34 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA04670; Sat, 29 Jul 89 12:46:54 -0500 Date: Sat, 29 Jul 89 12:46:54 -0500 Message-Id: <8907291746.AA04670@yoda.ncsa.uiuc.edu> From: joe@wri.UUCP (Joe Grohens) Subject: Mathematica at SIGGRAPH Apparently-To: mathgroup-out@yoda.ncsa.uiuc.edu Status: RO [For those of you going to SIGGRAPH in Boston, here is some information on WRI people who will be there. I will be there also. - Steve Christensen.] Attending Siggraph will be: Theodore Gray Igor Rivin Stephen Wolfram Yossi Friedman Paul Abbot Kevin McIssac (I think) Mathematica will be at several booths. ......................................................................... Mathematica at SIGGRAPH '89 As well as being used to work out the mathematics in many SIGGRAPH papers, Mathematica can be seen in action in several places this year: - Stellar/Apple 2D and 3D Visualization Workshop: July 31, 8:30-5:30 - Ongoing demonstrations at these exhibits: Apple (#1518); Apollo (#404); and DEC (#318). Mathematica product literature is available at these demonstrations. See our ad on the back cover of the current Communications of the ACM. ..................................................................... From mathgroup-adm@yoda.ncsa.uiuc.edu Sun Jul 30 01:45:13 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA05584; Sun, 30 Jul 89 01:45:12 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA07401; Sun, 30 Jul 89 01:43:50 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA05285; Sun, 30 Jul 89 01:43:49 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA05574; Sun, 30 Jul 89 00:45:39 -0500 Date: Sun, 30 Jul 89 00:45:39 -0500 Message-Id: <8907300545.AA05574@yoda.ncsa.uiuc.edu> From: dhj@rice.edu Subject: Matrix Algebra Package Apparently-To: mathgroup-out@yoda.ncsa.uiuc.edu Status: RO Has anyone developed a matrix algrebra package for Mathematica? I need one that knows about matrix dimensions, manipulation rules, (esp. invertibility rules), and other goodies such as trace and determinant rules. I know this is fairly straightforward, but someone must have written one somewhere. Don Johnson Electrical & Computer Engineering Rice University (dhj@rice.edu) From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Aug 29 23:40:30 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA05543; Tue, 29 Aug 89 23:40:29 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA08667; Tue, 29 Aug 89 23:41:24 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA23606; Tue, 29 Aug 89 23:41:22 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA05451; Tue, 29 Aug 89 21:54:04 -0500 Date: Tue, 29 Aug 89 21:54:04 -0500 Message-Id: <8908300254.AA05451@yoda.ncsa.uiuc.edu> From: Ron Heasley Subject: Notebooks for NeXT Apparently-To: mathgroup-out@yoda.ncsa.uiuc.edu Status: RO What can anyone tell me about the availability of commercial or public domain notebooks that will work on the NeXT computer? Ron Heasley Academic Computing Allegheny College rheasley@allegvm.bitnet From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Aug 30 00:37:27 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA06218; Wed, 30 Aug 89 00:37:26 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA09997; Wed, 30 Aug 89 00:38:20 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA25360; Wed, 30 Aug 89 00:38:19 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA05455; Tue, 29 Aug 89 21:55:15 -0500 Date: Tue, 29 Aug 89 21:55:15 -0500 Message-Id: <8908300255.AA05455@yoda.ncsa.uiuc.edu> Subject: Using MathExec From: Ron I. Herman Apparently-To: mathgroup-out@yoda.ncsa.uiuc.edu Status: RO I running Mathematica(1.1) on under Sun 4.0.3 and am trying to use MathExec from an external C program. I've been unable to get anything returned to the C program. According to the text on pg. 586, the results of MathExec are returned as a string. Does this really work on the Sun? Any suggestions? Thanks. Ron Herman(Federal Reserve) From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Aug 30 01:10:34 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA06292; Wed, 30 Aug 89 01:10:33 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA10035; Wed, 30 Aug 89 01:11:31 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA25639; Wed, 30 Aug 89 01:11:29 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA05458; Tue, 29 Aug 89 21:56:16 -0500 Date: Tue, 29 Aug 89 21:56:16 -0500 Message-Id: <8908300256.AA05458@yoda.ncsa.uiuc.edu> From: Victor Sparrow Subject: Something for the Mathematica mailing list Apparently-To: mathgroup-out@yoda.ncsa.uiuc.edu Status: RO Steve, this is for the Mathematica mailing list: Does anyone know of how to make ListPlot[] use plotting points other than filled circles? I have several classes of discrete data I need plot on one graph. It would be nice if one class of data was plotted as circles, another class as squares, another as triangles, etc. Graphics programming is not my forte. Thanks. Vic Sparrow sparrow@osiris.cso.uiuc.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Aug 30 01:18:32 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA06297; Wed, 30 Aug 89 01:18:31 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA10062; Wed, 30 Aug 89 01:19:26 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA25787; Wed, 30 Aug 89 01:19:24 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA05449; Tue, 29 Aug 89 21:53:35 -0500 Date: Tue, 29 Aug 89 21:53:35 -0500 Message-Id: <8908300253.AA05449@yoda.ncsa.uiuc.edu> From: stevec@yoda.ncsa.uiuc.edu Subject: MathGroup mailing list Apparently-To: mathgroup-out@yoda.ncsa.uiuc.edu Status: RO Various hardware, software and time constraints have slowed down the mailing list, but all now seems to be in order again. The ftp server had disks problems but now is operational. Somehow the mailer software got corrupted but our local mail guru fixed it. I have been out of town most of August. The archives will be updated in the next few weeks and some new packages will be installed. I will send a message to the list when I have that completed. I strongly urge you to submit packages, functions, nice graphics or other Mathematica good stuff for archiving. Mathematica is now at level 1.2 with some nice new features in the front end on the Mac and NeXT versions and some significant additions and fixes. I urge those of you using older versions to upgrade. There are now nearly 400 sites or persons on the list and I am sure many of you have interesting programs or comments. Please help to make the list active. Steve Christensen University of Illinois at Urbana-Champaign From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Aug 30 01:42:26 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA06347; Wed, 30 Aug 89 01:42:25 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA10101; Wed, 30 Aug 89 01:43:20 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA26133; Wed, 30 Aug 89 01:43:19 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA05465; Tue, 29 Aug 89 21:59:25 -0500 Date: Tue, 29 Aug 89 21:59:25 -0500 Message-Id: <8908300259.AA05465@yoda.ncsa.uiuc.edu> From: DCRUZ%T9ACC1@sc.intel.com Subject: RATES Problem Apparently-To: mathgroup-out@yoda.ncsa.uiuc.edu Status: RO Hi, I've just been added to the mathematica mailing list. I've problem setting the equation for this one. This is a MAXIMA-MINIMA problem. The cost of fuel per hour for running a ship is proportional to the cube of the speed and is $ 27 per hour when the speed is 12 miles per hour. Other costs amounts to $ 128 per hour regardless of the speed. Express the cost per mile as a function of the speed, & find the speed that makes the cost minimum. The equation I was able to set up was: C = V^3 + 128 But from there I don't know how to go about getting the $ 27 per hr when V=12 miles per hour into the system of equations. Could someone please help me solve this problem and also pls elaborate on how to think through problems like these. Take care & thanks to all Dave Cruz dcruz@t9acc1.intel.com From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Aug 30 02:08:06 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA06425; Wed, 30 Aug 89 02:08:05 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA10231; Wed, 30 Aug 89 02:08:56 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA26338; Wed, 30 Aug 89 02:08:53 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA05453; Tue, 29 Aug 89 21:54:41 -0500 Date: Tue, 29 Aug 89 21:54:41 -0500 Message-Id: <8908300254.AA05453@yoda.ncsa.uiuc.edu> From: lisa@wri.UUCP Subject: New in Version 1.2 Apparently-To: mathgroup-out@yoda.ncsa.uiuc.edu Status: RO Mathematica--New in Version 1.2 Overview -------- Many minor problems have been fixed. Many operations have been made much more efficient. Various new features have been added. The new features are compatible with Version 1.1. Basic System Features --------------------- Responsiveness to interrupts has been improved throughout the system. Hash tables have been introduced to allow lists of rules to be scanned more rapidly. The function Dispatch allows explicit lists of rules to be optimized using hash tables. Hash tables are introduced automatically in assignments, making function definitions that involve dynamic programming much more efficient. [S. Wolfram] The main evaluator has been restructured so that many recursive operations have been made iterative. This increases speed and saves stack space. It does mean that some calculations which used to be stopped by $RecursionLimit now continue until interrupted. [H. Cejtin] Block[{vars}, body /; test] has been introduced, to allow local variables to be shared between tests and function bodies. [S. Wolfram] Operations that modify elements of lists and other structures have been made much more efficient. Copying of internal data structures is now avoided in almost all cases. [H. Cejtin] Certain pattern-matching operations involving commutative functions have been greatly speeded up. [K. McIsaac and S. Wolfram] Input and Output ---------------- The appearance and speed of OutputForm output has been improved. Line breaks are more consistent, and exponents more compact. MatrixForm now prints matrices more compactly, with dimensions distinguished by spacing. [B. Smith and S. Wolfram] Encode has been added to allow external files to be stored in an encoded form. Encode also allows files to be keyed, or to be accessible only on machines with particular ID's. [D. Ballman] Definitions now print out with their formatting directives given verbatim. [B. Smith] The infix forms lhs === rhs and lhs =!= rhs have been added for SameQ[lhs, rhs] and UnsameQ[lhs, rhs]. [H. Cejtin] Mathematical Operations ----------------------- Symbolic integration has been greatly enhanced. A much larger class of integrals can now be done, and results are given in simpler and more useful forms. [D. Withoff] Multivariate polynomial GCD and factorization has been made much more efficient. [R. Maeder and I. Rivin] Algebraic functions can now handle approximate real numbers in many more situations. [R. Maeder] Solve has been taught to solve transcendental and other equations that require explicit use of inverse functions. [D. Grayson] The linear programming functions LinearProgramming, ContrainedMax and ConstrainedMin have been added. [I. Rivin] Rudimentary differential equation solving capabilities have been introduced in the function DSolve. [I. Rivin] Power series have been speeded up, and have been extended to deal with many classes of special functions. [J. Keiper and I. Rivin] MatrixPower and MatrixExp have been added. [I. Rivin] The functions GCD for numbers, and PolynomialGCD for polynomials, have been separated. [R. Maeder] Modulus options have been added to Det, Inverse and LinearSolve. [I. Rivin] The function Residue, for finding residues at poles, has been added. [D. Grayson] The function GroebnerBasis, which gives explicit forms of Grbner bases, has been added. [D. Grayson] Numerical Operations -------------------- The granularity in numerical precision has been reduced. SetPrecision and Set-Accuracy have been added to provide additional control over the properties of approximate numbers. [D. Grayson] Matrix multiplication and related operations have been greatly speeded up. [I. Rivin] The function Digits, which gives lists of digits of numbers in particular bases, has been added. [D. Grayson] TheInterpolatingPolynomial function has been added, to give exact interpolating polynomials. [I. Rivin] Graphics -------- Axes and labels can now be drawn on three-dimensional plots. [H. Cejtin] Scaled has been enhanced to allow scaled offsets to be specified. [H. Cejtin] Circle and Disk primitives have been added for two- dimensional graphics. [H. Cejtin] The Ticks option has been enhanced, to allow more flexible placement and labeling of tick marks. [H. Cejtin] New options Background, DefaultColor, Prolog,Epilog, AxesStyle, etc. have been added to give more flexibility in the rendering of plots. [S. Wolfram] Graphics3D[SurfaceGraphics[...]] converts a surface into general 3D graphics representation. [S. Wolfram] The graphics primitive PostScript has been added, to allow verbatim PostScript code to be included in graphics output. [S. Wolfram] Packages -------- Many new standard packages have been added, notably ones for statistics and graphics. Packages are now organized into several directories. Macintosh Front End ------------------- Overview -------- A number of new features have been added, and some aspects of the user interface have been reorganized. Notebooks created under Version 1.1 are fully compatible with Version 1.2 (though not vice versa). Basic System Features --------------------- Kernel computations can now run concurrently with front end opera-tions such as Notebook browsing and editing. While Kernel compu-tations are occuring, Running... is displayed in the title bar of the current window. Cells whose execution is pending are indicated with outlined cell brackets. [T. Gray] Kernel computations can now be run in the background under MultiFinder. (It is also possible in this way to have multiple concurrent Mathematica processes.) Kernel start up can now occur con-currently with front end opera-tions. Starting... is displayed in the menu bar in this case. Menus have been rearranged. Graph has been added to themain menu bar, replacing the Special Effects submenu. Preference settings have been collected in the Settings submenu of the Edit menu. New commands include Divide Cell and Merge Cells. Cell styles are now given in the Cell Style submenu, rather than directly under the Style menu. The Format submenu allows special formatting of individual cells, replacing the Formats menu that appeared when the Styles Window was in front. User Interface Feature ---------------------- A 3D ViewPoint Selector dialog box has been added. It displays a cube that can be rotated in real time using the mouse, and whose orientation can be pasted into Mathematica input in several ways. [T. Gray] A Color Selector dialog box has been added, allowing RGBColor specifications to be chosen using the standard Macintosh color wheel. New graphical controls for anima-tion have been added, mimicking those found on VCRs. Real-time scrolling has been added as an option. Various Command-Shift key equivalents have been added for commands. Most dialog boxes are now modeless, so that they can remain visible while other operations are done. Graphics Features ----------------- Adobe Illustrator 1.1 PostScript file format has been added as an option in the Convert Clipboard dialog box. Various options for conversion from RGB (display) to CMYK (printing) colors are provided. [T. Gray] A Convert to InputForm command has been added to allow graphics stored in a Notebook in either PICT or PostScript form to be converted to Mathematica input form. This allows graphics and images from other programs to be imported into Mathematica and manipulated using Mathematica Kernel functions. The Convert to PostScript command has been enhanced to include bitmaps as well as objects. Also colorimage objects can be produced. Rendering of density plots has been made faster, and there is no restriction on size. Communication ------------- Communication with the Mathematica Kernel via TCP/IP has been added. It runs over both Ethernet and LocalTalk. Standard Apple MacTCP drivers are used. [R. Murtagh] The Phone menu has been renamed Connections, and now has entries for both phone numbers and network hostnames. From mathgroup-adm@yoda.ncsa.uiuc.edu Sun Sep 10 17:26:09 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA21563; Sun, 10 Sep 89 17:26:08 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA05102; Sun, 10 Sep 89 17:27:18 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA00161; Sun, 10 Sep 89 17:27:16 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA21541; Sun, 10 Sep 89 16:12:27 -0500 Date: Sun, 10 Sep 89 16:12:27 -0500 Message-Id: <8909102112.AA21541@yoda.ncsa.uiuc.edu> From: davis@groucho.ucar.edu (Glenn P. Davis) Subject: "External Functions" Apparently-To: mathgroup-out@yoda.ncsa.uiuc.edu Status: RO I'm interested in using the "External Functions" hook into Mathematica described in Appendix B.7.6 of the book (pg 585). I'm working on a NeXT under NeXT release 0.9. I found the necessary 'mathlink' modules and have compiled the example in the Appendix. What I don't know is how to get this executable and Mathematica communicating. EG, what do I type in Mathematica to set this up? Does my new executable need to be in a magic directory? Any clarification would be appreciated. Glenn P. Davis UCAR / Unidata PO Box 3000 1685 38th St. Boulder, CO 80307-3000 Boulder, CO 80301 davis@groucho.ucar.edu (303) 497 8643 From mathgroup-adm@yoda.ncsa.uiuc.edu Mon Sep 11 14:30:23 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA23207; Mon, 11 Sep 89 14:30:22 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA09867; Mon, 11 Sep 89 14:31:25 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA15349; Mon, 11 Sep 89 14:31:21 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA23006; Mon, 11 Sep 89 13:44:19 -0500 Date: Mon, 11 Sep 89 13:44:19 -0500 Message-Id: <8909111844.AA23006@yoda.ncsa.uiuc.edu> From: henry@Math.nwu.edu Subject: Re: "External Functions" Apparently-To: mathgroup-out@yoda.ncsa.uiuc.edu Status: RO Yes, the manual section on page 585 leaves out the critical point of how to start up the external function. The secret function is StartProcess[]. It is described on page 688 and pages 303-304. Henry Cejtin From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Sep 12 15:14:54 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA24915; Tue, 12 Sep 89 15:14:53 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA02148; Tue, 12 Sep 89 15:15:59 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA02402; Tue, 12 Sep 89 15:15:57 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA24739; Tue, 12 Sep 89 13:33:47 -0500 Date: Tue, 12 Sep 89 13:33:47 -0500 Message-Id: <8909121833.AA24739@yoda.ncsa.uiuc.edu> From: COLEMAN@uregina1.bitnet Subject: Printing Mathematica Graphics on Laserwriter NT from sun3/50 sun3/60 Apparently-To: mathgroup-out@yoda.ncsa.uiuc.edu Status: RO We have Mathematica version 1.2 running on SUN3/50 and SUN3/60 under SUN OS 3.5. I have tried generating a simple graphics using Plot3D[Sin[x]Cos[y],{x,-Pi,Pi},{y,-Pi,Pi}] which works fine. When I try to Print it using PSPrint[%] the green light begins to wink on the laserprinter but after a time the light becomes steady and nothiong is printed. How does one print graphics on a laserwriter NT. I also want to be able to capture the graphics and include it in a \special in a LaTeX document. We have dvi2ps running and I am able to dump the screen and use psraster to generate a postscript file which can then be included as a \special, but it would be better to be able to use the postscript generated by mathematica directly because of the higher resolution. Please respond either to mathgroup or to coleman@uregina2.bitnet Thank you Robert Coleman From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Sep 14 18:15:20 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA28540; Thu, 14 Sep 89 18:15:19 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA14112; Thu, 14 Sep 89 18:16:30 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA06558; Thu, 14 Sep 89 18:16:27 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA28410; Thu, 14 Sep 89 15:38:46 -0500 Date: Thu, 14 Sep 89 15:38:46 -0500 Message-Id: <8909142038.AA28410@yoda.ncsa.uiuc.edu> From: mckenney@spam.istc.sri.com Subject: Fancy plot labeling in Mathematica? Apparently-To: mathgroup-out@yoda.ncsa.uiuc.edu Status: RO Does anyone know of any way to get fancier plot labels in Mathematica? Desireable features might include printing the y-axis label rotated 90 degrees so that the text ran parallel to the y-axis along the left-hand side of the plot, printing the x-axis label at the bottom of the plot, allowing control of character sizes, and printing of special characters (such as greek letters). Thanx in advance, Paul mckenney@sri.com mckenney@spam.istc.sri.com From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Sep 14 22:14:02 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA28849; Thu, 14 Sep 89 22:14:01 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA14629; Thu, 14 Sep 89 22:15:15 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA08951; Thu, 14 Sep 89 22:15:12 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA28786; Thu, 14 Sep 89 20:32:54 -0500 Date: Thu, 14 Sep 89 20:32:54 -0500 Message-Id: <8909150132.AA28786@yoda.ncsa.uiuc.edu> From: COLEMAN@uregina1.bitnet Subject: Re: Printing mathematica graphics on a Laserwriter II NT Apparently-To: mathgroup-out@yoda.ncsa.uiuc.edu Status: RO We have mathematica running on a SUN3/50 and a SUN3/60. The Laserwriter II NT is connected to the serial port of the 3/50. Here is what my version of mathematica says about printing graphics Mathematica (sun3.68881) 1.2 (June 24, 1989) [With pre-loaded data] by S. Wolfram, D. Grayson, R. Maaeder, H. Cejtin, S. Omohundro, D. Ballman and J. Keiper with I. Rivin and D. Withoff Copyright 1988,1989 Wolfram Research Inc. -- SunView graphics initialized -- In[1]:= ??LaserPrint LaserPrint Attributes[LaserPrint] = {Protected} LaserPrint = PSPrint In[1]:= ??PSPrint PSPrint[-graphics-] sends graphics to a printer. Attributes[PSPrint] = {Protected} PSPrint/: PSPrint[System`Private`x_] := > (Display["!psfix | lpr", System`Private`x]; System`Private`x) In[1]:= ??Display Display[channel, graphics] writes graphics to the specified output channel. Attributes[Display] = {Protected} I hope the square brackets come out ok. I unfortunately must for a while yet send from an IBM mainframe which likes to change square brackets into double quotes. When I do a Plot either 2D or 3D and then use PSPrint[%] or LaserPrint[%] something is sent to the laserwriter but the printer eventually hangs. Following the advice of James Blanchard I defined lw[x_]:= (Display["!psfix > file.ps",x];x) and used lw[%] to capture the file. I then sent the postscript file to the printer from a regular shell using lpr and it printed with no problem; however, if I change the definition by replacing the > with a pipe | ( in a fresh session) something goes to the printer but it eventually hangs. Has anyone else encountered this problem? As far as incoporating a graphic in a LaTeX file using \special and dvi2ps, I found that it was necessary to leave space above the special and shrink the file using dvi2ps' hscale and vscale. Unfortunately changing the scale seems to alter the position the \special appears on the page. Does anyone have advice on how to compute appropriate values for hoffset and voffset for given values for hscale and vscale? Thanks for the help Robert Coleman coleman@uregina2.bitnet From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Sep 14 22:50:55 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA28920; Thu, 14 Sep 89 22:50:53 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA14758; Thu, 14 Sep 89 22:52:09 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA09396; Thu, 14 Sep 89 22:52:06 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA28822; Thu, 14 Sep 89 20:55:28 -0500 Date: Thu, 14 Sep 89 20:55:28 -0500 Message-Id: <8909150155.AA28822@yoda.ncsa.uiuc.edu> From: resumes@wri.com Subject: WANTED: MATHEMATICAL ENTYMOLOGISTS Apparently-To: mathgroup-out@yoda.ncsa.uiuc.edu Status: RO WANTED: MATHEMATICAL ENTYMOLOGISTS We are looking for people who know Mathematica to help us systematically track down bugs in the system. If you are well organized, and preferably have a perverse turn of mind, please contact us. Working hours are totally flexible. Send mail to resumes@wri.com Or call Wolfram Research at 398-0700 ************ thanks -- joe grohens From mathgroup-adm@yoda.ncsa.uiuc.edu Mon Sep 18 13:31:41 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA04564; Mon, 18 Sep 89 13:31:40 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA03397; Mon, 18 Sep 89 13:32:54 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA14667; Mon, 18 Sep 89 13:32:51 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA04477; Mon, 18 Sep 89 12:17:53 -0500 Date: Mon, 18 Sep 89 12:17:53 -0500 Message-Id: <8909181717.AA04477@yoda.ncsa.uiuc.edu> From: marzetta@iam.unibe.ch Subject: WRI Apparently-To: mathgroup-out@yoda.ncsa.uiuc.edu Status: RO I thank all the people who have answered my message where I seeked for "Alternatives to WRI". One of the last steps I did before posting my message to this newsgroup was to fax my request to WRI without mentioning the past; Terri Wenson answered me very kindly on September 5, sending me all the information I wanted; unfortunately the letter arrived here only on September 13, just one day too late ... Markus Marzetta marzetta@iam.unibe.ch From mathgroup-adm@yoda.ncsa.uiuc.edu Mon Sep 18 22:49:01 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA04872; Mon, 18 Sep 89 22:48:59 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA05608; Mon, 18 Sep 89 22:50:13 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA22118; Mon, 18 Sep 89 22:50:11 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA04837; Mon, 18 Sep 89 21:37:58 -0500 Date: Mon, 18 Sep 89 21:37:58 -0500 Message-Id: <8909190237.AA04837@yoda.ncsa.uiuc.edu> From: valiquet@wri.com Subject: Available Packages Apparently-To: mathgroup-out@yoda.ncsa.uiuc.edu Status: RO Silicon Graphics packages are now available for shipment. A recap of available packages: MS-DOS 386, 386/7, 386/Weitek Ver 1.11 Mac Enhanced, Standard Ver 1.20 Apollo Ver 1.21 Sun 3, 4, 386i Ver 1.22 DECstation 3100 Ver 1.21 HP 9000/300, 825 & 835, 840, 850, & 855 Ver 1.20 SGI Personal Iris, Iris 4D/50-80GT, Iris 4D/120-240GTX Ver 1.20 All packages are either in stock, or can be available with 24 hours notice. I will continue to make these announcements as new packages become available. Chris Valiquet valiquet@wri.com From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Sep 20 01:37:19 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA06590; Wed, 20 Sep 89 01:37:18 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA13950; Wed, 20 Sep 89 01:38:27 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA19398; Wed, 20 Sep 89 01:38:10 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA05954; Tue, 19 Sep 89 23:56:17 -0500 Date: Tue, 19 Sep 89 23:56:17 -0500 Message-Id: <8909200456.AA05954@yoda.ncsa.uiuc.edu> From: wheeler@super.org Subject: Prime bug Apparently-To: mathgroup-out@yoda.ncsa.uiuc.edu Status: RO Here is a code fragment for computing the number of primes <= x for moderate values of x. PrimePi[x_?NumberQ] := Block[{n, m, avg, flrx = Floor[x]}, m = LogIntegral[N[flrx]]; n = Ceiling[m - LogIntegral[Sqrt[N[flrx]]]]; m = Floor[m]; While[ m != n+1, avg = Quotient[n+m,2]; Print[n," ", Prime[n]]; If[ flrx < Prime[avg], m = avg, n = avg] ]; n ] The thing to look at is the Print statement in the While loop. Watch this: Mathematica (sun3.68881) 1.2 (August 3, 1989) [With pre-loaded data] by S. Wolfram, D. Grayson, R. Maeder, H. Cejtin, S. Omohundro, D. Ballman and J. Keiper with I. Rivin and D. Withoff Copyright 1988,1989 Wolfram Research Inc. In[1]:= < Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA02019; Wed, 20 Sep 89 15:59:51 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA06920; Wed, 20 Sep 89 14:15:04 -0500 Date: Wed, 20 Sep 89 14:15:04 -0500 Message-Id: <8909201915.AA06920@yoda.ncsa.uiuc.edu> From: steve@ncsa.uiuc.edu Subject: removal messages Apparently-To: mathgroup-out@yoda.ncsa.uiuc.edu Status: RO I am sorry once again to the list members who are getting removal messages. Some users have been sending to an incorrect address which is getting out to the list. Please send only to mathgroup-request@yoda.ncsa.uiuc.edu or mathgroup@yoda.ncsa.uiuc.edu or steve@yoda.ncsa.uiuc.edu. Thanks. Steve Christensen ~ From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Sep 22 12:46:59 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA09149; Fri, 22 Sep 89 12:46:58 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA26517; Fri, 22 Sep 89 12:48:18 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA05879; Fri, 22 Sep 89 12:48:15 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA09101; Fri, 22 Sep 89 11:26:21 -0500 Date: Fri, 22 Sep 89 11:26:21 -0500 Message-Id: <8909221626.AA09101@yoda.ncsa.uiuc.edu> From: hauser@united.berkeley.edu Subject: Plot3D + Graphics3D Apparently-To: mathgroup-out@yoda.ncsa.uiuc.edu Status: RO Is there a simple way to superimpose some 3D graphics (curves, vectors, small planes) on top of the SurfaceGraphics produced by Plot3D? Clearly, I can build up the surface graphics from polygons and then draw the lines. Is there a set of routines to generate the surface in the 3D graphics form? (I would rather not rewrite Plot3D!) thanks, John Hauser From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Sep 22 14:00:03 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA09264; Fri, 22 Sep 89 14:00:02 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA26824; Fri, 22 Sep 89 14:01:22 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA07373; Fri, 22 Sep 89 14:01:16 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA09097; Fri, 22 Sep 89 11:24:48 -0500 Date: Fri, 22 Sep 89 11:24:48 -0500 Message-Id: <8909221624.AA09097@yoda.ncsa.uiuc.edu> From: SMITHW@byuvax.bitnet Subject: linear algebra bugs Apparently-To: mathgroup-out@yoda.ncsa.uiuc.edu Status: RO I have encountered some interesting bugs in the linear algebra package in mathematica on the MIPS(beta version), the Mac (1.1,1.2) and NeXT (.9 and 1.0). Try the following: In[1]:= {{1,2,3},{a,b,c},{1,2,3}} In[2]:= Eigensystem[Out[1]] Eigensystem::eifl: Algorithm failed to find eigenvectors. Now the same thing in Macsyma: [ 1 2 3 ] [ ] (D7) [ A 0 C ] [ ] [ 1 2 3 ] (C9) Eigenvectors(d7); (D9) [[[2 - SQRT(2) SQRT(C + A + 2), SQRT(2) SQRT(C + A + 2) + 2, 0], SQRT(2) SQRT(C + A + 2) + 2 [1, 1, 1]], [1, - ---------------------------, 1], 2 SQRT(2) SQRT(C + A + 2) - 2 C - 3 A A [1, ---------------------------, 1], [1, - -------, - -]] 2 2 C C This is not the only example... From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Oct 18 04:39:05 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA14275; Wed, 18 Oct 89 04:39:04 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA12021; Wed, 18 Oct 89 04:38:47 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA28507; Wed, 18 Oct 89 04:38:37 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA14230; Wed, 18 Oct 89 00:38:38 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA14226; Wed, 18 Oct 89 00:38:37 -0500 Date: Wed, 18 Oct 89 00:38:37 -0500 Message-Id: <8910180538.AA14226@yoda.ncsa.uiuc.edu> From: steve@yoda.ncsa.uiuc.edu Subject: Mathematica mailing list To: mathgroup@yoda.ncsa.uiuc.edu Status: RO Dear list members: As you may have noticed, you might have been getting either empty or perhaps duplicate messages from the MathGroup mailer in the last few weeks. We believe that this has now been fixed. My local mail expert - Paul Pomes - has been working hard to provide me with the tools I need to prevent problems in the future. I can now test the mailing of each message before it goes out. Thanks to those of you who pointed out the problems. I will now transmit those messages that have been waiting to go out. Steve Christensen From testgroup-adm@yoda.ncsa.uiuc.edu Wed Oct 18 11:16:16 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA14564; Wed, 18 Oct 89 11:16:14 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA14979; Wed, 18 Oct 89 11:16:00 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA05855; Wed, 18 Oct 89 11:15:53 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA14425; Wed, 18 Oct 89 10:25:29 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA14421; Wed, 18 Oct 89 10:25:27 -0500 Date: Wed, 18 Oct 89 10:25:27 -0500 Message-Id: <8910181525.AA14421@yoda.ncsa.uiuc.edu> From: cho@compsci.aberystwyth.ac.uk Subject: New Mathematica User To: mathgroup@yoda.ncsa.uiuc.edu Status: RO Hi, Do you know if anyone has extended MM's ability to deal with modified Bessel functions apart from just evaluating them, particularly infinite integrals involving these functions (!) ? cho@compsci.aberystwyth.ac.uk From testgroup-adm@yoda.ncsa.uiuc.edu Wed Oct 18 11:17:30 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA14573; Wed, 18 Oct 89 11:17:29 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA14988; Wed, 18 Oct 89 11:17:16 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA05878; Wed, 18 Oct 89 11:17:11 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA14445; Wed, 18 Oct 89 10:29:46 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA14441; Wed, 18 Oct 89 10:29:44 -0500 Date: Wed, 18 Oct 89 10:29:44 -0500 Message-Id: <8910181529.AA14441@yoda.ncsa.uiuc.edu> From: kant@SLCS.SLB.COM Subject: boolean simplication question To: mathgroup@yoda.ncsa.uiuc.edu Status: RO Does anyone have a Mathematica package that can simplify expressions with And, Or, etc. so that And[A, !A] goes to False and so on? Second clarification message: To clarify my previous message, we have written part of a simplification package ourselves but there seem to be some strange problems. Part of the problem with redefining or defining your own versions of And and Or seems to be that if you add the attribute "Flat", definitions like AND[X__, A_, Y___, !A_, X___] := False don't seem to work/match. If you make these definitions without the Flat attribute, they work ok. I don't understand why that happens either. Any suggestions? Thanks. -- Elaine kant@SLCS.SLB.COM From testgroup-adm@yoda.ncsa.uiuc.edu Wed Oct 18 11:17:32 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA14579; Wed, 18 Oct 89 11:17:31 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA14991; Wed, 18 Oct 89 11:17:18 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA05881; Wed, 18 Oct 89 11:17:14 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA14464; Wed, 18 Oct 89 10:41:28 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA14460; Wed, 18 Oct 89 10:41:26 -0500 Message-Id: <8910181541.AA14460@yoda.ncsa.uiuc.edu> Date: Mon, 16 Oct 89 21:31 PDT From: DCRUZ%A2ACC1@sc.intel.com Subject: Hi, question on U.S. edu system To: mathgroup@yoda.ncsa.uiuc.edu Status: RO [Here is a message slightly out of the Mathematica area. Please answer directly to the address below.] Hi, I have a friend in Ireland. He needs some details about the American education system, i.e. what topics in maths are studied at what ages. He would like to compare it with the Irish system. If you have the details pls send them to me and I'll send them to my friend in Ireland. Take care & thanks in advance, Dave Cruz @ Intel Philippines dcruz@t9acc1.intel.com From testgroup-adm@yoda.ncsa.uiuc.edu Wed Oct 18 11:17:34 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA14584; Wed, 18 Oct 89 11:17:33 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA14994; Wed, 18 Oct 89 11:17:20 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA05884; Wed, 18 Oct 89 11:17:16 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA14458; Wed, 18 Oct 89 10:38:40 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA14454; Wed, 18 Oct 89 10:38:39 -0500 Message-Id: <8910181538.AA14454@yoda.ncsa.uiuc.edu> Date: Mon, 16 Oct 89 18:47:44 EDT From: LEONARDZ@uoguelph.bitnet Subject: X-Windows versions ( Or SGI,Sun,Apollo ) To: mathgroup@yoda.ncsa.uiuc.edu Status: RO We have several workstations here used for research which are not NeXT or Macs. We have a requirement for a symbolic manipulation package with all the attributes of the NeXT/Mac versions of Mathematica,eg. the Notebook facility, on a wide range of Unix workstations (Sun, Apollo and SGI in particular). Does X-Window version support all these features ? When do you expect them to be ready ?? Will all of the above ( which have X-Window support ), X-Window termin als, etc. be able to run this version (X-Term support of front end only I presume) ?? Thanks. Regards Len Zaifman From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Oct 18 14:16:22 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA14884; Wed, 18 Oct 89 14:16:18 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA16766; Wed, 18 Oct 89 14:16:01 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA10310; Wed, 18 Oct 89 14:15:56 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA14592; Wed, 18 Oct 89 11:17:56 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA14588; Wed, 18 Oct 89 11:17:54 -0500 Date: Wed, 18 Oct 89 11:17:54 -0500 Message-Id: <8910181617.AA14588@yoda.ncsa.uiuc.edu> From: cho@compsci.aberystwyth.ac.uk Subject: New Mathematica User To: mathgroup@yoda.ncsa.uiuc.edu Status: RO Hi, Do you know if anyone has extended MM's ability to deal with modified Bessel functions apart from just evaluating them, particularly infinite integrals involving these functions (!) ? cho@compsci.aberystwyth.ac.uk From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Oct 18 14:15:06 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA14860; Wed, 18 Oct 89 14:15:05 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA16730; Wed, 18 Oct 89 14:14:46 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA10250; Wed, 18 Oct 89 14:14:41 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA14611; Wed, 18 Oct 89 11:19:05 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA14607; Wed, 18 Oct 89 11:19:04 -0500 Message-Id: <8910181619.AA14607@yoda.ncsa.uiuc.edu> Date: Mon, 16 Oct 89 21:31 PDT From: DCRUZ%A2ACC1@sc.intel.com Subject: Hi, question on U.S. edu system To: mathgroup@yoda.ncsa.uiuc.edu Status: RO [Here is a message slightly out of the Mathematica area. Please answer directly to the address below.] Hi, I have a friend in Ireland. He needs some details about the American education system, i.e. what topics in maths are studied at what ages. He would like to compare it with the Irish system. If you have the details pls send them to me and I'll send them to my friend in Ireland. Take care & thanks in advance, Dave Cruz @ Intel Philippines dcruz@t9acc1.intel.com From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Oct 18 15:01:54 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA15001; Wed, 18 Oct 89 15:01:53 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA17166; Wed, 18 Oct 89 15:01:34 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA11138; Wed, 18 Oct 89 15:01:28 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA14598; Wed, 18 Oct 89 11:18:18 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA14594; Wed, 18 Oct 89 11:18:17 -0500 Date: Wed, 18 Oct 89 11:18:17 -0500 Message-Id: <8910181618.AA14594@yoda.ncsa.uiuc.edu> From: kant@SLCS.SLB.COM Subject: boolean simplication question To: mathgroup@yoda.ncsa.uiuc.edu Status: RO Does anyone have a Mathematica package that can simplify expressions with And, Or, etc. so that And[A, !A] goes to False and so on? Second clarification message: To clarify my previous message, we have written part of a simplification package ourselves but there seem to be some strange problems. Part of the problem with redefining or defining your own versions of And and Or seems to be that if you add the attribute "Flat", definitions like AND[X__, A_, Y___, !A_, X___] := False don't seem to work/match. If you make these definitions without the Flat attribute, they work ok. I don't understand why that happens either. Any suggestions? Thanks. -- Elaine kant@SLCS.SLB.COM From paul@uxc.cso.uiuc.edu Wed Oct 18 15:04:58 1989 Received: from uxc.cso.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA15009; Wed, 18 Oct 89 15:04:56 -0500 Received: by uxc.cso.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA04949; Wed, 18 Oct 89 15:04:28 -0500 To: Steve Christensen Subject: Re: another problem In-Reply-To: Your message of Wed, 18 Oct 89 14:58:14 CDT. <8910181958.AA14978@yoda.ncsa.uiuc.edu> Date: Wed, 18 Oct 89 15:04:25 CDT Message-Id: <4946.624744265@uxc.cso.uiuc.edu> From: "Paul Pomes (I'm the NRA!)" Status: RO The way the list is set up now is probably the most reliable way for mail to go as described. If a user uses the 'R' command, only the From: address is going to see it. If that's the mathgroup-adm address (which is in the From (no colon) address, btw), then the original sender is going to miss the reply. If the original sender is in the From: field, then the mathgroup (you) is going to be missed. Any other reply command is going to include to the To: mathgroup (you) address (or it should anyway). /pbp From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Oct 18 16:07:35 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA15132; Wed, 18 Oct 89 16:07:34 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA17712; Wed, 18 Oct 89 16:07:15 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA12475; Wed, 18 Oct 89 16:07:09 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA14606; Wed, 18 Oct 89 11:18:55 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA14602; Wed, 18 Oct 89 11:18:54 -0500 Message-Id: <8910181618.AA14602@yoda.ncsa.uiuc.edu> Date: Mon, 16 Oct 89 18:47:44 EDT From: LEONARDZ@uoguelph.bitnet Subject: X-Windows versions ( Or SGI,Sun,Apollo ) To: mathgroup@yoda.ncsa.uiuc.edu Status: RO We have several workstations here used for research which are not NeXT or Macs. We have a requirement for a symbolic manipulation package with all the attributes of the NeXT/Mac versions of Mathematica,eg. the Notebook facility, on a wide range of Unix workstations (Sun, Apollo and SGI in particular). Does X-Window version support all these features ? When do you expect them to be ready ?? Will all of the above ( which have X-Window support ), X-Window termin als, etc. be able to run this version (X-Term support of front end only I presume) ?? Thanks. Regards Len Zaifman From testgroup-adm@yoda.ncsa.uiuc.edu Thu Oct 19 14:18:48 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA16258; Thu, 19 Oct 89 14:18:47 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA03240; Thu, 19 Oct 89 14:18:32 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA06152; Thu, 19 Oct 89 14:18:15 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA16245; Thu, 19 Oct 89 13:36:20 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA16241; Thu, 19 Oct 89 13:36:19 -0500 Message-Id: <8910191836.AA16241@yoda.ncsa.uiuc.edu> Date: Wed, 18 Oct 89 15:28 PDT From: DCRUZ%T9ACC1@sc.intel.com Subject: Californian quake & questions To: mathgroup@yoda.ncsa.uiuc.edu Status: RO [Please respond to the address below and not to the mailing list. -- smc] Dear Mathematica list, I saw on TV last night (Manila time) the California earthquake. I hope all of you there are safe and well. I just learned that Mathematica is a program that does symbolic math. I want to thank all of you who answered my question on calculus last time. Does anyone know how I can subscribe to a Mathematics discussion group? Is it ok with everyone if I continue to ask questions in calculus? Sorry if my questions were off the purpose of this discussion group. I didn't know until recently that Mathematica was a program and mistook it for a math discussion group. Take Care & thanks to all, Dave Cruz @ Intel Philippines dcruz@t9acc1.intel.com From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Oct 19 17:22:15 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA16381; Thu, 19 Oct 89 17:22:15 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA04835; Thu, 19 Oct 89 17:21:56 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA10481; Thu, 19 Oct 89 17:21:41 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA16282; Thu, 19 Oct 89 15:26:21 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA16278; Thu, 19 Oct 89 15:26:19 -0500 Message-Id: <8910192026.AA16278@yoda.ncsa.uiuc.edu> Date: Wed, 18 Oct 89 15:28 PDT From: DCRUZ%T9ACC1@sc.intel.com Subject: Californian quake & questions To: mathgroup@yoda.ncsa.uiuc.edu Status: RO [Please respond to the address below and not to the mailing list. -- smc] Dear Mathematica list, I saw on TV last night (Manila time) the California earthquake. I hope all of you there are safe and well. I just learned that Mathematica is a program that does symbolic math. I want to thank all of you who answered my question on calculus last time. Does anyone know how I can subscribe to a Mathematics discussion group? Is it ok with everyone if I continue to ask questions in calculus? Sorry if my questions were off the purpose of this discussion group. I didn't know until recently that Mathematica was a program and mistook it for a math discussion group. Take Care & thanks to all, Dave Cruz @ Intel Philippines dcruz@t9acc1.intel.com From testgroup-adm@yoda.ncsa.uiuc.edu Tue Oct 24 01:16:17 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA22524; Tue, 24 Oct 89 01:16:15 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA08664; Tue, 24 Oct 89 01:15:50 CDT Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA02860; Tue, 24 Oct 89 01:15:48 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA22501; Tue, 24 Oct 89 00:51:13 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA22497; Tue, 24 Oct 89 00:51:11 -0500 Message-Id: <8910240551.AA22497@yoda.ncsa.uiuc.edu> Date: Mon, 23 Oct 89 22:44:40 PDT From: ghe@nucthy.PHYSICS.ORST.EDU (Guangliang He) To: Mathematica Mailling list Subject: Mathematica on a SE/30 Status: RO Is it possible to get a Mac II version of Mathematica running on a Mac SE/30? What kind problem could possiblly happen? I'm interested to see the results. Thank you all for your time. -- ======================================================================= USMAIL: Guangliang He | INTERNET: ghe@PHYSICS.ORST.EDU Department of Physics | BITNET: hegl@ORSTVM.BITNET Weniger Hall 301 | Oregon State University | Corvallis, OR 97331-6507 | PHONE: (503) 737-4631 ======================================================================= From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Oct 24 06:11:37 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA22586; Tue, 24 Oct 89 06:11:35 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA10084; Tue, 24 Oct 89 06:11:03 CDT Return-Path: Received: from uxc.cso.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA01146; Tue, 24 Oct 89 06:10:56 CDT Received: from yoda.ncsa.uiuc.edu by uxc.cso.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA25498; Tue, 24 Oct 89 04:37:34 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA22539; Tue, 24 Oct 89 01:21:17 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA22535; Tue, 24 Oct 89 01:21:15 -0500 Message-Id: <8910240621.AA22535@yoda.ncsa.uiuc.edu> Date: Mon, 23 Oct 89 22:44:40 PDT From: ghe@nucthy.PHYSICS.ORST.EDU (Guangliang He) To: Mathematica Mailling list Subject: Mathematica on a SE/30 Status: RO Is it possible to get a Mac II version of Mathematica running on a Mac SE/30? What kind problem could possiblly happen? I'm interested to see the results. Thank you all for your time. -- ======================================================================= USMAIL: Guangliang He | INTERNET: ghe@PHYSICS.ORST.EDU Department of Physics | BITNET: hegl@ORSTVM.BITNET Weniger Hall 301 | Oregon State University | Corvallis, OR 97331-6507 | PHONE: (503) 737-4631 ======================================================================= From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Nov 1 18:05:24 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA10214; Wed, 1 Nov 89 18:05:23 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA29029; Wed, 1 Nov 89 18:04:56 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA01667; Wed, 1 Nov 89 18:04:46 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA10105; Wed, 1 Nov 89 15:05:25 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA10101; Wed, 1 Nov 89 15:05:23 -0600 Message-Id: <8911012105.AA10101@yoda.ncsa.uiuc.edu> Date: Mon, 30 Oct 89 22:17:20 PST From: ghe@nucthy.PHYSICS.ORST.EDU (Guangliang He) To: Mathematica Mailling list Subject: Tensor operations in Mathematica Status: RO In Mathematica, Inner[f, u, v, g] contracts the last index of tensor u and first index of tensor v. But how can I contract 2 indexes of a rand r tensor T to get a rank (r-2) tensor? When r=2, that is just the trace of the matrix. But how about higher rank tensor? -- ======================================================================= USMAIL: Guangliang He | INTERNET: ghe@PHYSICS.ORST.EDU Department of Physics | BITNET: hegl@ORSTVM.BITNET Weniger Hall 301 | Oregon State University | Corvallis, OR 97331-6507 | PHONE: (503) 737-4631 ======================================================================= From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Nov 1 18:55:56 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA10241; Wed, 1 Nov 89 18:55:55 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA29149; Wed, 1 Nov 89 18:55:27 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA02208; Wed, 1 Nov 89 18:55:16 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA10110; Wed, 1 Nov 89 15:05:35 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA10106; Wed, 1 Nov 89 15:05:34 -0600 Message-Id: <8911012105.AA10106@yoda.ncsa.uiuc.edu> Date: Tue, 31 Oct 89 08:58:09 PST From: ghe@nucthy.PHYSICS.ORST.EDU (Guangliang He) To: Mathematica Mailling list Subject: Question about Transpose in Mathematica Status: RO Hello everybody, I have some problem with understanding the Transpose function in Mathetmatica. For example, I have a tensor a as a={{{1,2,3},{2,3,4}}} which has the dimension as Dimensions[a]={1,2,3} I thought that Transpose[a, {3,1,2}] should give a tensor with dimension {3,1,2}. But instead, Mathematica MacII version 1.1 gives the resulting tensor as {{{1}, {2}, {3}}, {{2}, {3}, {4}}} which has the dimension {2, 3, 1} As I understand, Transpose[a, {3,1,2}] should put the 3rd level of a to the first level of the output. So the leading dimension of the output should be 3, not 2. Am I misunderstanding something here? Any help will be welcome. -- ======================================================================= USMAIL: Guangliang He | INTERNET: ghe@PHYSICS.ORST.EDU Department of Physics | BITNET: hegl@ORSTVM.BITNET Weniger Hall 301 | Oregon State University | Corvallis, OR 97331-6507 | PHONE: (503) 737-4631 ======================================================================= From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Nov 1 19:48:34 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA10311; Wed, 1 Nov 89 19:48:33 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA29311; Wed, 1 Nov 89 19:48:08 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA02777; Wed, 1 Nov 89 19:47:57 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA10189; Wed, 1 Nov 89 16:02:09 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA10185; Wed, 1 Nov 89 16:02:07 -0600 Message-Id: <8911012202.AA10185@yoda.ncsa.uiuc.edu> Date: Wed, 1 Nov 89 13:49:30 CST From: kant@SLCS.SLB.COM To: stevec@yoda.ncsa.uiuc.edu Subject: Mathematica question Status: RO Does anyone have a good text string and/or user interface package? Example facilities desired: smart wrap around of lines indenting wrapped around lines to parameterized number of spaces, type checking of inputs (e.g. ask user for a number), etc. Thanks. -- Elaine Kant From testgroup-adm@yoda.ncsa.uiuc.edu Wed Nov 8 15:01:21 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA02023; Wed, 8 Nov 89 15:01:20 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA13059; Wed, 8 Nov 89 15:00:46 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA02001; Wed, 8 Nov 89 15:00:44 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA01961; Wed, 8 Nov 89 14:37:07 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA01957; Wed, 8 Nov 89 14:37:06 -0600 Message-Id: <8911082037.AA01957@yoda.ncsa.uiuc.edu> Date: Tue, 7 Nov 89 20:00:32 PST From: mdeale@vega.ACS.CalPoly.EDU (Myron Deale) To: mathgroup-request@yoda.ncsa.uiuc.edu Subject: question on CellularAutomata Status: RO Hello, Our University has Mathematica liscensed to run on two Sun 3 machines (under X11, Sunview, or NeWS). I would like to get the CellularAutomata example package to run. Has anyone tried this yet? Not being a wiz at CA I don't know how to produce some simple graphics / plots. Thanks in advance, -Myron // mdeale@cosmos.acs.calpoly.edu From testgroup-adm@yoda.ncsa.uiuc.edu Wed Nov 8 15:01:26 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA02030; Wed, 8 Nov 89 15:01:25 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA13062; Wed, 8 Nov 89 15:00:52 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA02004; Wed, 8 Nov 89 15:00:50 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA01955; Wed, 8 Nov 89 14:35:59 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA01951; Wed, 8 Nov 89 14:35:57 -0600 Message-Id: <8911082035.AA01951@yoda.ncsa.uiuc.edu> Date: Tue, 7 Nov 89 13:58:09 PST From: Walter Vogel - Biochem To: mathgroup@yoda.ncsa.uiuc.edu Subject: nonlinear regression curve fitting Status: RO Does anyone know of a package to do nonlinear regression curve fit to a function, possibly using Marquardt's algorithm? I am interested in fitting data to an equation of the form y=f(y,x) or z=f(x,y). Below is the equation I wish to fit. The equation: _ _ | | [L] | F1 F2 | Y= ----- | ------------------- + ------------------- | K | 1 + [I]/K1 + [L]/K 1 + [I]/K2 + [L]/K | |_ _| There are 4 parameters to be determined: K, K1, K2, F1 (since F1 + F2 =1, F2 is not a parameter. Our raw data is obtained as radioactive counts versus the independent variable, [I]. The counts are used to calculate both Y and [L] thus our dependent variable appears on both sides of the equation. Y=(T-n)/r and [L]=q-T. As written above the equation is a function of two variables [I] and [L] but it can be recast as function of one T=f(T([I]),[I]). Sincerely Walter K. Vogel vogelw@bionette.cgrb.orst.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Nov 9 13:24:58 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA03340; Thu, 9 Nov 89 13:24:57 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA25504; Thu, 9 Nov 89 13:24:22 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA28135; Thu, 9 Nov 89 13:24:19 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA03289; Thu, 9 Nov 89 11:44:46 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA03285; Thu, 9 Nov 89 11:44:44 -0600 Message-Id: <8911091744.AA03285@yoda.ncsa.uiuc.edu> Date: Tue, 7 Nov 89 13:58:09 PST From: Walter Vogel - Biochem To: mathgroup@yoda.ncsa.uiuc.edu Subject: nonlinear regression curve fitting Status: RO Does anyone know of a package to do nonlinear regression curve fit to a function, possibly using Marquardt's algorithm? I am interested in fitting data to an equation of the form y=f(y,x) or z=f(x,y). Below is the equation I wish to fit. The equation: _ _ | | [L] | F1 F2 | Y= ----- | ------------------- + ------------------- | K | 1 + [I]/K1 + [L]/K 1 + [I]/K2 + [L]/K | |_ _| There are 4 parameters to be determined: K, K1, K2, F1 (since F1 + F2 =1, F2 is not a parameter. Our raw data is obtained as radioactive counts versus the independent variable, [I]. The counts are used to calculate both Y and [L] thus our dependent variable appears on both sides of the equation. Y=(T-n)/r and [L]=q-T. As written above the equation is a function of two variables [I] and [L] but it can be recast as function of one T=f(T([I]),[I]). Sincerely Walter K. Vogel vogelw@bionette.cgrb.orst.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Nov 9 14:03:37 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA03414; Thu, 9 Nov 89 14:03:36 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA25944; Thu, 9 Nov 89 14:03:00 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA29071; Thu, 9 Nov 89 14:02:57 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA03294; Thu, 9 Nov 89 11:44:57 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA03290; Thu, 9 Nov 89 11:44:56 -0600 Message-Id: <8911091744.AA03290@yoda.ncsa.uiuc.edu> Date: Tue, 7 Nov 89 20:00:32 PST From: mdeale@vega.ACS.CalPoly.EDU (Myron Deale) To: mathgroup-request@yoda.ncsa.uiuc.edu Subject: question on CellularAutomata Status: RO Hello, Our University has Mathematica liscensed to run on two Sun 3 machines (under X11, Sunview, or NeWS). I would like to get the CellularAutomata example package to run. Has anyone tried this yet? Not being a wiz at CA I don't know how to produce some simple graphics / plots. Thanks in advance, -Myron // mdeale@cosmos.acs.calpoly.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Nov 9 14:51:25 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA03477; Thu, 9 Nov 89 14:51:24 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA26519; Thu, 9 Nov 89 14:50:49 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA00714; Thu, 9 Nov 89 14:50:47 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA03374; Thu, 9 Nov 89 13:36:01 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA03370; Thu, 9 Nov 89 13:36:00 -0600 Message-Id: <8911091936.AA03370@yoda.ncsa.uiuc.edu> Date: Thu, 9 Nov 89 11:42:11 -0600 From: Steve Christensen To: mathgroup@yoda.ncsa.uiuc.edu Subject: Programming in Mathematica files Status: RO Roman Maeder's new book - Programming in Mathematica - is about to be published by Addison-Wesley. He has kindly sent the files containing the programs from that book to me for inclusion in the Mathematica archive. These can be obtained by doing anonymous ftp to 128.174.2o.50 ftp.ncsa.uiuc.edu Once logged in by using the user name anonymous and any password, do a ftp> cd Symbolic/Mathematica/Packages There you will find two new files - Programming_in_Mathematica.1 Programming_in_Mathematica.2 You can get these files using ftp> mget Programming* and responding to the questions with y . Now log out of the server. These are shell archives. Follow the instructions given at the beginning of the .1 file to unpack the programs. Have fun. Steve Christensen NCSA, Illinois From testgroup-adm@yoda.ncsa.uiuc.edu Fri Nov 10 23:01:20 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA04863; Fri, 10 Nov 89 23:01:19 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA17285; Fri, 10 Nov 89 23:00:49 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA09817; Fri, 10 Nov 89 23:00:46 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA04856; Fri, 10 Nov 89 22:54:58 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA04852; Fri, 10 Nov 89 22:54:56 -0600 Message-Id: <8911110454.AA04852@yoda.ncsa.uiuc.edu> Date: Sat Nov 11 15:14:58 1989 From: leon@extro.ucc.su.oz.au (L. Poladian) To: mathgroup-adm@yoda.ncsa.uiuc.edu, mathgroup@yoda.ncsa.uiuc.edu Subject: Re: nonlinear regression curve fitting Status: RO In response to a recent enquiry about non-linear regression here are the definitions for a routine that can be used. I have not had time to set this all up correctly as a package with contexts etc. and have only briefly tested it. Therefore, use at your own peril. Given a function f = F[x,y,...,a,b,...] of several variables x,y,... which also depends on a number of parameters a,b,... and a list of data data = { {x1,y1,...,f1}, {x2,y2,...,f2}, ... } the routine attempts to find the values of a,b,... which minimizes the sum of the squares of the residuals. The only restriction on F[] is that Mathematica must be able to calculate symbolic derivatives of F with respect to a,b,.... An initial estimate of the paramters is required and the routine returns a "better" estimate of the parameters. If the original estimate is good enough, repeating the process will eventually produce a converged result. The definitions follow: LinearFit[list_,fun_,f0_,var_] :=Block[{n,n2,m,b}, n = Length[list]; n2 = Length[fun]; m = Table[ Sum[ (fun[[j]] fun[[k]] /. Thread[var -> Drop[list[[i]],-1]]), {i,1,n}], {j,1,n2}, {k,1,n2}]; b = Table[ Sum[ (fun[[j]] (list[[i,-1]]-f0) /. Thread[var -> Drop[list[[i]],-1]]), {i,1,n}], {j,1,n2}]; LinearSolve[m,b] ] NonLinearFit[list_,fun_,par_,init_,var_]:= Block[{npar,sub,linfun,f0,coeff}, npar = Length[par]; sub = Thread[par -> init]; linfun = Table[ D[ fun, par[[i]] ], {i,1,npar}] /.sub; f0 = fun /. sub; coeff = LinearFit[list,linfun,f0,var]; init+coeff ] The routine is used as follows: data = { {x1,y1,..,f1}, {x2,y2,...,f2}, ...}; function = F[x,y,...,a,b,...]; (* whatever function you are fitting *) pars = {a,b,... }; initialestimate = {a0, b0, ... }; (* reasonable values for the parameters *) vars = {x,y,...}; estimate = NonLinearFit[data,function,pars,initialestimate,vars] estimate = NonLinearFit[data,function,pars,estimate,vars] (*keep repeating*) Alternatively one can use FixedPoint estimate = FixedPoint[NonLinearFit[data,function,pars,#,vars]&,initialestimate] Leon Poladian Theoretical Physics University of Sydney leon@extro.ucc.su.oz From mathgroup-adm@yoda.ncsa.uiuc.edu Sat Nov 11 03:15:49 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA05659; Sat, 11 Nov 89 03:15:46 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA21249; Sat, 11 Nov 89 03:15:05 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA15439; Sat, 11 Nov 89 03:14:59 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA04897; Fri, 10 Nov 89 23:21:22 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA04893; Fri, 10 Nov 89 23:21:21 -0600 Message-Id: <8911110521.AA04893@yoda.ncsa.uiuc.edu> Date: Sat Nov 11 15:14:58 1989 From: leon@extro.ucc.su.oz.au (L. Poladian) To: mathgroup-adm@yoda.ncsa.uiuc.edu, mathgroup@yoda.ncsa.uiuc.edu Subject: Re: nonlinear regression curve fitting Status: RO In response to a recent enquiry about non-linear regression here are the definitions for a routine that can be used. I have not had time to set this all up correctly as a package with contexts etc. and have only briefly tested it. Therefore, use at your own peril. Given a function f = F[x,y,...,a,b,...] of several variables x,y,... which also depends on a number of parameters a,b,... and a list of data data = { {x1,y1,...,f1}, {x2,y2,...,f2}, ... } the routine attempts to find the values of a,b,... which minimizes the sum of the squares of the residuals. The only restriction on F[] is that Mathematica must be able to calculate symbolic derivatives of F with respect to a,b,.... An initial estimate of the paramters is required and the routine returns a "better" estimate of the parameters. If the original estimate is good enough, repeating the process will eventually produce a converged result. The definitions follow: LinearFit[list_,fun_,f0_,var_] :=Block[{n,n2,m,b}, n = Length[list]; n2 = Length[fun]; m = Table[ Sum[ (fun[[j]] fun[[k]] /. Thread[var -> Drop[list[[i]],-1]]), {i,1,n}], {j,1,n2}, {k,1,n2}]; b = Table[ Sum[ (fun[[j]] (list[[i,-1]]-f0) /. Thread[var -> Drop[list[[i]],-1]]), {i,1,n}], {j,1,n2}]; LinearSolve[m,b] ] NonLinearFit[list_,fun_,par_,init_,var_]:= Block[{npar,sub,linfun,f0,coeff}, npar = Length[par]; sub = Thread[par -> init]; linfun = Table[ D[ fun, par[[i]] ], {i,1,npar}] /.sub; f0 = fun /. sub; coeff = LinearFit[list,linfun,f0,var]; init+coeff ] The routine is used as follows: data = { {x1,y1,..,f1}, {x2,y2,...,f2}, ...}; function = F[x,y,...,a,b,...]; (* whatever function you are fitting *) pars = {a,b,... }; initialestimate = {a0, b0, ... }; (* reasonable values for the parameters *) vars = {x,y,...}; estimate = NonLinearFit[data,function,pars,initialestimate,vars] estimate = NonLinearFit[data,function,pars,estimate,vars] (*keep repeating*) Alternatively one can use FixedPoint estimate = FixedPoint[NonLinearFit[data,function,pars,#,vars]&,initialestimate] Leon Poladian Theoretical Physics University of Sydney leon@extro.ucc.su.oz From testgroup-adm@yoda.ncsa.uiuc.edu Tue Nov 14 22:01:22 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA11502; Tue, 14 Nov 89 22:01:21 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA18573; Tue, 14 Nov 89 22:00:55 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA03676; Tue, 14 Nov 89 22:00:51 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA11483; Tue, 14 Nov 89 21:50:37 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA11479; Tue, 14 Nov 89 21:50:35 -0600 Message-Id: <8911150350.AA11479@yoda.ncsa.uiuc.edu> Date: Tue, 14 Nov 89 21:48:57 -0600 From: Steve Christensen To: mathgroup@yoda.ncsa.uiuc.edu Subject: Mathematica SIG and SUG Status: RO There will be a Special Interest Group meeting on Mathematica at 5:15pm on Thursday, Dec. 7 at the Anaheim, CA Sun User Group Conference. If you would like to give a short 10-15 minute presentation at this SIG, please email me ASAP. Please send your name, title and organization and a one paragraph summary of what you would like to say. Since I want to leave some time for discussion, I can accept only 3-4 short talks. Please email me at steve@ncsa.uiuc.edu. Nancy Blachman will be giving a one hour presentation entitled "The Advantages of Running Mathematica Under UNIX" at 4pm the same day. Steve Christensen NCSA & Beckman Institute University of Illinois From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Nov 15 02:23:00 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA12349; Wed, 15 Nov 89 02:22:59 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA22680; Wed, 15 Nov 89 02:22:30 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA09854; Wed, 15 Nov 89 02:22:26 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA11570; Tue, 14 Nov 89 23:43:25 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA11566; Tue, 14 Nov 89 23:43:24 -0600 Message-Id: <8911150543.AA11566@yoda.ncsa.uiuc.edu> Date: Tue, 14 Nov 89 21:48:57 -0600 From: Steve Christensen To: mathgroup@yoda.ncsa.uiuc.edu Subject: Mathematica SIG and SUG Status: RO There will be a Special Interest Group meeting on Mathematica at 5:15pm on Thursday, Dec. 7 at the Anaheim, CA Sun User Group Conference. If you would like to give a short 10-15 minute presentation at this SIG, please email me ASAP. Please send your name, title and organization and a one paragraph summary of what you would like to say. Since I want to leave some time for discussion, I can accept only 3-4 short talks. Please email me at steve@ncsa.uiuc.edu. Nancy Blachman will be giving a one hour presentation entitled "The Advantages of Running Mathematica Under UNIX" at 4pm the same day. Steve Christensen NCSA & Beckman Institute University of Illinois From @uunet.UU.NET,@munnari:leon@extro.ucc.su.oz.au Thu Nov 16 09:38:05 1989 Received: from uunet.UU.NET by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA13644; Thu, 16 Nov 89 09:38:02 -0600 Received: from munnari.UUCP by uunet.uu.net (5.61/1.14) with UUCP id AA28664; Thu, 16 Nov 89 10:37:20 -0500 Message-Id: <8911161537.AA28664@uunet.uu.net> Received: from extro.ucc.su.oz (via munnari) by murtoa.cs.mu.OZ.AU with SunIII (5.5) id AA25607; Fri, 17 Nov 89 02:33:41 EST (from leon@extro.ucc.su.oz for uunet!mathgroup-adm@yoda.ncsa.uiuc.edu) Date: Sat Nov 11 15:14:58 1989 From: leon@extro.ucc.su.oz.au (L. Poladian) To: mathgroup-adm@yoda.ncsa.uiuc.edu, mathgroup@yoda.ncsa.uiuc.edu Subject: Re: nonlinear regression curve fitting Status: RO In response to a recent enquiry about non-linear regression here are the definitions for a routine that can be used. I have not had time to set this all up correctly as a package with contexts etc. and have only briefly tested it. Therefore, use at your own peril. Given a function f = F[x,y,...,a,b,...] of several variables x,y,... which also depends on a number of parameters a,b,... and a list of data data = { {x1,y1,...,f1}, {x2,y2,...,f2}, ... } the routine attempts to find the values of a,b,... which minimizes the sum of the squares of the residuals. The only restriction on F[] is that Mathematica must be able to calculate symbolic derivatives of F with respect to a,b,.... An initial estimate of the paramters is required and the routine returns a "better" estimate of the parameters. If the original estimate is good enough, repeating the process will eventually produce a converged result. The definitions follow: LinearFit[list_,fun_,f0_,var_] :=Block[{n,n2,m,b}, n = Length[list]; n2 = Length[fun]; m = Table[ Sum[ (fun[[j]] fun[[k]] /. Thread[var -> Drop[list[[i]],-1]]), {i,1,n}], {j,1,n2}, {k,1,n2}]; b = Table[ Sum[ (fun[[j]] (list[[i,-1]]-f0) /. Thread[var -> Drop[list[[i]],-1]]), {i,1,n}], {j,1,n2}]; LinearSolve[m,b] ] NonLinearFit[list_,fun_,par_,init_,var_]:= Block[{npar,sub,linfun,f0,coeff}, npar = Length[par]; sub = Thread[par -> init]; linfun = Table[ D[ fun, par[[i]] ], {i,1,npar}] /.sub; f0 = fun /. sub; coeff = LinearFit[list,linfun,f0,var]; init+coeff ] The routine is used as follows: data = { {x1,y1,..,f1}, {x2,y2,...,f2}, ...}; function = F[x,y,...,a,b,...]; (* whatever function you are fitting *) pars = {a,b,... }; initialestimate = {a0, b0, ... }; (* reasonable values for the parameters *) vars = {x,y,...}; estimate = NonLinearFit[data,function,pars,initialestimate,vars] estimate = NonLinearFit[data,function,pars,estimate,vars] (*keep repeating*) Alternatively one can use FixedPoint estimate = FixedPoint[NonLinearFit[data,function,pars,#,vars]&,initialestimate] Leon Poladian Theoretical Physics University of Sydney leon@extro.ucc.su.oz From testgroup-adm@yoda.ncsa.uiuc.edu Wed Nov 15 23:01:24 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA12921; Wed, 15 Nov 89 23:01:23 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA05413; Wed, 15 Nov 89 23:00:58 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA06057; Wed, 15 Nov 89 23:00:53 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA12902; Wed, 15 Nov 89 22:25:44 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA12898; Wed, 15 Nov 89 22:25:43 -0600 Message-Id: <8911160425.AA12898@yoda.ncsa.uiuc.edu> From: tim@merlin.bhpmrl.oz.au (Tim Monks) Subject: New books from Addison Wesley ? To: mathgroup@yoda.ncsa.uiuc.edu (mathgroup) Date: Thu, 16 Nov 89 14:17:23 EST Status: RO Can anybody tell me what the publication dates are on the following books ? Maeder : Programming for Mathematica Crandall : Scientific Applications of Mathematica Both books have been listed in Addison Wesley catalogues for a while - even with ISB numbers, but the local A-W office does not know when they are due out. Thanks, Tim Monks Image Processing & Data Analysis Group | (direct) +61-3-566-7448 BHP Melbourne Research Laboratories | (switch) +61-3-560-7066 245 Wellington Rd, Mulgrave, 3170, | (fax) +61-3-561-6709 AUSTRALIA | (EMAIL) tim@merlin.bhpmrl.oz.au From lie@itk.unit.no Wed Nov 15 09:17:22 1989 Received: from loke.idt.unit.no by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA12454; Wed, 15 Nov 89 09:17:10 -0600 Received: from adam.itk.unit.no by loke.idt.unit.no; Wed, 15 Nov 89 16:16:26 +0100 Date: Wed, 15 Nov 89 16:16:15 GMT Received: from [129.241.10.55] by adam.itk.unit.no; Wed, 15 Nov 89 16:16:15 GMT From: lie@itk.unit.no Message-Id: <8911151518.AA03031@rudolf.itk.unit.no> To: mathgroup@yoda.ncsa.uiuc.edu Subject: ContourPlot Status: RO Re: Mixture of ContourPlot and Plot in Show. Problem: I have a constrained optimization problem that I want to illustrate graphically. The object function is z[x,y], and I want to use ContourPlot to map it into the (x,y) plane. Then I want to overlay this plot with constraints of the form y[x]. I tried to Show both plots in the same picture, but this was apparently not possible (according to the error message). Does anyone have a suggestion on how to solve my "problem"? Bernt Lie e-mail: lie@itk.unit.no From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Nov 16 13:04:40 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA13805; Thu, 16 Nov 89 13:04:37 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA15306; Thu, 16 Nov 89 13:04:09 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA03910; Thu, 16 Nov 89 13:04:02 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA13687; Thu, 16 Nov 89 10:21:23 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA13683; Thu, 16 Nov 89 10:21:21 -0600 Message-Id: <8911161621.AA13683@yoda.ncsa.uiuc.edu> Date: Wed, 15 Nov 89 16:16:15 GMT From: lie@itk.unit.no To: mathgroup@yoda.ncsa.uiuc.edu Subject: ContourPlot Status: RO Re: Mixture of ContourPlot and Plot in Show. Problem: I have a constrained optimization problem that I want to illustrate graphically. The object function is z[x,y], and I want to use ContourPlot to map it into the (x,y) plane. Then I want to overlay this plot with constraints of the form y[x]. I tried to Show both plots in the same picture, but this was apparently not possible (according to the error message). Does anyone have a suggestion on how to solve my "problem"? Bernt Lie e-mail: lie@itk.unit.no From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Nov 16 13:51:06 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA13849; Thu, 16 Nov 89 13:51:04 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA15883; Thu, 16 Nov 89 13:50:36 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA05163; Thu, 16 Nov 89 13:50:30 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA13677; Thu, 16 Nov 89 10:21:05 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA13673; Thu, 16 Nov 89 10:21:03 -0600 Message-Id: <8911161621.AA13673@yoda.ncsa.uiuc.edu> From: tim@merlin.bhpmrl.oz.au (Tim Monks) Subject: New books from Addison Wesley ? To: mathgroup@yoda.ncsa.uiuc.edu (mathgroup) Date: Thu, 16 Nov 89 14:17:23 EST Status: RO Can anybody tell me what the publication dates are on the following books ? Maeder : Programming for Mathematica Crandall : Scientific Applications of Mathematica Both books have been listed in Addison Wesley catalogues for a while - even with ISB numbers, but the local A-W office does not know when they are due out. Thanks, Tim Monks Image Processing & Data Analysis Group | (direct) +61-3-566-7448 BHP Melbourne Research Laboratories | (switch) +61-3-560-7066 245 Wellington Rd, Mulgrave, 3170, | (fax) +61-3-561-6709 AUSTRALIA | (EMAIL) tim@merlin.bhpmrl.oz.au From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Nov 16 14:43:13 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA13959; Thu, 16 Nov 89 14:43:12 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA16525; Thu, 16 Nov 89 14:42:43 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA06432; Thu, 16 Nov 89 14:42:37 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA13682; Thu, 16 Nov 89 10:21:12 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA13678; Thu, 16 Nov 89 10:21:10 -0600 Message-Id: <8911161621.AA13678@yoda.ncsa.uiuc.edu> Date: Sat Nov 11 15:14:58 1989 From: leon@extro.ucc.su.oz.au (L. Poladian) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: nonlinear regression curve fitting Status: RO In response to a recent enquiry about non-linear regression here are the definitions for a routine that can be used. I have not had time to set this all up correctly as a package with contexts etc. and have only briefly tested it. Therefore, use at your own peril. Given a function f = F[x,y,...,a,b,...] of several variables x,y,... which also depends on a number of parameters a,b,... and a list of data data = { {x1,y1,...,f1}, {x2,y2,...,f2}, ... } the routine attempts to find the values of a,b,... which minimizes the sum of the squares of the residuals. The only restriction on F[] is that Mathematica must be able to calculate symbolic derivatives of F with respect to a,b,.... An initial estimate of the paramters is required and the routine returns a "better" estimate of the parameters. If the original estimate is good enough, repeating the process will eventually produce a converged result. The definitions follow: LinearFit[list_,fun_,f0_,var_] :=Block[{n,n2,m,b}, n = Length[list]; n2 = Length[fun]; m = Table[ Sum[ (fun[[j]] fun[[k]] /. Thread[var -> Drop[list[[i]],-1]]), {i,1,n}], {j,1,n2}, {k,1,n2}]; b = Table[ Sum[ (fun[[j]] (list[[i,-1]]-f0) /. Thread[var -> Drop[list[[i]],-1]]), {i,1,n}], {j,1,n2}]; LinearSolve[m,b] ] NonLinearFit[list_,fun_,par_,init_,var_]:= Block[{npar,sub,linfun,f0,coeff}, npar = Length[par]; sub = Thread[par -> init]; linfun = Table[ D[ fun, par[[i]] ], {i,1,npar}] /.sub; f0 = fun /. sub; coeff = LinearFit[list,linfun,f0,var]; init+coeff ] The routine is used as follows: data = { {x1,y1,..,f1}, {x2,y2,...,f2}, ...}; function = F[x,y,...,a,b,...]; (* whatever function you are fitting *) pars = {a,b,... }; initialestimate = {a0, b0, ... }; (* reasonable values for the parameters *) vars = {x,y,...}; estimate = NonLinearFit[data,function,pars,initialestimate,vars] estimate = NonLinearFit[data,function,pars,estimate,vars] (*keep repeating*) Alternatively one can use FixedPoint estimate = FixedPoint[NonLinearFit[data,function,pars,#,vars]&,initialestimate] Leon Poladian Theoretical Physics University of Sydney leon@extro.ucc.su.oz From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Nov 16 14:46:10 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA13964; Thu, 16 Nov 89 14:46:08 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA16573; Thu, 16 Nov 89 14:45:39 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA06532; Thu, 16 Nov 89 14:45:33 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA13732; Thu, 16 Nov 89 10:52:28 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA13728; Thu, 16 Nov 89 10:52:27 -0600 Message-Id: <8911161652.AA13728@yoda.ncsa.uiuc.edu> Date: Thu, 16 Nov 89 17:35:19 GMT From: lie@itk.unit.no To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: ContourPlot Status: RO [Here are more details on the question regarding contour plots previously sent to the mailing list. -s christensen] More details. Assume that you want to pick the pair (x,y) that minimize the function f[x_,y_]={x-3,y-5}.{{5,2},{2,5}}.{x-3,y-5} By simplifying this expression, you get: f[x_,y_]=230 - 50x + 5x^2 - 62y + 4x y + 5y^2 The minimum is obviously the pair (x=3,y=5). Now, suppose that the solution is constrained to lie on the curve: y[x_]=6 - 0.5x What is then the pair (x,y) that minimize f[x,y]? This can be solved graphically by plotting the contours of f[x,y] into the x-y plane for different values of f. Then plot the constraint (y[x]) in the x-y plane of the same display. This will produce a visualization of the solution. I tried to: 1. ContourPlot[f[x,y],{x,-1,5},{y,0,8}] 2. Plot[z[x],{x,-1,5}] (I denoted y[x] by z[x]) 3. Show[%(no. of ContourPlot output), %(no. of Plot output)] The result: a. Warning: Show::nocombine: Graphics of type ContourGraphics cannot be combined. b. Out[nn]=Show[-ContourGraphics-,-Graphics-] Question: How can I solve my problem, i.e., how can I plot a ContourPlot in the same display as an ordinary plot?? Thanks! Bernt Lie, e-mail: lie@itk.unit.no From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Nov 17 15:35:44 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA15764; Fri, 17 Nov 89 15:35:41 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA05241; Fri, 17 Nov 89 15:35:13 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA09435; Fri, 17 Nov 89 15:35:03 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA15624; Fri, 17 Nov 89 13:57:58 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA15620; Fri, 17 Nov 89 13:57:56 -0600 Date: Fri, 17 Nov 89 13:57:56 -0600 Message-Id: <8911171957.AA15620@yoda.ncsa.uiuc.edu> From: tori@itk.unit.no To: mathgroup@yoda.ncsa.uiuc.edu Subject: MathTalk Status: RO I'm writing a program where I want to call Mathematica to perform symbolic and numerical operations. In the User's Guide for SUN Work- stations it says that Mathematica supports communication with front ends and application-programs through the packet-based protocol MathTalk. I've got the MathTalk utility programs control leftcrc leftend rightcrc rightend twoway but there is no information on *how* to use these programs. Question: Can anyone help me with some hints or examples on how to communicate with Mathematica through the MathTalk protocol from a general application program / front end? (I'm running Mathematica version 1.2 on a SUN 3/60 Work- station) Tor Ivar Eikaas Research Scientist SINTEF Automatic Control NORWAY Phone: +47-7-59449 email: tori@itk.unit.no From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Nov 17 15:51:00 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA15782; Fri, 17 Nov 89 15:50:59 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA05429; Fri, 17 Nov 89 15:50:31 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA09828; Fri, 17 Nov 89 15:50:24 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA15630; Fri, 17 Nov 89 13:59:26 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA15626; Fri, 17 Nov 89 13:59:24 -0600 Message-Id: <8911171959.AA15626@yoda.ncsa.uiuc.edu> To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Workshops in Mathematica Date: Fri, 17 Nov 89 01:41:44 -0800 From: nb@Polya.Stanford.EDU Status: RO ---------------- Problem Solving with Mathematica Taught by Nancy Blachman This workshop offers a comprehensive introduction to Mathematica, The course is targeted for engineers, physicists, financial analysts, academic professionals, or anyone whose work or study involves mathematical problem solving or analysis. It focuses on using Mathematica effectively to solve problems in such areas as calculus, data analysis, algebra, number theory, and discrete mathematics. Class participants will receive a 150-page class manual as well as set of reference cards (listing all functions built into Mathematica). Course Organization: Introduction to Mathematica Numerical, algebraic or symbolic, and graphics capabilities Data analysis Programming Mathematica's internal representation Data Types Contexts, scoping of variables I/O Interfacing to other programs C, PostScript, TeX Programming techniques Procedural Pattern matching Debugging techniques Writing packages (collections of functions) Problem Solving An assortment of problems will be presented Documentation Notebooks TeX Nancy Blachman worked at Wolfram Research, Inc. in 1988 and 1989 and recently started her own training and consulting business. Nancy has a B.S. in Mathematics from the University of Birmingham, U.K., an M.S. in Operations Research from UC Berkeley, and an M.S. in Computer Science from Stanford University. In addition to instructing a graduate level course in Computer Graphics, and working as a teaching assistant in a course in Concrete Mathematics, Nancy has been a software developer at Bell Laboratories and at the Research Institute for Advanced Computer Science at NASA Ames. Below is a tentative list of the organizations where Nancy Blachman will be offering courses in Mathematica this fall and winter. These courses vary in length and content. ComputerWare 490 California Ave., Suite 202 Palo Alto, CA 94306 Tel: 415-323-7951 Contact: Anne Krause Cost: $350-400 Dates: February 8, 1990 Rice University Office of Continuing Studies P. O. Box 1892 Houston, TX 77251-1892 Contact: Edie Carlson-Abbey Tel: 713-527-4803 Cost: $150-200 Date: February 23, 1990 Stanford University Stanford Instructional Television Network (SITN) Computer Science Department Stanford, University CA 94305 Course Number: CS 193M Contact: Sally Kiester Tel: 415-725-3002 Dates: Winter quarter, Tuesday 12 noon-1:05 pm UC Berkeley Extension Continuing Education 2223 Fulton Street Berkeley, CA 94720 Contact: Nanette Pike Tel: 415-642-4151 UC Santa Cruz Extension 5201 Great America Parkway Santa Clara, CA 95054 Contact: Tim Johnson Tel: 408-562-5726 Cost: $600 Dates: February 15-16, 1990 Nancy Blachman also gives private courses in Mathematica. Variable Symbols 1701 Lincoln Street * Berkeley, CA 94703 * 415-486-8073 Email: nb@polya.stanford.edu or uunet.uu.net!polya.stanford.edu!nb From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Nov 17 17:00:15 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA15870; Fri, 17 Nov 89 16:59:33 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA06231; Fri, 17 Nov 89 16:59:06 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA11389; Fri, 17 Nov 89 16:58:58 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA15656; Fri, 17 Nov 89 14:09:24 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA15652; Fri, 17 Nov 89 14:09:22 -0600 Message-Id: <8911172009.AA15652@yoda.ncsa.uiuc.edu> Date: Fri, 17 Nov 89 19:44:25 GMT From: lie@itk.unit.no To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Combining plots Status: RO A partial solution to the problem of combining plots. This is a *partial* solution to the problem of combining different types of graphics in one plot. By partial is meant that the solution is cumbersome, and not very elegant. In general, two plots of different types (e.g., Plot and ContourPlot) cannot be combined in one plot by means of the Mathematica Show command. A solution to this problem is to save the plots with the Display["file",%out] command, one file per plot. The files are then merged into one file as they are. Finally, use the Wolfram Research program x11ps to display the merged file: ..path../x11ps < merged_file_name x11ps displays the file on an X11 terminal. For other types of terminals, use: sunps, tekps, ttyps (!), ... instead of x11ps. The PROBLEM is that it is highly unlikely that you are able to produce the plots such that the axis of the two plots coincide (i.e., I haven't found how to do it). Even by use of the Show options PlotRange and Axes, I didn't succed. A "dirty" way to solve this problem when combining a ContourPlot and a two- dimensional plot is examplified below: -Problem: Combine the plots (ContourPlot) of the object function: f[x_,y_]=x^2+2y^2 and the constraint: y[x_]=5-x in the region {x,-5,5}, {y,-5,5} -Amateurs solution: 1. ContourPlot[f[x,y],{x,-5,5},{y,-5,5}] --> out[n] (for instance) 2. It is very difficult to use Plot[y[x],{x,-5,5}], then Show[%,PlotRange->{-5,5},AspectRatio->Automatic] and make the axis overlay perfectly!! (i.e., for me). Solution: restate the constraint as: z[x_,y_]=5-x-y ContourPlot[z[x,y],{x,-5,5},{y,-5,5}] gives you a heap of contour lines, where the sought one is that at z[x,y]=0. Now you just Show the previous ContourPlot for z in the range of, say {-.001,.001}: Show[%,PlotRange->{-.001,.001}] --> out[m] (for instance) If z is plotted in the range {-.1,.1}, the "line" will become rather thick. 3. Display["fxy",%n] and Display["zxy",%m] will save the files, which may then be merged into file "fzxy". 4. The combined plots are shown with the command (on an x11- terminal): ...path../x11ps < fzxy As stated above, this is not a very proffesional way to do it. *Someone* should write a general Mathematica command/routine to do it in one batch. - Bernt Lie PS. Valuable tips has been received from rgf@terra.... and nb@Polya... From lie@itk.unit.no Sun Nov 19 08:56:01 1989 Received: from loke.idt.unit.no by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA17562; Sun, 19 Nov 89 08:54:28 -0600 Received: from adam.itk.unit.no by loke.idt.unit.no; Sun, 19 Nov 89 15:53:27 +0100 Date: Sun, 19 Nov 89 15:53:17 GMT Received: from [129.241.10.55] by adam.itk.unit.no; Sun, 19 Nov 89 15:53:17 GMT From: lie@itk.unit.no Message-Id: <8911191455.AA08408@rudolf.itk.unit.no> To: stevec@yoda.ncsa.uiuc.edu Status: RO Subject: Re: Combining plots A partial solution to the problem of combining plots. This is a *partial* solution to the problem of combining different types of graphics in one plot. By partial is meant that the solution is cumbersome, and not very elegant. In general, two plots of different types (e.g., Plot and ContourPlot) cannot be combined in one plot by means of the Mathematica Show command. A solution to this problem is to save the plots with the Display["file",%out] command, one file per plot. The files are then merged into one file as they are. Finally, use the Wolfram Research program x11ps to display the merged file: ..path../x11ps < merged_file_name x11ps displays the file on an X11 terminal. For other types of terminals, use: sunps, tekps, ttyps (!), ... instead of x11ps. The PROBLEM is that it is highly unlikely that you are able to produce the plots such that the axis of the two plots coincide (i.e., I haven't found how to do it). Even by use of the Show options PlotRange and Axes, I didn't succed. A "dirty" way to solve this problem when combining a ContourPlot and a two- dimensional plot is examplified below: -Problem: Combine the plots (ContourPlot) of the object function: f[x_,y_]=x^2+2y^2 and the constraint: y[x_]=5-x in the region {x,-5,5}, {y,-5,5} -Amateurs solution: 1. ContourPlot[f[x,y],{x,-5,5},{y,-5,5}] --> out[n] (for instance) 2. It is very difficult to use Plot[y[x],{x,-5,5}], then Show[%,PlotRange->{-5,5},AspectRatio->Automatic] and make the axis overlay perfectly!! (i.e., for me). Solution: restate the constraint as: z[x_,y_]=5-x-y ContourPlot[z[x,y],{x,-5,5},{y,-5,5}] gives you a heap of contour lines, where the sought one is that at z[x,y]=0. Now you just Show the previous ContourPlot for z in the range of, say {-.001,.001}: Show[%,PlotRange->{-.001,.001}] --> out[m] (for instance) If z is plotted in the range {-.1,.1}, the "line" will become rather thick. 3. Display["fxy",%n] and Display["zxy",%m] will save the files, which may then be merged into file "fzxy". 4. The combined plots are shown with the command (on an x11- terminal): ...path../x11ps < fzxy As stated above, this is not a very professional way to do it. *Someone* should write a general Mathematica command/routine to do it in one batch. - Bernt Lie PS. Valuable tips has been received from rgf@terra.... and nb@Polya... ----- End Included Message ----- From testgroup-adm@yoda.ncsa.uiuc.edu Sun Nov 19 19:01:31 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA17819; Sun, 19 Nov 89 19:01:30 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA08647; Sun, 19 Nov 89 19:01:09 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA06291; Sun, 19 Nov 89 19:00:58 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA17807; Sun, 19 Nov 89 18:27:58 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA17803; Sun, 19 Nov 89 18:27:55 -0600 Message-Id: <8911200027.AA17803@yoda.ncsa.uiuc.edu> Date: Sun, 19 Nov 89 16:16:36 PST From: campbell@garnet.berkeley.edu (Robert I. Campbell) To: mathgroup@garnet.berkeley.edu Subject: EMACS front end for Mathematica Status: RO [Any information on front end development out there in Mathematica land would be interesting. -s christensen] I understand that someone has written an EMACS front end for Mathematica (sort of a poor man's Notebook system without fonts or graphics). Is this the case, and if so, how can I get a copy of it? - Robert Campbell - campbell@math.berkeley.edu Math Dept, UCBerkeley From mathgroup-adm@yoda.ncsa.uiuc.edu Sun Nov 19 21:38:19 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA17878; Sun, 19 Nov 89 21:38:18 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA10151; Sun, 19 Nov 89 21:37:53 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA08852; Sun, 19 Nov 89 21:37:47 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA17835; Sun, 19 Nov 89 19:06:01 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA17831; Sun, 19 Nov 89 19:05:59 -0600 Message-Id: <8911200105.AA17831@yoda.ncsa.uiuc.edu> Date: Sun, 19 Nov 89 16:16:36 PST From: campbell@garnet.berkeley.edu (Robert I. Campbell) To: mathgroup@garnet.berkeley.edu Subject: EMACS front end for Mathematica Status: RO [Any information on front end development out there in Mathematica land would be interesting. -s christensen] I understand that someone has written an EMACS front end for Mathematica (sort of a poor man's Notebook system without fonts or graphics). Is this the case, and if so, how can I get a copy of it? - Robert Campbell - campbell@math.berkeley.edu Math Dept, UCBerkeley From mathgroup-adm@yoda.ncsa.uiuc.edu Mon Nov 20 11:13:10 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA18944; Mon, 20 Nov 89 11:13:09 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA20240; Mon, 20 Nov 89 11:12:43 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA26198; Mon, 20 Nov 89 11:12:37 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA18823; Mon, 20 Nov 89 09:32:28 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA18819; Mon, 20 Nov 89 09:32:26 -0600 Message-Id: <8911201532.AA18819@yoda.ncsa.uiuc.edu> Date: 20 Nov 1989 08:11:45 EST From: JIM.THOMPSON@kbesrl.me.uiuc.edu To: mathgroup@yoda.ncsa.uiuc.edu Subject: Mathematica front end in Lisp Status: RO > [Any information on front end development out there > in Mathematica land would be interesting. -s christensen] I have a front-end written in Common Lisp using CLOS (Common Lisp Object System). It presently runs on a Symbolics machine and relies on a few Symbolics Common Lisp functions to create networked tcp byte streams connected to a Sun running a Mathematica kernel. I think it would be a relatively easy port to a non-Lisp-machine Lisp and would be interested in such a version. No graphics display capability! I use it for a "mathematics computation server" for programs running in Lisp. Anyone interested? Jim Thompson Knowledge-Based Engineering Systems Research Laboratory University of Illinois at Urbana-Champaign Department of Mechanical & Industrial Engineering 1206 W. Green St. Urbana IL 61801 217-244-0292 jb-thompson@uiuc.edu From conal@kestrel.edu Thu Dec 14 12:03:58 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA02639; Thu, 14 Dec 89 12:03:56 -0600 Received: from ncsa.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA23814; Thu, 14 Dec 89 12:03:44 CST Return-Path: Received: from kestrel.kestrel.edu (kestrel.edu) by ncsa.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA21284; Thu, 14 Dec 89 12:02:53 CST Received: from raven.kestrel.edu by kestrel.kestrel.edu (5.58/SMI-DDN) id AA15638; Thu, 14 Dec 89 09:59:02 PDT Received: from localhost by raven.kestrel.edu (4.0/SMI-4.0) id AA06775; Thu, 14 Dec 89 10:02:39 PST To: mathgroup Reply-To: Conal Elliott Subject: Polyhedra Date: Thu, 14 Dec 89 10:02:38 PST Message-Id: <6774.629661758@raven.kestrel.edu> From: conal@kestrel.edu Status: RO I'm curious about how the coordinates of the vertices of the polyhedra in polyhedra.m were computed. Any pointers? Also, has anybody worked out a program for doing "REAL" stellations, which conceptually are formed by extending faces and clipping at plane intersections, as opposed to adding pyramids to faces? Thanks, Conal Elliott Kestrel Institute 3260 Hillview Ave. Palo Alto, CA 94304 (415) 493-6871 conal@kestrel.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Dec 14 14:40:46 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA02854; Thu, 14 Dec 89 14:40:45 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA25732; Thu, 14 Dec 89 14:40:28 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA13024; Thu, 14 Dec 89 14:40:09 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA02782; Thu, 14 Dec 89 13:31:27 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA02778; Thu, 14 Dec 89 13:31:25 -0600 Message-Id: <8912141931.AA02778@yoda.ncsa.uiuc.edu> To: mathgroup Subject: Polyhedra Date: Thu, 14 Dec 89 10:02:38 PST From: conal@kestrel.edu Status: RO I'm curious about how the coordinates of the vertices of the polyhedra in polyhedra.m were computed. Any pointers? Also, has anybody worked out a program for doing "REAL" stellations, which conceptually are formed by extending faces and clipping at plane intersections, as opposed to adding pyramids to faces? Thanks, Conal Elliott Kestrel Institute 3260 Hillview Ave. Palo Alto, CA 94304 (415) 493-6871 conal@kestrel.edu From stevec Wed Dec 20 00:26:35 1989 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA09897; Wed, 20 Dec 89 00:26:33 -0600 Date: Wed, 20 Dec 89 00:26:33 -0600 From: Steve Christensen Message-Id: <8912200626.AA09897@yoda.ncsa.uiuc.edu> To: mathgroup@yoda.ncsa.uiuc.edu Subject: Sci.math.symbolic archive and NeWS.view Status: RO Mark Phillips from the University of Maryland has very generously volunteered to archive Mathematica related entries in the sci.math.symbolic newsgroup and other newsgroups on the net. He has sent me the latest archive called Archive4 and the NeWS graphics upgrade for Mathematica from Roman Maeder called NeWS.view. Both of these have been placed on the MathGroup anonymous ftp server. If you cannot reach the archive, I can email you a shar file containing the above files. Mark will send more archives as he collects them. Thanks to Mark. Steve Christensen From stevec Wed Dec 27 02:24:44 1989 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA04197; Wed, 27 Dec 89 02:24:43 -0600 Date: Wed, 27 Dec 89 02:24:43 -0600 From: Steve Christensen Message-Id: <8912270824.AA04197@yoda.ncsa.uiuc.edu> To: stevec@yoda.ncsa.uiuc.edu Subject: Mathematica Reference Card Status: RO From: ----------------------------------------------------------------------------- Variable Symbols provides reference material, training courses, software, and other products to people who use or plan to use Mathematica. We developed a set of Mathematica reference cards listing all functions, options, variables, etc. built into Mathematica. Each set includes four laminated cards displaying the usage statements included in the file info.m distributed with version 1.2 of Mathematica. The cards also list aliases and special forms. The list price for these cards is $9.95. They are available from various bookstores and Mathematica dealers including M.A.C. (2156A University Ave., Berkeley, CA 94704, FAX (415) 644-0584, tel. (415) 644-0516). When ordering directly from Variable Symbols, include $2 for postage and handling. California residents include 7% for sales tax. One complimentary set of cards is included for each set of 10 cards purchased directly from Variable Symbols. Nancy Blachman (415) 486-8073 Email: nb@polya.stanford.edu Variable Symbols * 1701 Lincoln Street * Berkeley, CA 94703-1308 * 415 486 8073 _______________________________________________________________________________ Mathematica Reference Card Order Form Variable Symbols provides reference material, training courses, software, and other products of interest to people who use or plan to use Mathematica. You may use this form to order Mathematica reference cards from Variable Symbols. Name___________________________________________________________________________ Job Title______________________________________________________________________ Firm___________________________________________________________________________ Street Address_________________________________________________________________ City, State ZIP (postal code), Country_________________________________________ Electronic Address_____________________________________________________________ FAX____________________________________________________________________________ Telephone______________________________________________________________________ Order Information Description Price Quantity Total Mathematica reference cards $9.95 __________ $________ Postage and handling $2.00 $ 2.00 California residents include 7% sales tax $________ Total price $________ Make your check payable to Variable Symbols. Name (printed) ________________________________________ Date___________________ Signature______________________________________________________________________ We provide workshops in Mathematica. Would you be interested in (mark all that apply)? __ On-site training __ Video tapes __ Notification of Workshops in your area __ Off-site training __ On-line tutorials _______________________________________________________________________________ Variable Symbols * 1701 Lincoln Street * Berkeley, CA 94703-1308 * 415 486 8073 From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Dec 27 05:05:04 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA04265; Wed, 27 Dec 89 05:05:03 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA07929; Wed, 27 Dec 89 05:04:47 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA18556; Wed, 27 Dec 89 05:04:42 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA04214; Wed, 27 Dec 89 02:28:09 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA04210; Wed, 27 Dec 89 02:28:08 -0600 Message-Id: <8912270828.AA04210@yoda.ncsa.uiuc.edu> Date: Wed, 27 Dec 89 02:24:43 -0600 From: stevec@yoda.ncsa.uiuc.edu To: mathgroup@yoda.ncsa.uiuc.edu Subject: Mathematica Reference Card Status: RO I have been asked to post this to the mailing list. ----------------------------------------------------------------------------- Variable Symbols provides reference material, training courses, software, and other products to people who use or plan to use Mathematica. We developed a set of Mathematica reference cards listing all functions, options, variables, etc. built into Mathematica. Each set includes four laminated cards displaying the usage statements included in the file info.m distributed with version 1.2 of Mathematica. The cards also list aliases and special forms. The list price for these cards is $9.95. They are available from various bookstores and Mathematica dealers including M.A.C. (2156A University Ave., Berkeley, CA 94704, FAX (415) 644-0584, tel. (415) 644-0516). When ordering directly from Variable Symbols, include $2 for postage and handling. California residents include 7% for sales tax. One complimentary set of cards is included for each set of 10 cards purchased directly from Variable Symbols. Nancy Blachman (415) 486-8073 Email: nb@polya.stanford.edu Variable Symbols * 1701 Lincoln Street * Berkeley, CA 94703-1308 * 415 486 8073 _______________________________________________________________________________ Mathematica Reference Card Order Form Variable Symbols provides reference material, training courses, software, and other products of interest to people who use or plan to use Mathematica. You may use this form to order Mathematica reference cards from Variable Symbols. Name___________________________________________________________________________ Job Title______________________________________________________________________ Firm___________________________________________________________________________ Street Address_________________________________________________________________ City, State ZIP (postal code), Country_________________________________________ Electronic Address_____________________________________________________________ FAX____________________________________________________________________________ Telephone______________________________________________________________________ Order Information Description Price Quantity Total Mathematica reference cards $9.95 __________ $________ Postage and handling $2.00 $ 2.00 California residents include 7% sales tax $________ Total price $________ Make your check payable to Variable Symbols. Name (printed) ________________________________________ Date___________________ Signature______________________________________________________________________ We provide workshops in Mathematica. Would you be interested in (mark all that apply)? __ On-site training __ Video tapes __ Notification of Workshops in your area __ Off-site training __ On-line tutorials _______________________________________________________________________________ Variable Symbols * 1701 Lincoln Street * Berkeley, CA 94703-1308 * 415 486 8073 From mathgroup-adm@yoda.ncsa.uiuc.edu Sat Dec 30 04:49:13 1989 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA07230; Sat, 30 Dec 89 04:49:12 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA22325; Sat, 30 Dec 89 04:49:00 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA11973; Sat, 30 Dec 89 04:48:54 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA07200; Sat, 30 Dec 89 02:20:02 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA07196; Sat, 30 Dec 89 02:20:01 -0600 Message-Id: <8912300820.AA07196@yoda.ncsa.uiuc.edu> From: ssa@wri.com Date: Fri, 29 Dec 89 14:37:02 CST To: mathgroup@ncsa.uiuc.edu Subject: SUN upgrades Status: RO Please post information about upgrading the copies of Mathematica that were sold directly by SUN. If a user has a "PILOT" copy or 1.1 copy of SunMathematica, they are eligible for a free upgrade. To do the upgrade we need the following information: 1. Original Sun invoice number 2. Original Sun sales order (S.O.) number 3. Machine type they are running the software on 4. Host name 5. CPU ID 6. password Once we have verified ( against the list from Sun ) they have purchased the stated number of copies of software, we will ship out a new tape, update release notes and new installation instructions. Unlike Sun, we will only send out one binary form of the software. Sun provided the customer with 386i, Sun3 and Sun4 version and let them chose. So we have to know which machine the have been running the software on. If users have questions about the program, they can contact me at 217-398-0700. Thanks!! Stuart Ariewitz From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Jan 2 20:05:21 1990 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA10390; Tue, 2 Jan 90 20:05:20 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA14001; Tue, 2 Jan 90 20:05:13 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA15752; Tue, 2 Jan 90 20:05:06 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA10367; Tue, 2 Jan 90 18:28:39 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA10363; Tue, 2 Jan 90 18:28:38 -0600 Message-Id: <9001030028.AA10363@yoda.ncsa.uiuc.edu> Date: Tue, 2 Jan 90 15:59:48 PST From: kenward@mdivax1.UUCP (Gary Kenward) To: mathgroup-request@yoda.ncsa.uiuc.edu Subject: looking for DSP algorithms in Mathematica Status: RO I am interested in finding a source for Mathematica implementations of various DSP algorithms: FIR filter design (Parks-McClellan, bilinear transform), IIR filter design (Prony, Yule-Walker), power spectral estimation, FFTs (1 and 2 dimensions), windows (Blackman, Kaiser, Hamming, Hanning, etc.), decimation and interpolation, pole-zero plots, and so forth. Shareware would be nice, but any leads to a good source would be appreciated. Thanks in advance. Gary W. Kenward Advanced Technology and Communications Standards Mobile Data International Inc. Richmond B.C. Canada. From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Jan 2 21:10:31 1990 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA10463; Tue, 2 Jan 90 21:10:30 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA14594; Tue, 2 Jan 90 21:10:24 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA16800; Tue, 2 Jan 90 21:10:17 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA10372; Tue, 2 Jan 90 18:28:49 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA10368; Tue, 2 Jan 90 18:28:47 -0600 Message-Id: <9001030028.AA10368@yoda.ncsa.uiuc.edu> Date: Tue, 2 Jan 90 17:57:50 EST From: crm@summanulla.nbsr.duke.edu (Charles R. Martin) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Mathematica and External Numeric Packages. Status: RO We are considering re-implementing or extending our existing simulation package by using Mathematica; I've been thinking about ways in which fast numeric packages for special problems might be made accessible through Mathematica. So far, my cursory reading of the Mathematica book suggests that a program can be run subsidiary to Mathematica through a pipe and the results returned. This could be nearly useful, but some details of how the results are obtained and their formats are unclear to me. Also, I wonder if it might not be possible to implement new primitives in C and import them somehow. This is all prologue to asking anyone who has had experience with implementing new numeric routines, especially those which are not coded in Mathematica form, to share with me any information they can. Thanks very much, Charlie Martin (...!mcnc!duke!crm, crm@summanulla.mc.duke.edu) NBSR/Box 3709/Duke University Medical Center/Durham, NC 27710 From @uunet.UU.NET:smay@wri.UUCP Fri Jan 5 17:26:22 1990 Received: from uunet.UU.NET by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA14728; Fri, 5 Jan 90 17:26:17 -0600 Received: from wri.UUCP by uunet.uu.net (5.61/1.14) with UUCP id AA16500; Fri, 5 Jan 90 18:25:21 -0500 Received: by WRI.com (3.2/SMI-3.0DEV3) id AA03340; Fri, 5 Jan 90 17:22:02 CST Date: Fri, 5 Jan 90 17:22:02 CST From: smay@wri.UUCP (Scott May) Message-Id: <9001052322.AA03340@WRI.com> To: stevec@yoda.ncsa.uiuc.edu Subject: fourier Status: RO This may have to do with the trouble those guys were having with fourier >From ebneter Thu Jan 4 12:20:31 1990 Date: Thu, 4 Jan 90 12:20:23 CST From: ebneter (Kate Ebneter) To: koch@vms1.engr.utk.edu, smay Status: RO Unfortunately, Fourier transforms are one of those areas of mathematics where several different conventions are used, both for the normalization constants and for the integrand. A search of several mathematics handbooks reveals that both definitions of the forward and inverse Fourier transform are used, with engineering-oriented texts leaning heavily towards the opposite convention from the one which we used. The convention we chose is, for example, used in Press et al., Numerical Recipes and many other texts. In cases like this we have to make a design decision about which convention to use. Thank you for your interest in Mathematica. Kate Ebneter Software Quality Assurance Manager Wolfram Research, Inc. From u12253@ux.ncsa.uiuc.edu Mon Feb 12 13:21:59 1990 Received: from ncsa.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA28179; Mon, 12 Feb 90 13:21:58 -0600 Return-Path: Received: from ux.ncsa.uiuc.edu by ncsa.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA21740; Mon, 12 Feb 90 13:21:23 CST Received: by ux.ncsa.uiuc.edu id AA51690; 5.61/CRI-%I%; Mon, 12 Feb 90 13:20:36 -0600 Date: Mon, 12 Feb 90 13:20:36 -0600 From: u12253@ux.ncsa.uiuc.edu (Charles G. Fleming) Message-Id: <9002121920.AA51690@ux.ncsa.uiuc.edu> To: steve@ncsa.ncsa.uiuc.edu Status: RO splice I have been using Mathematica to generate some systems of differential equations and then splice the resulting equations into a FORTRAN (gag) program so that they can be numberically solved using the imsl package. The problem is that if the equations are too long for FORTRAN splice does not break the output into several lines with continuation markers. In other words, it seems that FortranForm on Mathematica doesn't work as it should. I wrote a C program to reformat splice's output, but this is something that FortranForm should do. Perhaps I'm not using the correct options with splice. Are you familiar with this problem or do you know someone at WRI that could give me a work-around? Thanks. chuck fleming From testgroup-adm@yoda.ncsa.uiuc.edu Fri Mar 2 02:08:02 1990 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA09058; Fri, 2 Mar 90 02:08:01 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA00715; Fri, 2 Mar 90 02:06:52 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA11143; Fri, 2 Mar 90 02:06:52 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA09027; Fri, 2 Mar 90 01:13:20 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA09023; Fri, 2 Mar 90 01:13:19 -0600 Message-Id: <9003020713.AA09023@yoda.ncsa.uiuc.edu> Date: Tue, 27 Feb 90 12:37:20 EST From: Carl L. Gardner Subject: graphics questions Apparently-To: testgroup-send@yoda.ncsa.uiuc.edu Status: RO I have three graphics questions: (1) On my SPARCstation (which has a graphics accelerator), if I zoom a plot to full screen, the lines become very blobby. If I close the window, & then reopen it, the lines are reasonably thin (correct). Is this a bug--sunview or graphics accelerator? (2) Do you know how to get Greek letters & math symbols on the Mathematica plots? (3) Is there a standard coloring for 3D plots, i.e., can I get a spectrum instead of gray tones easily? (I know how to color the plots "by hand", but there ought to be a default spectrum & coloring.) Thanks very much! --Carl From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Mar 2 14:15:15 1990 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA09252; Fri, 2 Mar 90 14:15:14 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA10494; Fri, 2 Mar 90 14:13:55 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA01685; Fri, 2 Mar 90 14:13:54 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA09209; Fri, 2 Mar 90 12:15:13 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA09205; Fri, 2 Mar 90 12:15:11 -0600 Message-Id: <9003021815.AA09205@yoda.ncsa.uiuc.edu> Date: Tue, 27 Feb 90 12:37:20 EST From: Carl L. Gardner Subject: graphics questions Apparently-To: mathgroup-send@yoda.ncsa.uiuc.edu Status: RO I have three graphics questions: (1) On my SPARCstation (which has a graphics accelerator), if I zoom a plot to full screen, the lines become very blobby. If I close the window, & then reopen it, the lines are reasonably thin (correct). Is this a bug--sunview or graphics accelerator? (2) Do you know how to get Greek letters & math symbols on the Mathematica plots? (3) Is there a standard coloring for 3D plots, i.e., can I get a spectrum instead of gray tones easily? (I know how to color the plots "by hand", but there ought to be a default spectrum & coloring.) Thanks very much! --Carl From gardner@cs.duke.edu Tue Feb 27 11:39:13 1990 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA06107; Tue, 27 Feb 90 11:39:12 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA23341; Tue, 27 Feb 90 11:38:17 CST Return-Path: Received: from duke.cs.duke.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA07741; Tue, 27 Feb 90 11:37:42 CST Received: from babel-17.cs.duke.edu by duke.cs.duke.edu (5.59/DUKE/08-19-88) id AA15977; Tue, 27 Feb 90 12:37:28 EST Received: by babel-17.cs.duke.edu (5.59/DUKE/08-19-88) id AA06635; Tue, 27 Feb 90 12:37:20 EST Date: Tue, 27 Feb 90 12:37:20 EST From: Carl L. Gardner Message-Id: <9002271737.AA06635@babel-17.cs.duke.edu> To: stevec@ncsa.uiuc.edu Subject: graphics questions Cc: gardner@cs.duke.edu Status: RO I have three graphics questions: (1) On my SPARCstation (which has a graphics accelerator), if I zoom a plot to full screen, the lines become very blobby. If I close the window, & then reopen it, the lines are reasonably thin (correct). Is this a bug--sunview or graphics accelerator? (2) Do you know how to get Greek letters & math symbols on the Mathematica plots? (3) Is there a standard coloring for 3D plots, i.e., can I get a spectrum instead of gray tones easily? (I know how to color the plots "by hand", but there ought to be a default spectrum & coloring.) Thanks very much! --Carl From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Mar 9 13:17:42 1990 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA17357; Fri, 9 Mar 90 13:17:40 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA04595; Fri, 9 Mar 90 13:16:38 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA16175; Fri, 9 Mar 90 13:16:25 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA17080; Fri, 9 Mar 90 10:55:13 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA17076; Fri, 9 Mar 90 10:55:12 -0600 Message-Id: <9003091655.AA17076@yoda.ncsa.uiuc.edu> Date: Tue, 6 Mar 90 14:59:06 EST From: jack@sun.acs.udel.edu Subject: Use of Literal Apparently-To: mathgroup-send@yoda.ncsa.uiuc.edu Status: RO I want to define a function of Mathematica built-in function. I can do this but to evaluate it seems a little awkward. I must be doing something wrong!? In[1]:= f[Literal[Integrate[g_,x_]]]:=Integrate[g,x] + Sin[x] In[2]:= f[Integrate[q[t],t]] Out[2]= Integrate[q[t], t] + Sin[t] In[3]:= %/.q[t]->t^3 4 t Out[3]= -- + Sin[t] 4 In[4]:= "However................" In[5]:= r[t]:=t^3 In[6]:= f[Integrate[r[t],t]] 4 t Out[6]= f[--] 4 In[7]:= "or...."; In[8]:= r[t_]:=t^3 In[9]:= f[Integrate[r[t],t]] 4 t Out[9]= f[--] From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Mar 9 15:28:09 1990 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA17668; Fri, 9 Mar 90 15:28:08 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA06785; Fri, 9 Mar 90 15:27:04 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA20202; Fri, 9 Mar 90 15:26:52 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA17237; Fri, 9 Mar 90 12:38:37 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA17233; Fri, 9 Mar 90 12:38:36 -0600 Message-Id: <9003091838.AA17233@yoda.ncsa.uiuc.edu> Date: Fri, 09 Mar 90 10:33:58 PST From: jacobson@cello.hpl.hp.com Subject: Re: Literal Apparently-To: mathgroup-send@yoda.ncsa.uiuc.edu Status: RO jack@sun.acs.udel.edu writes: I want to define a function of Mathematica built-in function. I can do this but to evaluate it seems a little awkward. I must be doing something wrong!? In[1]:= f[Literal[Integrate[g_,x_]]]:=Integrate[g,x] + Sin[x] r[t_]:=t^3 ... In[9]:= f[Integrate[r[t],t]] 4 t Out[9]= f[--] 4 The problem has nothing to do with literal, but rather with the fact that f[] evaluates its argument. Since Integrate[r[t],t] evaluates to t^4/4, all f ever gets to see is f[t^4/4], and that won't evaluate, so that is what it gives you. If before defining f you make f have the HoldAll attribute, everything will work fine. ---------------------- In[1]:= SetAttributes[f,HoldAll] In[2]:= f[Literal[Integrate[g_,x_]]]:=Integrate[g,x] + Sin[x] In[3]:= r[t_] := t^3 In[4]:= f[Integrate[r[t],t]] 4 t Out[4]= -- + Sin[t] 4 --------------- -- David Jacobson From PIOTR.FLATAU@ARIES.ATMOS.COLOSTATE.EDU Sun Mar 11 00:49:02 1990 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA19894; Sun, 11 Mar 90 00:49:01 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA03040; Sun, 11 Mar 90 00:48:04 CST Return-Path: Received: from ccncsu.ColoState.EDU by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA24549; Sun, 11 Mar 90 00:47:50 CST Received: from aries.ATMOS.ColoState.EDU by ccncsu.ColoState.EDU (5.59/Ultrix2.0-B) id AA14808; Sat, 10 Mar 90 23:44:27 MST Message-Id: <9003110644.AA14808@ccncsu.ColoState.EDU> Date: 10 Mar 1990 23:46:30 EST From: PIOTR.FLATAU@ARIES.ATMOS.COLOSTATE.EDU To: STEVE@ncsa.uiuc.edu Subject: Status: RO Steve, I wonder if it is possible to overlap two surfaces in Mathematica (on one plot). Something like, say: a:= 2x+y b:=x+y pl1:= Plot3D[a, {x,0,1}, {y,0,1}] pl2:= Plot3D[b, {x,0,1}, {y,0,1}] Show[pl1,pl2] -----------------------------> doesn't work or Plot3D[{a,b}, {x, 0,1}, {y,0,1}] ------> doesn't work I read the first 5 archives but nothing there except, possibly, Ken Yip's question ? Peter flatau@handel.cs.colostate.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Sun Mar 11 20:28:07 1990 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA20239; Sun, 11 Mar 90 20:28:06 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA16514; Sun, 11 Mar 90 20:28:13 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA13069; Sun, 11 Mar 90 20:28:00 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA20135; Sun, 11 Mar 90 16:29:14 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA20131; Sun, 11 Mar 90 16:29:13 -0600 Message-Id: <9003112229.AA20131@yoda.ncsa.uiuc.edu> Date: Sat, 10 Mar 90 17:08:00 CST From: paul@wri.UUCP (Paul Abbott) Subject: Re: Use of Literal Apparently-To: mathgroup-send@yoda.ncsa.uiuc.edu Status: RO I would use HoldFirst (or HoldAll) instead: Mathematica (sun3.68881) 1.2 (November 6, 1989) [With pre-loaded data] by S. Wolfram, D. Grayson, R. Maeder, H. Cejtin, S. Omohundro, D. Ballman and J. Keiper with I. Rivin and D. Withoff Copyright 1988,1989 Wolfram Research Inc. -- Terminal graphics initialized -- In[1]:= SetAttributes[f,HoldFirst] In[2]:= f[Integrate[g_,x_]] := Integrate[g,x] + Sin[x] In[3]:= f[Integrate[x^2,x]] 3 x Out[3]= -- + Sin[x] 3 In[4]:= ^D From mathgroup-adm@yoda.ncsa.uiuc.edu Sun Mar 11 21:22:13 1990 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA20343; Sun, 11 Mar 90 21:22:12 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA17108; Sun, 11 Mar 90 21:22:20 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA13851; Sun, 11 Mar 90 21:22:07 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA20147; Sun, 11 Mar 90 16:30:52 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA20143; Sun, 11 Mar 90 16:30:50 -0600 Message-Id: <9003112230.AA20143@yoda.ncsa.uiuc.edu> Date: 10 Mar 1990 23:46:30 EST From: PIOTR.FLATAU@ARIES.ATMOS.COLOSTATE.EDU Subject: Plotting two surfaces Apparently-To: mathgroup-send@yoda.ncsa.uiuc.edu Status: RO I wonder if it is possible to overlap two surfaces in Mathematica (on one plot). Something like, say: a:= 2x+y b:=x+y pl1:= Plot3D[a, {x,0,1}, {y,0,1}] pl2:= Plot3D[b, {x,0,1}, {y,0,1}] Show[pl1,pl2] -----------------------------> doesn't work or Plot3D[{a,b}, {x, 0,1}, {y,0,1}] ------> doesn't work I read the first 5 archives but nothing there except, possibly, Ken Yip's question ? Peter flatau@handel.cs.colostate.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Sun Mar 11 21:41:21 1990 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA20445; Sun, 11 Mar 90 21:41:20 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA17332; Sun, 11 Mar 90 21:41:28 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA14169; Sun, 11 Mar 90 21:41:15 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA20141; Sun, 11 Mar 90 16:29:53 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA20137; Sun, 11 Mar 90 16:29:51 -0600 Message-Id: <9003112229.AA20137@yoda.ncsa.uiuc.edu> Date: Sat, 10 Mar 90 17:11:26 CST From: paul@wri.UUCP (Paul Abbott) Subject: Re: DSolve Apparently-To: mathgroup-send@yoda.ncsa.uiuc.edu Status: RO I think that I posted a solution to this before. Here is another attempt. Note that DSolve allows the boundary conditions to be entered as equations: Mathematica (sun3.68881) 1.2 (November 6, 1989) [With pre-loaded data] by S. Wolfram, D. Grayson, R. Maeder, H. Cejtin, S. Omohundro, D. Ballman and J. Keiper with I. Rivin and D. Withoff Copyright 1988,1989 Wolfram Research Inc. -- Terminal graphics initialized -- In[1]:= ?DSolve DSolve[eqn, y[x], x] solves differential equations for the function y[x] with independent variable x. DSolve[{eqn1, eqn2, ...}, {y1[x1], y2[x2], ...}, {x1, x2, ...}] solves a list of differential equations. Equations can either be differential equations or constraints: a differential equation may have the form F[y[x], y'[x], ..., Derivative[n][y][x], x] == 0; constraints may be of the form Derivative[k][y][pti]== vali. In[1]:= DSolve[{x'[t]==-t, x[0]==1},x[t],t] 2 t Out[1]= {{x[t] -> 1 - --}} 2 In[2]:= ^D From @uunet.UU.NET:paul@wri.UUCP Mon Mar 12 02:28:17 1990 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA22153; Mon, 12 Mar 90 02:28:15 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA22349; Mon, 12 Mar 90 02:28:27 CST Return-Path: Received: from uunet.uu.net by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA20131; Mon, 12 Mar 90 02:28:14 CST Received: from wri.UUCP by uunet.uu.net (5.61/1.14) with UUCP id AA24635; Mon, 12 Mar 90 03:26:26 -0500 From: paul@wri.UUCP Received: by WRI.com (3.2/SMI-3.0DEV3) id AA09999; Mon, 12 Mar 90 02:19:21 CST Message-Id: <9003120819.AA09999@WRI.com> Date: Mon, 12 Mar 90 02:19:16 CST To: PIOTR.FLATAU@ARIES.ATMOS.COLOSTATE.EDU Subject: Re: Plotting two surfaces Cc: mathgroup@uunet.UU.NET Status: RO One way of doing this is to convert the -SurfaceGraphics- to -Graphics3D- objects first. plot1 = Plot3D[2x+y, {x,0,1}, {y,0,1}] plot2 = Plot3D[x+y, {x,0,1}, {y,0,1}] This is easily done using graphics1 = Graphics3D[plot1]; graphics2 = Graphics3D[plot2]; You then show the two graphics together: Show[graphics1,graphics2] From @uunet.UU.NET:paul@wri.UUCP Sun Mar 11 15:09:47 1990 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA20078; Sun, 11 Mar 90 15:09:45 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA12959; Sun, 11 Mar 90 15:09:57 CST Return-Path: Received: from uunet.uu.net by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA08316; Sun, 11 Mar 90 15:09:43 CST Received: from wri.UUCP by uunet.uu.net (5.61/1.14) with UUCP id AA03861; Sun, 11 Mar 90 16:09:04 -0500 Received: by WRI.com (3.2/SMI-3.0DEV3) id AA00590; Sat, 10 Mar 90 17:08:00 CST Date: Sat, 10 Mar 90 17:08:00 CST From: paul@wri.UUCP (Paul Abbott) Message-Id: <9003102308.AA00590@WRI.com> To: jack@sun.acs.udel.edu Subject: Re: Use of Literal Cc: mathgroup@uunet.UU.NET Status: RO I would use HoldFirst (or HoldAll) instead: Mathematica (sun3.68881) 1.2 (November 6, 1989) [With pre-loaded data] by S. Wolfram, D. Grayson, R. Maeder, H. Cejtin, S. Omohundro, D. Ballman and J. Keiper with I. Rivin and D. Withoff Copyright 1988,1989 Wolfram Research Inc. -- Terminal graphics initialized -- In[1]:= SetAttributes[f,HoldFirst] In[2]:= f[Integrate[g_,x_]] := Integrate[g,x] + Sin[x] In[3]:= f[Integrate[x^2,x]] 3 x Out[3]= -- + Sin[x] 3 In[4]:= ^D From @uunet.UU.NET:paul@wri.UUCP Sun Mar 11 15:12:30 1990 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA20083; Sun, 11 Mar 90 15:12:28 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA13012; Sun, 11 Mar 90 15:12:40 CST Return-Path: Received: from uunet.uu.net by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA08379; Sun, 11 Mar 90 15:12:26 CST Received: from wri.UUCP by uunet.uu.net (5.61/1.14) with UUCP id AA04885; Sun, 11 Mar 90 16:11:56 -0500 Received: by WRI.com (3.2/SMI-3.0DEV3) id AA00616; Sat, 10 Mar 90 17:11:26 CST Date: Sat, 10 Mar 90 17:11:26 CST From: paul@wri.UUCP (Paul Abbott) Message-Id: <9003102311.AA00616@WRI.com> To: jack@sun.acs.udel.edu Subject: Re: DSolve Cc: mathgroup@uunet.UU.NET Status: RO I think that I posted a solution to this before. Here is another attempt. Note that DSolve allows the boundary conditions to be entered as equations: Mathematica (sun3.68881) 1.2 (November 6, 1989) [With pre-loaded data] by S. Wolfram, D. Grayson, R. Maeder, H. Cejtin, S. Omohundro, D. Ballman and J. Keiper with I. Rivin and D. Withoff Copyright 1988,1989 Wolfram Research Inc. -- Terminal graphics initialized -- In[1]:= ?DSolve DSolve[eqn, y[x], x] solves differential equations for the function y[x] with independent variable x. DSolve[{eqn1, eqn2, ...}, {y1[x1], y2[x2], ...}, {x1, x2, ...}] solves a list of differential equations. Equations can either be differential equations or constraints: a differential equation may have the form F[y[x], y'[x], ..., Derivative[n][y][x], x] == 0; constraints may be of the form Derivative[k][y][pti]== vali. In[1]:= DSolve[{x'[t]==-t, x[0]==1},x[t],t] 2 t Out[1]= {{x[t] -> 1 - --}} 2 In[2]:= ^D From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Mar 13 01:20:55 1990 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA23951; Tue, 13 Mar 90 01:20:53 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA18046; Tue, 13 Mar 90 01:20:47 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA21697; Tue, 13 Mar 90 01:20:45 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA22843; Mon, 12 Mar 90 20:10:10 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA22839; Mon, 12 Mar 90 20:10:09 -0600 Message-Id: <9003130210.AA22839@yoda.ncsa.uiuc.edu> Date: Mon, 12 Mar 90 16:16:34 PST From: campbell@garnet.berkeley.edu (Robert I. Campbell) Subject: Re: Plotting two surfaces Apparently-To: mathgroup-send@yoda.ncsa.uiuc.edu Status: RO >I wonder if it is possible to overlap two surfaces in Mathematica >(on one plot). > >Peter >flatau@handel.cs.colostate.edu Basically, the way to do this is to convert both surfaces (SurfaceGraphics objects) to Graphics3D objects, then Show the resulting Graphics3D objects. It would be nice to be able to directly combine SurfaceGraphics objects, but the whole idea of such an object is that if it can be assumed to be a graph of a SINGLE function of two variables, then the hidden line algorithms sued in displaying it are much simplified. Try the following: plot1=Plot3D[Sin[x y],{x,-Pi,Pi},{y,-Pi,Pi}] plot2=Plot3D[(x^2-y^2)/9,{x,-Pi,Pi},{y,-Pi,Pi}] plot1=Graphics3D[plot1] (* Converts to Graphics3D object *) plot2=Graphics3D[plot2] Show[{plot1,plot2}] Alternatively, I wrote a widget to do this called MultiPlot3D. It is in a package called "Student.m", which I will append to this letter. It is also available for anonymous ftp from otter.stanford.edu in the /ftp/mma directory. - Robert Campbell - Math Dept, UC Berkeley BeginPackage["Student`"] (* Copyright 1990 Robert Campbell *) Bezier::usage = "Bezier[{{x0,y0},...,{x3,y3}}] computes the cubic bezier curve with control points {xi,yi}, prints out its parametric description, and then draws the curve and its control polygon, and returns the parametric description. Bezier[{{x0,y0},...},nodraw] returns a list of the two components of the parametric description." Midpoint::usage = "Midpoint[f,{x,xmin,xmax},n] will compute the numeric integral of the function f(x) on the interval [xmin,xmax], using the midpoint method with n divisions. The numeric result and the error, or difference from the system command NIntegrate, will be printed and the result returned will be a graph of the process. Midpoint[f,{x,xmin,xmax},n,nodraw] prints the error and returns the numeric result without graphing it." MultiPlot3D::usage = "MultiPlot3D[{f1,...},{x_,x0_,x1_},{y_,y0_,y1_}] extends the function Plot3D by allowing the user to plot several functions of two variables on the same set of axes. The result is a Graphics3D object, not a SurfaceGraphics object. The function can use the same options as Plot3D (Not entirely true at present 14 Feb, 1990). THIS IS A VERY SLOW AND EXPENSIVE PROGRAM." Newton::usage = "Newton[f,{x,xstart},n] will use n steps of Newton's method to try to compute a root of f(x), starting at the point x=xstart and will return a graph of the process. Newton[f,{x,xstart},n,nodraw] will print the result at each step of the process, and will return a list of the values." Polyapprox::usage = "Polyapprox[f,x,{x0,...,xn}] will compute the polynomial of degree (n-1) which interpolates f(x) at the points {x0,...}. It will print this polynomial and then graph it on the same plot with f along with f." Trapezoid::usage = "Trapezoid[f,{x,xmin,xmax},n] will compute the numeric integral of f(x) on the interval [xmin,xmax], using the trapezoid method with n divisions. The numeric result and the error, or difference from the system command NIntegrate, will be printed and a graph will be returned. Trapezoid[f,{x,xmin,xmax},n,nodraw] prints the error and returns the numeric result without graphing it." nodraw; Begin["`Private`"] Bezier[{{x0_,y0_},{x1_,y1_},{x2_,y2_},{x3_,y3_}}]:= (* Compute and display the cubic Bzier curve with the specified control pts.*) Block[{xcoord,ycoord,plot,points,poly,paramname,t}, (* Define the x and y coordinates of the point on the curve with parameter un. Generate a new name, of the form un, for the parametric variable used in Bezier. *) paramname = Unique["u"]; xcoord=x0*(1-paramname)^3 + 3*x1*paramname*(1-paramname)^2 \ + 3*x2*paramname^2*(1-paramname) + x3*paramname^3; ycoord=y0*(1-paramname)^3 + 3*y1*paramname*(1-paramname)^2 \ + 3*y2*paramname^2*(1-paramname) + y3*paramname^3; Print["The Bzier curve is:"]; Print["x(",paramname,") = ",xcoord]; Print["y(",paramname,") = ",ycoord]; (* recompute the curve using an internal variable parameter *) xcoord=x0*(1-t)^3 + 3*x1*t*(1-t)^2 + 3*x2*t^2*(1-t) + x3*t^3; ycoord=y0*(1-t)^3 + 3*y1*t*(1-t)^2 + 3*y2*t^2*(1-t) + y3*t^3; (* Now draw the curve invisibly *) plot=ParametricPlot[{xcoord,ycoord},{t,0,1},DisplayFunction->Identity]; (* Prepare to draw the control points *) points={Point[{x0,y0}],Point[{x1,y1}],Point[{x2,y2}],Point[{x3,y3}]}; (* Connect the control points to get the control polygon. *) poly=Line[{{x0,y0},{x1,y1},{x2,y2},{x3,y3}}]; (* combine the graph with the control points, and display them. *) Show[Graphics[{PointSize[0.02],points,poly}],plot,\ DisplayFunction->$DisplayFunction] ] Bezier[{{x0_,y0_},{x1_,y1_},{x2_,y2_},{x3_,y3_}},nodraw]:= (* Compute the cubic Bzier curve with the specified control pts and return it as a parametric curve in "un".*) Block[{xcoord,ycoord,paramname}, (* Generate a new name, of the form un, for the parametric variable used in Bezier. *) paramname = Unique["u"]; xcoord=x0*(1-paramname)^3 + 3*x1*paramname*(1-paramname)^2 \ + 3*x2*paramname^2*(1-paramname) + x3*paramname^3; ycoord=y0*(1-paramname)^3 + 3*y1*paramname*(1-paramname)^2 \ + 3*y2*paramname^2*(1-paramname) + y3*paramname^3; {xcoord,ycoord} ] Midpoint[f_,{x_,xmin_,xmax_},n_]:= (* This routine will compute the numeric integral of the function f(x) on the interval [xmin,xmax], using the midpoint method with n divisions. The numeric result and the error, or difference from the system NIntegrate, will be printed and the result returned will be a graph of the process.*) Block[{mp,error,i,j,rectlist,linelist,val,step,plot}, mp=0; step=(xmax-xmin)/n; For[i=0,i xmin+(i+0.5) step; mp=mp+val[i] step; ]; rectlist=Table[Rectangle[{xmin+j*step,0},{xmin+(j+1) step,val[j]}]\ ,{j,0,n-1}]; linelist=Table[Line[{{xmin+j*step,0},{xmin+j*step,val[j]},\ {xmin+(j+1) step,val[j]},{xmin+(j+1) step,0}}],{j,0,n-1}]; rectlist=Prepend[rectlist,GrayLevel[0.6]]; linelist=Prepend[linelist,GrayLevel[0]]; plot=Plot[f,{x,xmin,xmax},DisplayFunction->Identity]; error=Abs[N[mp-NIntegrate[f,{x,xmin,xmax}]]]; Print["The integral is approximately ",N[mp]]; Print["error=",error]; Show[Graphics[Join[rectlist,linelist]],plot,\ DisplayFunction->$DisplayFunction] ] Midpoint[f_,{x_,xmin_,xmax_},n_,nodraw]:= (* This routine will compute the numeric integral of the function f(x) on the interval [xmin,xmax], using the midpoint method with n divisions. The error, or difference from the system NIntegrate, will be printed and the result returned will be the numeric result. *) Block[{mp,error,i,j,rectlist,val,step}, mp=0; step=(xmax-xmin)/n; For[i=0,i xmin+(i+0.5) step; mp=mp+val[i] step; ]; error=Abs[N[mp-NIntegrate[f,{x,xmin,xmax}]]]; Print["error=",error]; N[mp] ] MultiPlot3D[fcns_List,{x_,x0_,x1_},{y_,y0_,y1_},opts___]:= (* This routine extends the function Plot3D by allowing the user to plot several functions of two variables on the same set of axes. The result is a Graphics3D object, not a SurfaceGraphics object. At present those options which are valid for Graphics3D, as well as the Mesh option, are not properly passed or acted on *) Block[{plotopts,showopts,plotoptstest}, (* Strip out those options which are unique to Plot3D, as opposed to those options understood by Graphics3D *) plotoptstest=(MatchQ[#,PlotPoints->_] || MatchQ[#,ClipFill->_] || MatchQ[#,HiddenSurface->_] || MatchQ[#,Mesh->_] || MatchQ[#,MeshStyle->_])&; plotopts=Cases[{opts},_?plotoptstest]; showopts=Cases[{opts},_?(Not[plotoptstest[#]]&)]; Show[Map[Graphics3D,Map[Plot3D[#,{x,x0,x1},{y,y0,y1},plotopts,\ DisplayFunction->Identity]&,fcns]],showopts,\ DisplayFunction->$DisplayFunction] ] Newton[f_,{x_,xstart_},n_,nodraw]:= (* This routine will use Newton's method to solve the equation f(x)=0 for x. The initial guess, xstart, is supplied by the user, as is the desired number of iterations, n. At each step the routine prints out the new estimate, xi, the value of the function at xi, and the amount the new estimate differs from the previous estimate. *) Block[{fprime,xi,xiold,xlist}, xlist = {xstart}; fprime:=D[f,x]; xi=xstart; (* We start out with our first guess *) For[i=1,ixi),60]; AppendTo[xlist,xi]; (* And add it to our list of guesses *) Print[i]; Print["xi=",N[xi,10]]; (* Print guess to 10 digits *) Print["f(xi)=",N[(f /. x->xi),10]];(* Print function value *) Print["xi-x(i-1)=",N[xi-xiold,10]];(* Change in guess *) (* Print out the relevant information *) ]; N[xlist,10] (* Return 10 digits as a final value *) ] Newton[f_,{x_,xstart_},n_]:= (* This routine will use Newton's method to solve the equation f(x)=0 for x. The initial guess, xstart, is supplied by the user, as is the desired number of iterations, n. The output is a graph which shows a plot of the function f, each successive estimate, xi, and the value of f at xi. The plot also draws the tangent line to f at {xi,f(xi)} which is used to get the next estimate. *) Block[{fprime,xi,xiold,i,pointlist,linelist,xmin,xmax,plot}, (* Keep track of max and min x to get the plot bounds *) xmin = xstart; xmax = xstart; fprime := D[f,x]; xi = N[xstart]; (* Put in the initial elements of the graphics lists *) pointlist={Point[N[{xstart,f/.x->xstart}]]}; linelist={}; For[i=1,i<=n,i++, xiold = xi; (* Save the old value of xi *) xi = xi-((f/fprime)/.x->xi); (* Use Newton's Method to find a better guess *) (* Draw the line and the new point *) pointlist=Append[pointlist,Point[{xi,f/.x->xi}]]; linelist=Append[linelist,Line[{{xiold,f/.x->xiold},{xi,0}}]]; (* Keep track of max and min x to get the plot bounds *) If[xixmax,xmax=xi,]; ]; (* First we plot the graph invisibly, adding some space on each end *) plot=Plot[f,{x,xmin-0.2(xmax-xmin),xmax+0.2(xmax-xmin)},\ DisplayFunction->Identity]; (* Then we plot all the desired information *) Show[Graphics[Join[{PointSize[0.02]},pointlist,linelist]],plot\ ,DisplayFunction->$DisplayFunction] ] Polyapprox[f_,x_,p_]:= (* This function will find the polynomial of least degree which passes through the points {x0,f(x0)},{x1,f(x1},... It will print this polynomial and then plot the polynomial on the same graph with f(x). Actually, the command Fit can be used to do the same thing.*) Block[{i,soln,pts,points,a,plot}, pts=Table[{p[[i]],f/.x->p[[i]]},{i,Length[p]}]; poly=Fit[pts,Table[x^i,{i,0,Length[p]-1}],x]; points=Table[Point[{p[[i]],poly/.x->p[[i]]}],{i,1,Length[p]}]; plot=Plot[{f,poly},{x,Min[p]-1,Max[p]+1},DisplayFunction->Identity]; Show[Graphics[{PointSize[0.02],points}],plot,\ DisplayFunction->$DisplayFunction]; poly ] Trapezoid[f_,{x_,xmin_,xmax_},n_]:= (* This routine will compute the numeric integral of the function f(x) on the interval [xmin,xmax], using the trapezoid method with n divisions. The numeric result and the error, or difference from the system NIntegrate, will be printed and the result returned will be a graph of the process.*) Block[{trap,error,i,j,rectlist,linelist,val,step,plot}, Array[val,n,0]; mp=0; step=(xmax-xmin)/n; val[0]=f/. x->xmin; For[j=0,j xmin+(j+1)*step]; j=.; trap=Sum[(val[i]+val[i+1])*step/2,{i,0,n-1}]; rectlist=Table[Polygon[{{xmin+j*step,0},{xmin+j*step,val[j]}\ ,{xmin+(j+1) step,val[j+1]},{xmin+(j+1) step,0}}],{j,0,n-1}]; linelist=Table[Line[{{xmin+j*step,0},{xmin+j*step,val[j]},\ {xmin+(j+1) step,val[j+1]},{xmin+(j+1) step,0}}],{j,0,n-1}]; rectlist=Prepend[rectlist,GrayLevel[0.6]]; linelist=Prepend[linelist,GrayLevel[0]]; plot=Plot[f,{x,xmin,xmax},DisplayFunction->Identity]; error=Abs[N[trap-NIntegrate[f,{x,xmin,xmax}]]]; Print["The integral is approximately ",N[trap]]; Print["error=",error]; N[trap]; Show[Graphics[Join[rectlist,linelist]],plot,\ DisplayFunction->$DisplayFunction] ] Trapezoid[f_,{x_,xmin_,xmax_},n_,nodraw]:= (* This routine will compute the numeric integral of the function f(x) on the interval [xmin,xmax], using the trapezoid method with n divisions. The error, or difference from the system NIntegrate, will be printed and the result returned will be the numeric result. *) Block[{trap,error,j,val,step}, Array[val,n,0]; mp=0; step=(xmax-xmin)/n; val[0]=f/. x->xmin; For[j=0,j xmin+(j+1)*step]; j=.; trap=Sum[(val[i]+val[i+1])*step/2,{i,0,n-1}]; error=Abs[N[trap-NIntegrate[f,{x,xmin,xmax}]]]; Print["error=",error]; N[trap] ] End[] EndPackage[] From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Mar 13 16:08:13 1990 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA24728; Tue, 13 Mar 90 16:08:11 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA00250; Tue, 13 Mar 90 16:08:08 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA11506; Tue, 13 Mar 90 16:08:07 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA24641; Tue, 13 Mar 90 13:57:07 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA24637; Tue, 13 Mar 90 13:57:05 -0600 Message-Id: <9003131957.AA24637@yoda.ncsa.uiuc.edu> To: mathgroup@yoda.ncsa.uiuc.edu Subject: Speeding up Mathematica Date: Tue, 13 Mar 90 03:26:30 -0500 From: ksuzuki@caen.engin.umich.edu Status: RO I am now playing with Mathematica, adding up several numerical algorithms. Capability of matrix and vector form and a lot of built-in functions makes codes so simple, compared to C and FORTRAN, its symbolic manupulating capa- bility enables what traditional languages could not do. (e.g. analytical differentiation when doing Newton Rapson algorithm) Also its capability of graphics makes results so easy to visualize. It is really epoch making software in the field of numerical analysis, needless to say, in the field of analytical mathematics. Its biggest drawback I felt, however, is its speed compared to compilable language like C or FORTRAN. I wonder if Wolfram Research is going to develop compiler of Mathematica. With compiler, Mathematica really can replace tradi- tional computer languages, but not now. Does anybody has infomation about compiler on Mathematica? Or any way to speeding up? Any comments? ---------------------------------------------------------------------------- Katsu Suzuki University of Michigan, Ann Arbor From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Mar 13 17:14:48 1990 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA24793; Tue, 13 Mar 90 17:14:46 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA01404; Tue, 13 Mar 90 17:14:44 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA13534; Tue, 13 Mar 90 17:14:42 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA24647; Tue, 13 Mar 90 13:58:17 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA24643; Tue, 13 Mar 90 13:58:15 -0600 Message-Id: <9003131958.AA24643@yoda.ncsa.uiuc.edu> Date: Tue, 13 Mar 90 12:46:20 EST From: rsarava@splash.Princeton.EDU (R Saravanan) To: mathgroup@yoda.ncsa.uiuc.edu Subject: supressing argument evaluation by function Part Status: RO I have been trying to define a formula using the variable "lamsq", which is a list to be defined later. When I give the following input lines to Mathematica- lhs = { { -(k^2 + lamsq[[n]]), lamsq[[n]] }, { lamsq[[n]], -(k^2 + lamsq[[n]]) } } rhs = { { -(k^2 + lamsq[[n]]) u1[[n]], lamsq[[n]] u1[[n]] }, { lamsq[[n]] u2[[n]], -(k^2 + lamsq[[n]]) u2[[n]] } } cmatrix[k_,n_] = Inverse[lhs] . rhs I get the following error messages- Part::selectform: Part specification n is neither an integer nor a list of nonzero integers. Part::selectform: Part specification n is neither an integer nor a list of nonzero integers. Part::selectform: Part specification n is neither an integer nor a list of nonzero integers. General::stop: Further output of Part::selectform will be suppressed during this calculation. Although the end result (i.e. "cmatrix") turns out to be what I want, I would like to avoid these error messages. Basically, I would like to prevent the function "Part" from evaluating the argument "n". One way out may be to define "lamsq" to be a function, rather than a list. But in my problem, "lamsq" actually happens to be a list of 33 numbers, and I would like to avoid defining auxiliary functions, unless I really have to. Does anybody have any comments/suggestions? Saravanan From 76446.564@compuserve.com Tue Mar 13 22:01:17 1990 Received: from saqqara.cis.ohio-state.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA24981; Tue, 13 Mar 90 22:01:12 -0600 Received: by saqqara.cis.ohio-state.edu (5.61-kk/5.900309) id AA13606; Tue, 13 Mar 90 23:01:04 -0500 Date: 13 Mar 90 22:06:58 EST From: James Spottiswoode <76446.564@compuserve.com> To: mathematica Subject: Re Speeding Computations Message-Id: <"900314030657 76446.564 EHA50-1"@CompuServe.COM> Status: RO In reply to K. Suzuki, Mathematica is indeed a wonderfully rich and powerful language. But I doubt that it will ever have the speed of a lower level language like Fortran 77, even if a compiled version were produced. I am new to the language,but I have found a couple of things which speed up numerical analysis: Avoid extracting elements of a list below the top level. Transpose or Flatten to get the required elements to the 'top' level. Substitute dot products for summing operations where possible, e.g. x = Table[i,{i,100}]; y = x; Sum[x[[i]] y[[i]],{i,100}]//Timing {0.7 Second, 338350} x.y //Timing {0.1 Second, 338350} Has anyone any other advice for speeding the thing up, except faster hardware??? From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Mar 14 00:34:43 1990 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA25790; Wed, 14 Mar 90 00:34:41 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA08204; Wed, 14 Mar 90 00:34:38 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA22030; Wed, 14 Mar 90 00:34:36 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA24998; Tue, 13 Mar 90 22:04:02 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA24994; Tue, 13 Mar 90 22:04:00 -0600 Message-Id: <9003140404.AA24994@yoda.ncsa.uiuc.edu> Date: 13 Mar 90 22:06:58 EST From: James Spottiswoode <76446.564@compuserve.com> To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Speeding Computations Status: RO In reply to K. Suzuki, Mathematica is indeed a wonderfully rich and powerful language. But I doubt that it will ever have the speed of a lower level language like Fortran 77, even if a compiled version were produced. I am new to the language,but I have found a couple of things which speed up numerical analysis: Avoid extracting elements of a list below the top level. Transpose or Flatten to get the required elements to the 'top' level. Substitute dot products for summing operations where possible, e.g. x = Table[i,{i,100}]; y = x; Sum[x[[i]] y[[i]],{i,100}]//Timing {0.7 Second, 338350} x.y //Timing {0.1 Second, 338350} Has anyone any other advice for speeding the thing up, except faster hardware??? From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Mar 14 11:21:29 1990 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA26041; Wed, 14 Mar 90 11:21:28 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA17156; Wed, 14 Mar 90 11:20:32 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA20812; Wed, 14 Mar 90 11:20:30 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA25938; Wed, 14 Mar 90 09:46:07 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA25934; Wed, 14 Mar 90 09:46:05 -0600 Message-Id: <9003141546.AA25934@yoda.ncsa.uiuc.edu> Date: Wed, 14 Mar 90 09:44:38 EST From: Jim_Wendel@ub.cc.umich.edu To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Speeding Computations Status: RO Apply[Plus,x[[i]]y[[i]],{i,100}] should be faster than Sum, but maybe not as fast as dot-product. I'll test it. Jim Wendel From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Mar 14 12:14:09 1990 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA26115; Wed, 14 Mar 90 12:14:07 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA17937; Wed, 14 Mar 90 12:13:13 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA22067; Wed, 14 Mar 90 12:13:11 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA25933; Wed, 14 Mar 90 09:45:57 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA25929; Wed, 14 Mar 90 09:45:55 -0600 Message-Id: <9003141545.AA25929@yoda.ncsa.uiuc.edu> Date: Wed, 14 Mar 90 09:40:28 EST From: Jim_Wendel@ub.cc.umich.edu To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Speeding up Mathematica Status: RO I heard just yesterday that a compiler is under development. No idea how far along they are. But since you can reformulate Mathematica notebooks in Fortran or in C it's not that bad. Jim Wendel From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Mar 14 13:13:57 1990 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA26253; Wed, 14 Mar 90 13:13:55 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA18819; Wed, 14 Mar 90 13:12:57 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA23335; Wed, 14 Mar 90 13:12:55 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA25960; Wed, 14 Mar 90 10:15:01 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA25956; Wed, 14 Mar 90 10:14:59 -0600 Message-Id: <9003141614.AA25956@yoda.ncsa.uiuc.edu> Date: Wed, 14 Mar 90 09:57:41 -0600 From: Steve Christensen To: mathgroup@yoda.ncsa.uiuc.edu Subject: Mailing list Status: RO Greetings, Mathematica mailing listers: As you no doubt have noticed, the mailing list volume has started to grow. I am approaching 500 sites on the list and am beginning to get requests from people connected via Compuserve, and Bitnet people from places outside the US like Brazil, Japan, Taiwan, Austria, Norway, Germany, Italy and others. I think a critical mass of people who want to participate actively may have been reached. I am also pleased to say that Wolfram Research people are taking an active part in answering questions that come up. I am beginning to get questions about local Mathematica User Groups. If you have started one or want to, send me details and I will try to coordinate with those folks in WRI who are interested in supporting these efforts. As always, we want to archive any public domain Mathematica software you produce, so please send that my way. Keep those email messages coming. Steve Christensen NCSA, Illinois From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Mar 14 14:17:56 1990 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA26494; Wed, 14 Mar 90 14:17:55 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA00922; Wed, 14 Mar 90 14:17:01 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA01103; Wed, 14 Mar 90 14:16:50 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA25989; Wed, 14 Mar 90 10:40:06 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA25985; Wed, 14 Mar 90 10:40:04 -0600 Message-Id: <9003141640.AA25985@yoda.ncsa.uiuc.edu> To: mathgroup@yoda.ncsa.uiuc.edu Subject: More on speeding things up Date: Wed, 14 Mar 90 08:33:19 PST From: jacobson@cello.hpl.hp.com Status: RO Suppose foo is a list. If possible avoid Do[ ... foo[[i]] ..., {i,1,Length[foo]}] Instead use Scan[(... # ....)&,foo] which we be much faster. If you need to know the index you are at for any reason, initialize a counter to 0 and increment it at the beginning of the function in Scan. On big arrays subscripting is VERY slow, and the reason is that foo[[i]] is really Part[foo,i] and Part[] evaluates it arguments. So at every access it looks over the *entire* array for something that might expand to something else. You can avoid this by making the list be something that won't evaluate. I've speeding things up by orders of magnitude (yes) with the following trick: First execute SetAttributes[HoldList,HoldAll] Suppose some code that I'll abbreviate xxxxxxx generates foo. Instead of writing foo = xxxxxxxx I write foo = Apply[HoldList,xxxxxxxxx] Now when I write foo[[i]], the Part function tries to evalute foo, but since it has the HoldAll attributed, it goes no farther. Most list manipulating functions will work on these homemade HoldList objects. But be careful with /. and Map because the subitituions/transformations will be made but not evaluated. I've reported this idea to WRI's support people. I'd like to see them make it official and fix the few places that requrire real List objects to accept HoldList objects as well. -- David Jacobson From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Mar 14 13:51:43 1990 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA26440; Wed, 14 Mar 90 13:51:42 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA00233; Wed, 14 Mar 90 13:49:57 CST Return-Path: Received: from uxc.cso.uiuc.edu by newton.ncsa.uiuc.edu (4.0/NCSA-1.2) id AA00182; Wed, 14 Mar 90 13:49:40 CST Received: from yoda.ncsa.uiuc.edu by uxc.cso.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA02651; Wed, 14 Mar 90 13:49:34 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA25979; Wed, 14 Mar 90 10:36:56 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA25975; Wed, 14 Mar 90 10:36:54 -0600 Message-Id: <9003141636.AA25975@yoda.ncsa.uiuc.edu> Date: Wed, 14 Mar 90 10:21:49 CST From: paul%wri@yoda.ncsa.uiuc.edu (Paul Abbott) Subject: Re: Speeding up Mathematica To: mathgroup@yoda.ncsa.uiuc.edu Status: RO Stephen Wolfram has done quite a bit of work on a function compiler for Mathematica which he hopes to make available for the next release. Also, you remark that you find Mathematica slow compared to Fortran and C. This remark has to be taken into context because the algebraic and diverse programming styles available in Mathematica mean that there are several ways of attacking a problem and these may be comparable or in many cases even faster than straight procedural programming. Paul Abbott Wolfram Research [I can fully support Paul's comments here. I tried for several years to write some pattern matchers in C to do some of my quantum field theory calculations. I was able to do the same work in Mathematica in a few weeks and with more power. True, the compiled C code ran a bit faster at first, but considering development time, Mathematica won easily. I have also found it to be a lot of fun to find tricky ways to optimize Mathematica code using lower level Mathematica functions. Conversations with Paul and others at WRI convince me that there are lots of nice techniques one can try. - SMC] From stevec Wed Mar 14 20:56:50 1990 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA26918; Wed, 14 Mar 90 20:56:49 -0600 Date: Wed, 14 Mar 90 20:56:49 -0600 From: Steve Christensen Message-Id: <9003150256.AA26918@yoda.ncsa.uiuc.edu> To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Re: Speeding up Mathematica Status: RO I believe that my comments on "tricky ways to optimize" Mathematica were misinterpreted. Most of the code that I and my colleagues write is very straightforward high level Mathematica programming - not nearly as sophisticated as in Roman's book most of the time. After we write prototype code to do some function, we may or may not hack on it to make it faster or more powerful. I think that it is the sign of a good system that permits a user to get to the depths a bit and make things work better. This is true in any computer language. If you have ever tried to write good vectorized FORTRAN code, you know what I mean. It is my feeling that Maeder's book is a wonderful resource for those Mathematica users who want to go the extra mile to get really powerful and elegant programs running. If Mathematica is judged by the number of "gotchas" it has, then I would hate to have to describe most of theoretical physics or mathematics which at first sight seem to be nothing but "gotchas". Steve Christensen From malcolm@apple.com Wed Mar 14 20:01:18 1990 Received: from apple.com by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA26887; Wed, 14 Mar 90 20:01:16 -0600 Received: by apple.com with SMTP (5.61/25-eef) id AA28856; Wed, 14 Mar 90 18:00:11 -0800 for mathgroup@yoda.ncsa.uiuc.edu Message-Id: <9003150200.AA28856@apple.com> To: paul@wri.UUCP (Paul Abbott) Cc: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Speeding up Mathematica In-Reply-To: Your message of Wed, 14 Mar 90 10:21:49 -0600. <9003141636.AA25975@yoda.ncsa.uiuc.edu> Date: Wed, 14 Mar 90 18:00:09 -0800 From: malcolm@apple.com Status: RO I guess these are Steve's Christianson's comments.... I have also found it to be a lot of fun to find tricky ways to optimize Mathematica code using lower level Mathematica functions. Conversations with Paul and others at WRI convince me that there are lots of nice techniques one can try. - SMC] OK...that's the last straw. I read Roman Maeder's book on Mathematica programming and found it to remind me of all the reasons I *don't* like Mathematica. It is a really well written book, don't get me wrong, but why should it be necessary? I don't consider a system to be good when you need to know lots of really minor details about syntax and when things get evaluated. Consider this little excerpt from the first page (67) I opened to: An expression with head Sequence is very elusive. You cannot even look at it with FullForm[]. The book is just filled with "tricky" things like this. I realize that there are good reasons for each of these little gotchas. But on the whole I think Mathematica has way too many of them. Other languages (Lisp, C, Prolog) don't seem to have this problem. I think this (and the cost) are the biggest weak points for Mathematica. I'm still a heavy Mathematica notebook user. These statements aren't any sort of Apple policy. I'm just wondering aloud. Malcolm From crm@summanulla.nbsr.duke.edu Wed Mar 14 14:30:41 1990 Received: from duke.cs.duke.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA26518; Wed, 14 Mar 90 14:30:39 -0600 Received: from nbsr.nbsr.duke.edu by duke.cs.duke.edu (5.59/DUKE/08-19-88) id AA08260; Wed, 14 Mar 90 15:29:38 EST Received: from summanulla.nbsr.duke.edu by nbsr.duke.edu (4.1/SMI-4.0) id AA29327; Wed, 14 Mar 90 15:28:36 EST Received: by summanulla.nbsr.duke.edu (4.1/SMI-4.0) id AA20520; Wed, 14 Mar 90 15:28:39 EST Date: Wed, 14 Mar 90 15:28:39 EST From: crm@summanulla.nbsr.duke.edu (Charles R. Martin) Message-Id: <9003142028.AA20520@summanulla.nbsr.duke.edu> To: paul@wri.UUCP Cc: mathgroup@yoda.ncsa.uiuc.edu In-Reply-To: <9003141636.AA25975@yoda.ncsa.uiuc.edu> "wri!paul@yoda.ncsa.uiuc.edu" Subject: Speeding up Mathematica Status: RO Paul, Steve -- I've been following the discussion of compiled functions vs. Mathematica with great interest. Some of you may recall I asked related questions several months ago; here's what I've found out: (1) It is surprisingly easy to get Mathematica to take a function worked out in Mathematica and then generate C. You all knew that. (2) Using a sed script or the like, the generated code can be munged into a C program that can run on the end of a pipe; this program can then be used to generate values that Mathematica can use. (3) The net gain in speed by doing this is about a factor of 50, INCLUDING COMPILATION AND LINK TIME. (This is all stuff that was done by Vick Khera here at Duke. He's supposed to be writing a paper on it, but I haven't seen it yet.) Now, I understand these codes to be heavily numerical, so this speedup can't be applied to the pattern-matching problem Steve mentions. That factor of fifty, though, makes me suspicious that the gains to be gotten by fancy Mathematica optimizations are never going to give the gains that can be had by running the function in compiled code. Worse, running things at the end of a pipe is not available on all systems (e.g., the 386, at least with version 1.2) so this technique can't be directly applied. There are a number of applications that I would be interested in, mostly in biological modelling, that this kind of speedup would make all the difference between a usuable interactive program (a few minutes to an hour) and imitation batch mode (many hours or overnight.) A Mathematica compiler might mean a gain, but what I'd *really* like to see is some way of building C codes that fit some calling convention, and that can be linked with or dynamically loaded into Mathematica. Then I could build fast numerical methods from known algorithms, optimize them for greater speed, and call them from Mathematica as primitives. While there ae a lot of nice techniques for optimizing Mathematica functions, most of my users aren't interested in learning the joys of Mathematica hacking; they want to know what that organelle/cell/chunk of myocardium is doing. Being able to call a Crank-Nicholson solver that was *fast* might make a lot of problems a lot easier for the users I might recommend Mathematica to. (Gack what a horrible sentence.) Charlie Martin (...!mcnc!duke!crm, crm@summanulla.mc.duke.edu) NBSR/Box 3709/Duke University Medical Center/Durham, NC 27710 P.S. Let me know about Mathematica users groups. From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Mar 14 22:53:16 1990 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA27086; Wed, 14 Mar 90 22:53:15 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA08070; Wed, 14 Mar 90 22:52:20 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA12268; Wed, 14 Mar 90 22:52:09 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA26981; Wed, 14 Mar 90 21:21:17 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA26977; Wed, 14 Mar 90 21:21:16 -0600 Message-Id: <9003150321.AA26977@yoda.ncsa.uiuc.edu> Date: Wed, 14 Mar 90 20:56:49 -0600 From: Steve Christensen To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Re: Speeding up Mathematica Status: RO In reference to Malcolm@apply.com's comments: I believe that my comments on "tricky ways to optimize" Mathematica were misinterpreted. Most of the code that I and my colleagues write is very straightforward high level Mathematica programming - not nearly as sophisticated as in Roman's book most of the time. After we write prototype code to do some function, we may or may not hack on it to make it faster or more powerful. I think that it is the sign of a good system that permits a user to get to the depths a bit and make things work better. This is true in any computer language. If you have ever tried to write good vectorized FORTRAN code, you know what I mean. It is my feeling that Maeder's book is a wonderful resource for those Mathematica users who want to go the extra mile to get really powerful and elegant programs running. If Mathematica is judged by the number of "gotchas" it has, then I would hate to have to describe most of theoretical physics or mathematics which at first sight seem to be nothing but "gotchas". Steve Christensen From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Mar 15 01:16:05 1990 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA28038; Thu, 15 Mar 90 01:16:04 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA11262; Thu, 15 Mar 90 01:15:05 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA16192; Thu, 15 Mar 90 01:14:54 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA26986; Wed, 14 Mar 90 21:21:24 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA26982; Wed, 14 Mar 90 21:21:23 -0600 Message-Id: <9003150321.AA26982@yoda.ncsa.uiuc.edu> Date: Wed, 14 Mar 90 15:28:39 EST From: crm@summanulla.nbsr.duke.edu (Charles R. Martin) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Speeding up Mathematica Status: RO Paul, Steve -- I've been following the discussion of compiled functions vs. Mathematica with great interest. Some of you may recall I asked related questions several months ago; here's what I've found out: (1) It is surprisingly easy to get Mathematica to take a function worked out in Mathematica and then generate C. You all knew that. (2) Using a sed script or the like, the generated code can be munged into a C program that can run on the end of a pipe; this program can then be used to generate values that Mathematica can use. (3) The net gain in speed by doing this is about a factor of 50, INCLUDING COMPILATION AND LINK TIME. (This is all stuff that was done by Vick Khera here at Duke. He's supposed to be writing a paper on it, but I haven't seen it yet.) Now, I understand these codes to be heavily numerical, so this speedup can't be applied to the pattern-matching problem Steve mentions. That factor of fifty, though, makes me suspicious that the gains to be gotten by fancy Mathematica optimizations are never going to give the gains that can be had by running the function in compiled code. Worse, running things at the end of a pipe is not available on all systems (e.g., the 386, at least with version 1.2) so this technique can't be directly applied. There are a number of applications that I would be interested in, mostly in biological modelling, that this kind of speedup would make all the difference between a usuable interactive program (a few minutes to an hour) and imitation batch mode (many hours or overnight.) A Mathematica compiler might mean a gain, but what I'd *really* like to see is some way of building C codes that fit some calling convention, and that can be linked with or dynamically loaded into Mathematica. Then I could build fast numerical methods from known algorithms, optimize them for greater speed, and call them from Mathematica as primitives. While there ae a lot of nice techniques for optimizing Mathematica functions, most of my users aren't interested in learning the joys of Mathematica hacking; they want to know what that organelle/cell/chunk of myocardium is doing. Being able to call a Crank-Nicholson solver that was *fast* might make a lot of problems a lot easier for the users I might recommend Mathematica to. (Gack what a horrible sentence.) Charlie Martin (...!mcnc!duke!crm, crm@summanulla.mc.duke.edu) NBSR/Box 3709/Duke University Medical Center/Durham, NC 27710 P.S. Let me know about Mathematica users groups. From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Mar 15 00:05:52 1990 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA27907; Thu, 15 Mar 90 00:05:51 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA09224; Thu, 15 Mar 90 00:04:41 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA14127; Thu, 15 Mar 90 00:04:28 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA26976; Wed, 14 Mar 90 21:21:10 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA26972; Wed, 14 Mar 90 21:21:09 -0600 Message-Id: <9003150321.AA26972@yoda.ncsa.uiuc.edu> To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Speeding up Mathematica Date: Wed, 14 Mar 90 18:00:09 -0800 From: malcolm@apple.com Status: RO I guess these are Steve's Christensen's comments.... I have also found it to be a lot of fun to find tricky ways to optimize Mathematica code using lower level Mathematica functions. Conversations with Paul and others at WRI convince me that there are lots of nice techniques one can try. - SMC] OK...that's the last straw. I read Roman Maeder's book on Mathematica programming and found it to remind me of all the reasons I *don't* like Mathematica. It is a really well written book, don't get me wrong, but why should it be necessary? I don't consider a system to be good when you need to know lots of really minor details about syntax and when things get evaluated. Consider this little excerpt from the first page (67) I opened to: An expression with head Sequence is very elusive. You cannot even look at it with FullForm[]. The book is just filled with "tricky" things like this. I realize that there are good reasons for each of these little gotchas. But on the whole I think Mathematica has way too many of them. Other languages (Lisp, C, Prolog) don't seem to have this problem. I think this (and the cost) are the biggest weak points for Mathematica. I'm still a heavy Mathematica notebook user. These statements aren't any sort of Apple policy. I'm just wondering aloud. Malcolm From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Mar 15 00:12:40 1990 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA27914; Thu, 15 Mar 90 00:12:39 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA10390; Thu, 15 Mar 90 00:11:44 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA14870; Thu, 15 Mar 90 00:11:32 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA26991; Wed, 14 Mar 90 21:21:33 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA26987; Wed, 14 Mar 90 21:21:31 -0600 Message-Id: <9003150321.AA26987@yoda.ncsa.uiuc.edu> Date: Wed, 14 Mar 90 15:17:25 MST From: Rod Frehlich To: mathgroup@yoda.ncsa.uiuc.edu Subject: Complex I Status: RO The strange convention of placing negative signs with the complex number I produces errors with substitutions. For example, the following program AppendTo[$Echo, "stdout"] (* Error in Rules *) a = I*x/f-I*x/g+z a = a /.{x_/f-x_/g -> x/h} (* Error disappears if I is replaced by a variable *) b = v*x/f-v*x/g+z b = b /.{x_/f-x_/g -> x/h} results in Mathematica (sun3.68881) 1.2 (November 6, 1989) [With pre-loaded data] by S. Wolfram, D. Grayson, R. Maeder, H. Cejtin, S. Omohundro, D. Ballman and J. Keiper with I. Rivin and D. Withoff Copyright 1988,1989 Wolfram Research Inc. -- Terminal graphics initialized -- In[1]:= Out[1]= {stdout} In[2]:= (* Error in Rules *) In[3]:= a = I*x/f-I*x/g+z I x -I x Out[3]= --- + ---- + z f g In[4]:= a = a /.{x_/f-x_/g -> x/h} I x -I x Out[4]= --- + ---- + z f g In[5]:= (* Error disappears if I is replaced by a variable *) In[6]:= b = v*x/f-v*x/g+z v x v x Out[6]= --- - --- + z f g In[7]:= b = b /.{x_/f-x_/g -> x/h} v x Out[7]= --- + z h In[8]:= From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Mar 15 01:37:09 1990 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA28095; Thu, 15 Mar 90 01:37:08 -0600 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA11666; Thu, 15 Mar 90 01:36:15 CST Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA16646; Thu, 15 Mar 90 01:36:04 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA27044; Wed, 14 Mar 90 22:09:42 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA27040; Wed, 14 Mar 90 22:09:40 -0600 Message-Id: <9003150409.AA27040@yoda.ncsa.uiuc.edu> From: paul@wri.UUCP Date: Wed, 14 Mar 90 20:23:35 CST Subject: Re: Speeding up Mathematica To: mathgroup@yoda.ncsa.uiuc.edu Status: RO You may not be aware that preliminary documentation for the the MathLink protocol for Mathematica has been released (Please contact WRI, via lisa@wri.com for a copy of the documentation). MathLink will be included with the next release of Mathematica and, I think, will supply solutions to many of the problems that people have with linking Mathematica to running processes, calling Mathematica from C or Fortran and vice versa, etc ... Also, one of our users, Elaine Kant from Schlumberger (uunet!SLCS.SLB.COM!kant) is doing some of the things that you are also interested in. From @wimsey.bc.ca:kenward@mdivax1.UUCP Thu Mar 15 12:43:32 1990 Received: from van-bc.wimsey.bc.ca by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA28553; Thu, 15 Mar 90 12:42:52 -0600 Received: by wimsey.bc.ca (/\=-/\ Smail3.1.17.5 #17.80 sendmail) id ; Thu, 15 Mar 90 10:40 PST Received: by mdivax1.mdi.eng (5.57/SMI-3.2) id AA13597; Thu, 15 Mar 90 08:46:02 PST Received: by sun05f.mdi.eng (4.0/SMI-4.0) id AA10353; Thu, 15 Mar 90 08:46:42 PST Date: Thu, 15 Mar 90 08:46:42 PST From: kenward%mdivax1@van-bc.UUCP (Gary Kenward) Message-Id: <9003151646.AA10353@sun05f.mdi.eng> To: mathgroup-adm@yoda.ncsa.uiuc.edu Subject: Mathematica precision Status: RO How can I set the precision for a group of calculations: i.e. how can I set the precison of all my calculations for a Mathematica session; how can I set the precision for all calculations withing a function definition? I am sure this is in the text somewhere, but as yet, I have not been able to determine where. Thanks, Gary W. Kenward Radio Network Systems Engineering Mobile Data International, Inc. (a Motorola company) From @uunet.UU.NET:m1rih00@fed.UUCP Thu Mar 15 11:19:12 1990 Received: from uunet.UU.NET by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA28464; Thu, 15 Mar 90 11:19:09 -0600 Received: from fed.UUCP by uunet.uu.net (5.61/1.14) with UUCP id AA28583; Thu, 15 Mar 90 12:17:25 -0500 Received: from arcws9.FRB.GOV by fed.FRB.GOV (4.0/SMI-4.0) id AA06366; Thu, 15 Mar 90 11:45:50 EST Received: from localhost by arcws9.FRB.GOV (4.0/SMI-4.0) id AA14868; Thu, 15 Mar 90 11:46:55 EST Message-Id: <9003151646.AA14868@arcws9.FRB.GOV> To: mathgroup@yoda.ncsa.uiuc.edu Cc: m1rih00@arcws9.UUCP Subject: Mathematica User Group in Econometrics Date: Thu, 15 Mar 90 11:46:53 -0500 From: Ron I. Herman Status: RO Is there any Mathematica User Group primarily devoted to econometric applications? Ron Herman Federal Reserve Board From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Mar 15 17:26:54 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA28859; Thu, 15 Mar 90 17:26:53 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA06623; Thu, 15 Mar 90 17:22:08 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA28724; Thu, 15 Mar 90 15:38:28 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA28720; Thu, 15 Mar 90 15:38:27 -0600 Message-Id: <9003152138.AA28720@yoda.ncsa.uiuc.edu> To: mathgroup@yoda.ncsa.uiuc.edu Subject: Mathematica User Group in Econometrics Date: Thu, 15 Mar 90 11:46:53 -0500 From: Ron I. Herman Status: RO Is there any Mathematica User Group primarily devoted to econometric applications? Ron Herman Federal Reserve Board From mcdonald@quark.UMD.EDU Thu Mar 15 16:44:18 1990 Received: from quark.umd.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA28785; Thu, 15 Mar 90 16:44:16 -0600 Received: by quark.UMD.EDU (5.57/Ultrix3.0-C) id AA05364; Thu, 15 Mar 90 17:45:20 EST Date: Thu, 15 Mar 90 17:45:20 EST From: mcdonald@quark.umd.edu (Bill MacDonald) Message-Id: <9003152245.AA05364@quark.UMD.EDU> To: mathgroup@yoda.ncsa.uiuc.edu Subject: Problem defining delta function Status: RO I began to try to define the delta function, but the first step fails. Why? delta/: delta[x_]f_[x_]:=delta[x]f[0] Then if f[x_]=(x-a)^2 and I try delta[x]f[x] Mathematica simply gives back (-a + x)^2 delta[x] What is wrong ? From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Mar 15 18:32:43 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA28957; Thu, 15 Mar 90 18:32:42 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA07772; Thu, 15 Mar 90 18:27:57 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA28718; Thu, 15 Mar 90 15:37:44 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA28714; Thu, 15 Mar 90 15:37:43 -0600 Message-Id: <9003152137.AA28714@yoda.ncsa.uiuc.edu> Date: Thu, 15 Mar 90 08:46:42 PST From: kenward@mdivax1.UUCP (Gary Kenward) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Mathematica precision Status: RO How can I set the precision for a group of calculations: i.e. how can I set the precison of all my calculations for a Mathematica session; how can I set the precision for all calculations withing a function definition? I am sure this is in the text somewhere, but as yet, I have not been able to determine where. Thanks, Gary W. Kenward Radio Network Systems Engineering Mobile Data International, Inc. (a Motorola company) From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Mar 15 19:26:05 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA29063; Thu, 15 Mar 90 19:26:04 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA08622; Thu, 15 Mar 90 19:21:20 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA28878; Thu, 15 Mar 90 17:43:25 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA28874; Thu, 15 Mar 90 17:43:23 -0600 Message-Id: <9003152343.AA28874@yoda.ncsa.uiuc.edu> Date: Thu, 15 Mar 90 17:45:20 EST From: mcdonald@quark.umd.edu (Bill MacDonald) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Problem defining delta function Status: RO I began to try to define the delta function, but the first step fails. Why? delta/: delta[x_]f_[x_]:=delta[x]f[0] Then if f[x_]=(x-a)^2 and I try delta[x]f[x] Mathematica simply gives back (-a + x)^2 delta[x] What is wrong ? From 76446.564@compuserve.com Tue Mar 13 22:01:17 1990 Received: from saqqara.cis.ohio-state.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA24981; Tue, 13 Mar 90 22:01:12 -0600 Received: by saqqara.cis.ohio-state.edu (5.61-kk/5.900309) id AA13606; Tue, 13 Mar 90 23:01:04 -0500 Date: 13 Mar 90 22:06:58 EST From: James Spottiswoode <76446.564@compuserve.com> To: mathematica Subject: Re Speeding Computations Message-Id: <"900314030657 76446.564 EHA50-1"@CompuServe.COM> Status: RO In reply to K. Suzuki, Mathematica is indeed a wonderfully rich and powerful language. But I doubt that it will ever have the speed of a lower level language like Fortran 77, even if a compiled version were produced. I am new to the language,but I have found a couple of things which speed up numerical analysis: Avoid extracting elements of a list below the top level. Transpose or Flatten to get the required elements to the 'top' level. Substitute dot products for summing operations where possible, e.g. x = Table[i,{i,100}]; y = x; Sum[x[[i]] y[[i]],{i,100}]//Timing {0.7 Second, 338350} x.y //Timing {0.1 Second, 338350} Has anyone any other advice for speeding the thing up, except faster hardware??? From @uunet.UU.NET:paul@wri.UUCP Fri Mar 16 01:19:29 1990 To: kenward@yoda.ncsa.uiuc.edu Subject: Re: Mathematica precision Cc: mathgroup@uunet.UU.NET Status: RO Gary Kenward asks: > How can I set the precision for a group of calculations: > i.e. how can I set the precison of all my calculations for > a Mathematica session; how can I set the precision for > all calculations within a function definition? > > I am sure this is in the text somewhere, but as yet, > I have not been able to determine where. There are many ways of doing what you want: One (global) method would be to set $Pre = N[#,30]& which will numerically evaluate all expressions to 30 decimals from that point onward. Jerry Keiper from Wolfram Research has recently written up some tutorial notes on related topics which may be helpful. These can be obtained by contacting the marketing department at Wolfram Research (try lisa@wri.com). Paul C. Abbott From mathgroup-adm@yoda.ncsa.uiuc.edu Sun Mar 18 00:18:10 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA02891; Sun, 18 Mar 90 00:18:09 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA14825; Sun, 18 Mar 90 00:13:28 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA02092; Sat, 17 Mar 90 21:57:43 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA02088; Sat, 17 Mar 90 21:57:42 -0600 Date: Fri, 16 Mar 90 01:19:29 -0600 From: Steve Christensen Message-Id: <9003180357.AA02088@yoda.ncsa.uiuc.edu> Subject: Re: Mathematica precision To: mathgroup@yoda.ncsa.uiuc.edu Status: RO Gary Kenward asks: > How can I set the precision for a group of calculations: > i.e. how can I set the precison of all my calculations for > a Mathematica session; how can I set the precision for > all calculations within a function definition? > > I am sure this is in the text somewhere, but as yet, > I have not been able to determine where. There are many ways of doing what you want: One (global) method would be to set $Pre = N[#,30]& which will numerically evaluate all expressions to 30 decimals from that point onward. Jerry Keiper from Wolfram Research has recently written up some tutorial notes on related topics which may be helpful. These can be obtained by contacting the marketing department at Wolfram Research (try lisa@wri.com). Paul C. Abbott From jack@sun.acs.udel.edu Fri Mar 16 09:46:54 1990 To: mathgroup@yoda.ncsa.uiuc.edu, mcdonald@quark.umd.edu Subject: Re: Problem defining delta function Status: RO The following is not exactly the form you had, but gives the result you want. SetAttributes[delta,HoldAll] delta/: delta[f_[x_]]:=delta[x]f[0] Then, f[x_]:=(x-a)^2 delta[f[x]] gives 2 a delta[x] From fateman@renoir.Berkeley.EDU Sun Mar 18 14:59:45 1990 Received: from renoir.Berkeley.EDU by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA03625; Sun, 18 Mar 90 14:59:43 -0600 Received: by renoir.Berkeley.EDU (5.61/1.29) id AA00731; Sun, 18 Mar 90 12:58:50 -0800 Date: Sun, 18 Mar 90 12:58:50 -0800 From: fateman@renoir.Berkeley.EDU (Richard Fateman) Message-Id: <9003182058.AA00731@renoir.Berkeley.EDU> To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Speeding up Mathematica / numerical precision Status: RO The idea of sharing data structures (such as fortran arrays) between algebraic manipulation programs and Fortran / C stuff was promoted by Franz Lisp / Vaxima (c. 1979) when we decided to have the same structures for convenience of "foreign function" calls. I assumed that no Lisp compiler would do as good as the best Fortran compiler in compiling numerical code. Direct links to fortran code (NAG library, IMSL library, MINPACK) were handled fairly conveniently. About using N[ ...,30] around everything... this may not work because in Mathematica, f[N[...,30]] and N[f[...],30] are not the same. Richard Fateman From mathgroup-adm@yoda.ncsa.uiuc.edu Sun Mar 18 17:06:41 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA03718; Sun, 18 Mar 90 17:06:40 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA00475; Sun, 18 Mar 90 17:01:58 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA03641; Sun, 18 Mar 90 15:17:12 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA03637; Sun, 18 Mar 90 15:17:11 -0600 Message-Id: <9003182117.AA03637@yoda.ncsa.uiuc.edu> Date: Sun, 18 Mar 90 12:58:50 -0800 From: fateman@renoir.Berkeley.EDU (Richard Fateman) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Speeding up Mathematica / numerical precision Status: RO The idea of sharing data structures (such as fortran arrays) between algebraic manipulation programs and Fortran / C stuff was promoted by Franz Lisp / Vaxima (c. 1979) when we decided to have the same structures for convenience of "foreign function" calls. I assumed that no Lisp compiler would do as good as the best Fortran compiler in compiling numerical code. Direct links to fortran code (NAG library, IMSL library, MINPACK) were handled fairly conveniently. About using N[ ...,30] around everything... this may not work because in Mathematica, f[N[...,30]] and N[f[...],30] are not the same. Richard Fateman From dmaria@gmuvax.gmu.edu Mon Mar 19 12:35:13 1990 Received: from gmuvax.gmu.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA05212; Mon, 19 Mar 90 12:35:11 -0600 Message-Id: <9003191835.AA05212@yoda.ncsa.uiuc.edu> Date: 19 Mar 90 13:32:00 EDT From: "MARIA DWORZECKA" Subject: Mathematica To: "stevec" Status: RO Hello, My name is Maria Dworzecka (DMARIA@GMUVAX.Bitnet). I was told, that you run newsletter and some friendly help for new users of Mathematica. Please, add my name to your mailing list. I surely can use some help.!!! Regards and Thanks Maria From @uunet.UU.NET:paul@wri.UUCP Thu Mar 22 00:01:56 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA08960; Thu, 22 Mar 90 00:01:55 -0600 Return-Path: Received: from uunet.uu.net by newton.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA14821; Thu, 22 Mar 90 00:01:01 CST Received: from wri.UUCP by uunet.uu.net (5.61/1.14) with UUCP id AA04339; Thu, 22 Mar 90 01:00:24 -0500 Received: by WRI.com (3.2/SMI-3.0DEV3) id AA02791; Mon, 19 Mar 90 15:06:47 CST Date: Mon, 19 Mar 90 15:06:47 CST From: paul@wri.UUCP (Paul Abbott) Message-Id: <9003192106.AA02791@WRI.com> To: fateman@renoir.Berkeley.EDU Subject: Re: Speeding up Mathematica / numerical precision Cc: mathgroup@uunet.UU.NET Status: RO Richard Fateman states: > About using N[ ...,30] around everything... this may not work > because in Mathematica, f[N[...,30]] and N[f[...],30] are not the same. This is correct and reveals a subtle point about the use of N in Mathematica. Jerry Keiper's tutorial notes on this topic (available, as mentioned previously, directly from Wolfram Research) help to clarify this matter further. Paul C. Abbott From @uunet.UU.NET:paul@wri.UUCP Thu Mar 22 00:03:52 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA08966; Thu, 22 Mar 90 00:03:50 -0600 Return-Path: Received: from uunet.uu.net by newton.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA15228; Thu, 22 Mar 90 00:02:57 CST Received: from wri.UUCP by uunet.uu.net (5.61/1.14) with UUCP id AA05544; Thu, 22 Mar 90 01:02:18 -0500 Received: by WRI.com (3.2/SMI-3.0DEV3) id AA05909; Mon, 19 Mar 90 18:00:46 CST Date: Mon, 19 Mar 90 18:00:46 CST From: paul@wri.UUCP (Paul Abbott) Message-Id: <9003200000.AA05909@WRI.com> To: mathgroup@uunet.UU.NET Subject: Tutorial Notes Cc: @uunet.UUCP,@uunet.UU.NET, leonard@cosmos.phys.uwm.edu, jack@sun.acs.udel.edu Status: RO Sorry if I have created any confusion. The tutorial notes that I mentioned in previous messages to mathgroup are the same ones that many of you may have already heard about on sci.math.symbolic. If you want to order any of these, please fill out the following (electronic) form and send it to any of the addresses listed below: 1990 MATHEMATICA CONFERENCE Order Form for Tutorials and Conference Guide ============================================= Fill out this form using your editor and return to Wolfram Research. (See address information below.) TUTORIALS: --------- Algebraic Manipulation Igor Rivin (9 pages) Printed $1.70 each quantity [ ] Macintosh diskette $4.50 each quantity [ ] Applications Survey Paul Abbott (27 pages) Printed $2.10 each quantity [ ] Macintosh diskette $4.50 each quantity [ ] Data Analysis Dave Withoff (36 pages) Printed $2.50 each quantity [ ] Developing Mathematical and Scientific Software Sha Xin Wei (12 pages) Printed $1.70 each quantity [ ] Macintosh diskette $4.50 quantity [ ] Document Preparation Joe Grohens, Cameron Smith (6 pages) Printed $1.70 each quantity [ ] Macintosh diskette $4.50 each quantity [ ] Graphics Cameron Smith (14 pages) Printed $1.70 each quantity [ ] Macintosh diskette $4.50 each quantity [ ] Interfacing to External Programs (MathLink documentation) Henry Cejtin, Stephen Wolfram (37 pages) Printed $2.50 each quantity [ ] Internals and Algorithms Igor Rivin (9 pages) Printed $1.70 each quantity [ ] Macintosh diskette $4.50 each Networking Rob Brewer, Rory Murtagh (79 pages) Mac/TCP Installation Kit: $14.00 quantity [ ] Numerical Computation Jerry Keiper (22 pages) Printed $2.10 each quantity [ ] Problem Solving with Mathematica Nancy Blachman (73 pages) Printed $4.80 each quantity [ ] Programming in Mathematica Roman Maeder (44 pages) (excerpts from his book) Printed $2.90 each quantity [ ] OTHER: ------ Conference Guide: $25.00 each quantity [ ] Conference T-shirts: $10.00 each Large: quantity [ ] Extra Large: quantity [ ] Conference Buttons: free quantity [ ] Conference Posters: free quantity [ ] Shipping and handling included for U.S. and Canada. For overseas shipping, add $2.50: $ Illinois residents add 7.25% sales tax: $ Total Amount: $ --------------------------------------------------------------- Name: Organization: Street address: City: State: Zip: Country: Telephone (include area and country codes): Email address: Fax: [ ] Check enclosed, in U.S. dollars, payable to Wolfram Research, Inc. [ ] Bill my credit card (check one): [ ] Visa [ ] MasterCard Card number: Expr. date: Name printed: Date: Signature: Return completed order forms by mail, fax, or electronic mail to: Wolfram Research, Inc. P.O. Box 6059, Champaign, IL 61826-6059 info: (217) 398-0700 fax: (217) 398-0747 email: conf@wri.com, or uunet!wri!conf From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Mar 22 04:57:05 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA09182; Thu, 22 Mar 90 04:57:04 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA21174; Thu, 22 Mar 90 04:52:34 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA09038; Thu, 22 Mar 90 01:17:04 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA09034; Thu, 22 Mar 90 01:17:03 -0600 Message-Id: <9003220717.AA09034@yoda.ncsa.uiuc.edu> Date: Mon, 19 Mar 90 18:00:46 CST From: paul@wri.UUCP (Paul Abbott) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Tutorial Notes Status: RO Sorry if I have created any confusion. The tutorial notes that I mentioned in previous messages to mathgroup are the same ones that many of you may have already heard about on sci.math.symbolic. If you want to order any of these, please fill out the following (electronic) form and send it to any of the addresses listed below: 1990 MATHEMATICA CONFERENCE Order Form for Tutorials and Conference Guide ============================================= Fill out this form using your editor and return to Wolfram Research. (See address information below.) TUTORIALS: --------- Algebraic Manipulation Igor Rivin (9 pages) Printed $1.70 each quantity [ ] Macintosh diskette $4.50 each quantity [ ] Applications Survey Paul Abbott (27 pages) Printed $2.10 each quantity [ ] Macintosh diskette $4.50 each quantity [ ] Data Analysis Dave Withoff (36 pages) Printed $2.50 each quantity [ ] Developing Mathematical and Scientific Software Sha Xin Wei (12 pages) Printed $1.70 each quantity [ ] Macintosh diskette $4.50 quantity [ ] Document Preparation Joe Grohens, Cameron Smith (6 pages) Printed $1.70 each quantity [ ] Macintosh diskette $4.50 each quantity [ ] Graphics Cameron Smith (14 pages) Printed $1.70 each quantity [ ] Macintosh diskette $4.50 each quantity [ ] Interfacing to External Programs (MathLink documentation) Henry Cejtin, Stephen Wolfram (37 pages) Printed $2.50 each quantity [ ] Internals and Algorithms Igor Rivin (9 pages) Printed $1.70 each quantity [ ] Macintosh diskette $4.50 each Networking Rob Brewer, Rory Murtagh (79 pages) Mac/TCP Installation Kit: $14.00 quantity [ ] Numerical Computation Jerry Keiper (22 pages) Printed $2.10 each quantity [ ] Problem Solving with Mathematica Nancy Blachman (73 pages) Printed $4.80 each quantity [ ] Programming in Mathematica Roman Maeder (44 pages) (excerpts from his book) Printed $2.90 each quantity [ ] OTHER: ------ Conference Guide: $25.00 each quantity [ ] Conference T-shirts: $10.00 each Large: quantity [ ] Extra Large: quantity [ ] Conference Buttons: free quantity [ ] Conference Posters: free quantity [ ] Shipping and handling included for U.S. and Canada. For overseas shipping, add $2.50: $ Illinois residents add 7.25% sales tax: $ Total Amount: $ --------------------------------------------------------------- Name: Organization: Street address: City: State: Zip: Country: Telephone (include area and country codes): Email address: Fax: [ ] Check enclosed, in U.S. dollars, payable to Wolfram Research, Inc. [ ] Bill my credit card (check one): [ ] Visa [ ] MasterCard Card number: Expr. date: Name printed: Date: Signature: Return completed order forms by mail, fax, or electronic mail to: Wolfram Research, Inc. P.O. Box 6059, Champaign, IL 61826-6059 info: (217) 398-0700 fax: (217) 398-0747 email: conf@wri.com, or uunet!wri!conf From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Mar 22 04:21:40 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA09146; Thu, 22 Mar 90 04:21:39 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA20666; Thu, 22 Mar 90 04:17:09 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA09032; Thu, 22 Mar 90 01:16:07 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA09028; Thu, 22 Mar 90 01:16:06 -0600 Message-Id: <9003220716.AA09028@yoda.ncsa.uiuc.edu> Date: Mon, 19 Mar 90 15:06:47 CST From: paul@wri.UUCP (Paul Abbott) Subject: Re: Speeding up Mathematica / numerical precision To: mathgroup@yoda.ncsa.uiuc.edu Status: RO Richard Fateman states: > About using N[ ...,30] around everything... this may not work > because in Mathematica, f[N[...,30]] and N[f[...],30] are not the same. This is correct and reveals a subtle point about the use of N in Mathematica. Jerry Keiper's tutorial notes on this topic (available, as mentioned previously, directly from Wolfram Research) help to clarify this matter further. Paul C. Abbott From jacobson@cello.hpl.hp.com Thu Mar 22 10:22:10 1990 Received: from hplms2.hpl.hp.com by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA09341; Thu, 22 Mar 90 10:22:02 -0600 Received: from cello.hpl.hp.com by hplms2.hpl.hp.com with SMTP (15.11.1.3/15.5+IOS 3.20) id AA21083; Thu, 22 Mar 90 08:21:14 pst Received: from localhost by cello.HPL.HP.COM; Thu, 22 Mar 90 08:20:58 pst To: mathgroup@yoda.ncsa.uiuc.edu Subject: N Date: Thu, 22 Mar 90 08:20:47 PST Message-Id: <20238.638122847@cello> From: jacobson@cello.hpl.hp.com Status: RO There has been discussion recently about using N[...,30] around everything. It is been observed by Richard Fateman and confirmed by Paul Abbott that this may not work because f[N[...,30]] and N[f[...],30] are not the same. However there is a much more important reason why it won't work. N only reduces the accuracy of its first argument, it never increases it. Note the following: In[1]:= N[1.2,30] Out[1]= 1.2 In[2]:= Precision[%] Out[2]= 16 To get N to work right on decimal things I have to rewrite them as rationals, or use lots of zeros, then apply N. In[3]:= N[12/10,30] Out[3]= 1.2 In[4]:= Precision[%] Out[4]= 30 You can force the accuracy up by SetPrecision or SetAccuracy, but beware, because the number was first converted to binary in low precision form before SetPrecision or SetAccuracy got to it. So you are declaring an inaccurate value to be accurate. In[8]:= SetPrecision[1.2,30] Out[8]= 1.19999999999999995559107901499 In[9]:= Precision[%] Out[9]= 30 I know of no way to make the Mathematica "reader" convert decimal input to high accuracy other than appending a long string of zeros. If anybody know of a way, please speak up. -- David Jacobson From @vmd.cso.uiuc.edu:AN123651@UTHVM1.BITNET Thu Mar 22 12:42:28 1990 Received: from vmd.cso.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA09486; Thu, 22 Mar 90 12:42:26 -0600 Message-Id: <9003221842.AA09486@yoda.ncsa.uiuc.edu> Received: from UTHVM1.BITNET by VMD.CSO.UIUC.EDU (IBM VM SMTP R1.2) with BSMTP id 6166; Thu, 22 Mar 90 12:43:10 CST Received: from UTHVM1 (AN123651) by UTHVM1.BITNET (Mailer R2.05) with BSMTP id 8630; Thu, 22 Mar 90 12:41:47 CST Date: Thu, 22 Mar 90 12:41:28 CST From: "E. Neely Atkinson" Subject: D and Derivative - help please To: mathgroup@yoda.ncsa.uiuc.edu Status: RO I would appreciate some help with this from anyone who understands Mathematica better than I. Suppose I define a function: f[x_,y_] := x + y + Gamma[x,y] When I take its derivative using D, everything is fine. D[f[x,y],x] (1,0) 1 + Gamma [x, y] Derivative, on the other hand, can't get as far. Derivative[1,0][f] (1,0) f Now, suppose I define my own value for the derivative of the Gamma function. Derivative[1,0][Gamma] = Plus D understands this perfectly, but Derivative not at all. D[f[x,y],x] 1 + x + y Derivative[1,0][f] (1,0) f Derivative[1,0][f][x,y] (1,0) f [x, y] What's the difference here? How can I get Derivative to use my definition? Thanks for any help. E. Neely Atkinson AN123651 at UTHVM1.BITNET neely@mdaali.cancer.utexas.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Mar 22 13:29:08 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA09533; Thu, 22 Mar 90 13:29:07 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA17995; Thu, 22 Mar 90 13:24:35 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA09394; Thu, 22 Mar 90 11:08:21 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA09390; Thu, 22 Mar 90 11:08:19 -0600 Message-Id: <9003221708.AA09390@yoda.ncsa.uiuc.edu> To: mathgroup@yoda.ncsa.uiuc.edu Subject: N Date: Thu, 22 Mar 90 08:20:47 PST From: jacobson@cello.hpl.hp.com Status: RO There has been discussion recently about using N[...,30] around everything. It is been observed by Richard Fateman and confirmed by Paul Abbott that this may not work because f[N[...,30]] and N[f[...],30] are not the same. However there is a much more important reason why it won't work. N only reduces the accuracy of its first argument, it never increases it. Note the following: In[1]:= N[1.2,30] Out[1]= 1.2 In[2]:= Precision[%] Out[2]= 16 To get N to work right on decimal things I have to rewrite them as rationals, or use lots of zeros, then apply N. In[3]:= N[12/10,30] Out[3]= 1.2 In[4]:= Precision[%] Out[4]= 30 You can force the accuracy up by SetPrecision or SetAccuracy, but beware, because the number was first converted to binary in low precision form before SetPrecision or SetAccuracy got to it. So you are declaring an inaccurate value to be accurate. In[8]:= SetPrecision[1.2,30] Out[8]= 1.19999999999999995559107901499 In[9]:= Precision[%] Out[9]= 30 I know of no way to make the Mathematica "reader" convert decimal input to high accuracy other than appending a long string of zeros. If anybody know of a way, please speak up. -- David Jacobson From fateman@renoir.Berkeley.EDU Thu Mar 22 13:58:37 1990 Received: from renoir.Berkeley.EDU by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA09588; Thu, 22 Mar 90 13:58:34 -0600 Received: by renoir.Berkeley.EDU (5.61/1.29) id AA19124; Thu, 22 Mar 90 11:56:21 -0800 Date: Thu, 22 Mar 90 11:56:21 -0800 From: fateman@renoir.Berkeley.EDU (Richard Fateman) Message-Id: <9003221956.AA19124@renoir.Berkeley.EDU> To: jacobson@cello.hpl.hp.com, mathgroup@yoda.ncsa.uiuc.edu Subject: Re: N Cc: fateman@renoir.Berkeley.EDU Status: RO The notions of precision and accuracy as used in Mathematica are, in my view, wrong. I have argued at some length (and apparently with no effect) for a model in which a floating-point number's precision can be extended by adding 0's to its internal representation, if you wish. The mathematica model is (somewhat crudely) that if you write 0.5 you do not mean 0.500000... but any number between 0.450 and 0.5499.. . While this latter model may be reminiscent of a physics-lab approach of carrying significant figures in your measurements, it is not useful in computation. Numerical analysis texts talk about relative and absolute error, not precision and accuracy. Richard Fateman UC Berkeley From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Mar 22 14:47:36 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA09696; Thu, 22 Mar 90 14:47:35 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA19620; Thu, 22 Mar 90 14:43:04 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA09501; Thu, 22 Mar 90 12:53:38 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA09497; Thu, 22 Mar 90 12:53:36 -0600 Message-Id: <9003221853.AA09497@yoda.ncsa.uiuc.edu> Date: Thu, 22 Mar 90 12:41:28 CST From: AN123651@uthvm1.bitnet Subject: D and Derivative - help please To: mathgroup@yoda.ncsa.uiuc.edu Status: RO I would appreciate some help with this from anyone who understands Mathematica better than I. Suppose I define a function: f[x_,y_] := x + y + Gamma[x,y] When I take its derivative using D, everything is fine. D[f[x,y],x] (1,0) 1 + Gamma [x, y] Derivative, on the other hand, can't get as far. Derivative[1,0][f] (1,0) f Now, suppose I define my own value for the derivative of the Gamma function. Derivative[1,0][Gamma] = Plus D understands this perfectly, but Derivative not at all. D[f[x,y],x] 1 + x + y Derivative[1,0][f] (1,0) f Derivative[1,0][f][x,y] (1,0) f [x, y] What's the difference here? How can I get Derivative to use my definition? Thanks for any help. E. Neely Atkinson AN123651 at UTHVM1.BITNET neely@mdaali.cancer.utexas.edu From jacobson@cello.hpl.hp.com Thu Mar 22 15:50:18 1990 Received: from hplms2.hpl.hp.com by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA09821; Thu, 22 Mar 90 15:50:16 -0600 Received: from cello.hpl.hp.com by hplms2.hpl.hp.com with SMTP (15.11.1.3/15.5+IOS 3.20) id AA23620; Thu, 22 Mar 90 13:49:29 pst Received: from localhost by cello.HPL.HP.COM; Thu, 22 Mar 90 13:49:15 pst To: mathgroup@yoda.ncsa.uiuc.edu Subject: Mathematica speedup technique Date: Thu, 22 Mar 90 13:49:13 PST Message-Id: <20853.638142553@cello> From: jacobson@cello.hpl.hp.com Status: RO I am presently working on a project where we needed to assign values to MANY complicated expressions, as in FinishTime[packetToNet] = .1243 FinishTime[PE[PI[diskread],1]] = .345 This can get real slow. In[1]:= Timing[Do[FinishTime[PE[PI[diskread],i]] = i+1,{i,2000}]] Out[1]= {152.4 Second, Null} In[2]= Timing[FinishTime[PE[PI[diskread],500]]] Out[2]= {0.01 Second, 501} I found that I could hash the expression to a new symbol and then use it as the tag in a TagSet. This speeded things up a lot. I have coded this up in a package that defined a function "Wrap" to wrap around the expressions. The heart of the function is this definition: hashify[name_] := ToExpression[StringJoin["HASH$",ToString[Hash[name]]]] The whole package appears at the end. In[1]:= < Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA21849; Thu, 22 Mar 90 16:28:04 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA09670; Thu, 22 Mar 90 14:28:06 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA09666; Thu, 22 Mar 90 14:28:04 -0600 Message-Id: <9003222028.AA09666@yoda.ncsa.uiuc.edu> Date: Thu, 22 Mar 90 11:56:21 -0800 From: fateman@renoir.Berkeley.EDU (Richard Fateman) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: N Status: RO The notions of precision and accuracy as used in Mathematica are, in my view, wrong. I have argued at some length (and apparently with no effect) for a model in which a floating-point number's precision can be extended by adding 0's to its internal representation, if you wish. The mathematica model is (somewhat crudely) that if you write 0.5 you do not mean 0.500000... but any number between 0.450 and 0.5499.. . While this latter model may be reminiscent of a physics-lab approach of carrying significant figures in your measurements, it is not useful in computation. Numerical analysis texts talk about relative and absolute error, not precision and accuracy. Richard Fateman UC Berkeley From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Mar 22 17:36:03 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA09943; Thu, 22 Mar 90 17:36:02 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA23111; Thu, 22 Mar 90 17:31:30 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA09801; Thu, 22 Mar 90 15:45:23 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA09797; Thu, 22 Mar 90 15:45:22 -0600 Message-Id: <9003222145.AA09797@yoda.ncsa.uiuc.edu> To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: N Date: Thu, 22 Mar 90 13:37:12 PST From: jacobson@cello.hpl.hp.com Status: RO The real situation is even worse than Fateman claims. On input Mathematica uses trailing decimals to determine accuracy and precision, but only if the resulting precision is higher than machine precision. Furthermore, one can't use N to reliably force the precision down: N[...,3] seems to act as though it were N[...,Max[3,<>]]. In[39]:= 1. Out[39]= 1. In[40]:= Precision[%] Out[40]= 16 In[41]:= N[%39,3] Out[41]= 1. In[42]:= Precision[%] Out[42]= 16 At the Mathematica conference, one of the WRI folks, (Jerry Keiper or Igor Rivin, I believe) claimed than N[] only lowers precision, never raises it. However, here is a counter example. In[43]:= 1.000000000000000000000000001 - 1.0000000000000000000000000001 -28 Out[43]= 9. 10 In[44]:= Precision[%] Out[44]= 1 In[45]:= N[%43] -28 Out[45]= 8.99999 10 In[46]:= Precision[%] Out[46]= 16 and its not just that I used N with no second argument In[49]:= N[%43,16] -28 Out[49]= 8.99999388963799 10 In[50]:= Precision[%] Out[50]= 16 Finally, numbers seem to carry their precision around with them, but I can't seem to access it. I'd like to be able to do this in cases where I want to do my own error analysis. In[58]:= p3 = N[Pi,3] Out[58]= 3.14 In[59]:= p5=N[Pi,5] Out[59]= 3.1416 In[60]:= Precision[p3] Out[60]= 16 In[61]:= Precision[p5] Out[61]= 16 In[62]:= Accuracy[p3] Out[62]= 15 In[63]:= Accuracy[p5] Out[63]= 15 In[64]:= p3===p5 Out[64]= True Somehow p3 will print to 3 places and p5 will print to 5 places, but I don't know how the formatter knows that information. -- David Jacobson From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Mar 22 18:42:22 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA10035; Thu, 22 Mar 90 18:42:21 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA24089; Thu, 22 Mar 90 18:36:44 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA09834; Thu, 22 Mar 90 15:52:34 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA09830; Thu, 22 Mar 90 15:52:32 -0600 Message-Id: <9003222152.AA09830@yoda.ncsa.uiuc.edu> To: mathgroup@yoda.ncsa.uiuc.edu Subject: Mathematica speedup technique Date: Thu, 22 Mar 90 13:49:13 PST From: jacobson@cello.hpl.hp.com Status: RO I am presently working on a project where we needed to assign values to MANY complicated expressions, as in FinishTime[packetToNet] = .1243 FinishTime[PE[PI[diskread],1]] = .345 This can get real slow. In[1]:= Timing[Do[FinishTime[PE[PI[diskread],i]] = i+1,{i,2000}]] Out[1]= {152.4 Second, Null} In[2]= Timing[FinishTime[PE[PI[diskread],500]]] Out[2]= {0.01 Second, 501} I found that I could hash the expression to a new symbol and then use it as the tag in a TagSet. This speeded things up a lot. I have coded this up in a package that defined a function "Wrap" to wrap around the expressions. The heart of the function is this definition: hashify[name_] := ToExpression[StringJoin["HASH$",ToString[Hash[name]]]] The whole package appears at the end. In[1]:= < From: jacobson@cello.hpl.hp.com Status: RO Does anyone know how evaluation really works? I submit this example of funny behavior (compressed to single spacing for ease of reading): In[1]:= foo[x_] := BAZZZ /; (Print["hi there"];y===True) In[2]:= a = foo[xxx] hi there Out[2]= foo[xxx] In[3]:= b=a Out[3]= foo[xxx] In[4]:= y=True Out[4]= True In[5]:= c=a Out[5]= foo[xxx] In[6]:= foo[xxx] hi there Out[6]= BAZZZ Output 5, in particular, seems rather peculiar. At that point y is True, so it should be impossible to print anything that matches foo[_]. -- David Jacobson From @uunet.UU.NET:keiper@wri.UUCP Fri Mar 23 17:36:13 1990 Received: from uunet.UU.NET by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA11754; Fri, 23 Mar 90 17:36:10 -0600 Received: from wri.UUCP by uunet.uu.net (5.61/1.14) with UUCP id AA25418; Fri, 23 Mar 90 18:34:40 -0500 Received: by WRI.com (3.2/SMI-3.0DEV3) id AA17974; Fri, 23 Mar 90 17:33:12 CST Received: by dragonfly. (4.0/SMI-4.0) id AA19166; Fri, 23 Mar 90 17:33:09 CST Date: Fri, 23 Mar 90 17:33:09 CST From: keiper@wri.UUCP (Jerry Keiper) Message-Id: <9003232333.AA19166@dragonfly.> To: mathgroup@yoda.ncsa.uiuc.edu Subject: N[ ] Status: RO I stand by my statement that N[ ] never raises the precision of a number. But perhaps I need to clarify what I mean by that. There are two kinds of numbers in Mathematica: machine numbers and bignums. If a x is a machine number Precision[x] will always return whatever the precision of a double is; on a Sun that happens to be 16. Mathematica never keeps track of the precision of any machine number so Precision[x] tells you very little if x is a machine number; you won't even be able to verify that it is a machine number rather than a bignum with a certain precision. Furthermore, if the second argument to N[ ] is less than or equal to the precision of a machine number it produces a machine number and displays it with the number of digits requested (terminating zeros are suppressed). This leads us to the second question: How does it know how many digits to display in the case of a machine number? Most of the time it doesn't so it just shows 6 as a default. However if the number was either entered from the keyboard or resulted from N[ ] with a second argument less than or equal to the precision of a machine number then the number of digits to be displayed (NOT the precision) is stored in an int field in the number. As soon as you do anything other than add 0 or multiply by 1, since it is a machine number and Mathematica doesn't bother to keep track of its precision, the number of digits to be displayed is lost and it will display with the 6 digit default. In my opinion this convention is pretty much useless and it certainly leads to a great deal of confusion. Jerry B. Keiper Wolfram Research Inc. keiper@wri.com From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Mar 23 20:30:23 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA11942; Fri, 23 Mar 90 20:30:21 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA18907; Fri, 23 Mar 90 20:25:54 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA11799; Fri, 23 Mar 90 18:26:32 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA11795; Fri, 23 Mar 90 18:26:31 -0600 Message-Id: <9003240026.AA11795@yoda.ncsa.uiuc.edu> To: mathgroup@yoda.ncsa.uiuc.edu Subject: evaluation Date: Fri, 23 Mar 90 08:49:33 PST From: jacobson@cello.hpl.hp.com Status: RO Does anyone know how evaluation really works? I submit this example of funny behavior (compressed to single spacing for ease of reading): In[1]:= foo[x_] := BAZZZ /; (Print["hi there"];y===True) In[2]:= a = foo[xxx] hi there Out[2]= foo[xxx] In[3]:= b=a Out[3]= foo[xxx] In[4]:= y=True Out[4]= True In[5]:= c=a Out[5]= foo[xxx] In[6]:= foo[xxx] hi there Out[6]= BAZZZ Output 5, in particular, seems rather peculiar. At that point y is True, so it should be impossible to print anything that matches foo[_]. -- David Jacobson From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Mar 23 21:23:03 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA12066; Fri, 23 Mar 90 21:23:02 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-1.2) id AA19638; Fri, 23 Mar 90 21:18:35 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA11805; Fri, 23 Mar 90 18:31:29 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA11801; Fri, 23 Mar 90 18:31:28 -0600 Message-Id: <9003240031.AA11801@yoda.ncsa.uiuc.edu> Date: Fri, 23 Mar 90 17:33:09 CST From: keiper@wri.UUCP (Jerry Keiper) To: mathgroup@yoda.ncsa.uiuc.edu Subject: N[ ] Status: RO I stand by my statement that N[ ] never raises the precision of a number. But perhaps I need to clarify what I mean by that. There are two kinds of numbers in Mathematica: machine numbers and bignums. If a x is a machine number Precision[x] will always return whatever the precision of a double is; on a Sun that happens to be 16. Mathematica never keeps track of the precision of any machine number so Precision[x] tells you very little if x is a machine number; you won't even be able to verify that it is a machine number rather than a bignum with a certain precision. Furthermore, if the second argument to N[ ] is less than or equal to the precision of a machine number it produces a machine number and displays it with the number of digits requested (terminating zeros are suppressed). This leads us to the second question: How does it know how many digits to display in the case of a machine number? Most of the time it doesn't so it just shows 6 as a default. However if the number was either entered from the keyboard or resulted from N[ ] with a second argument less than or equal to the precision of a machine number then the number of digits to be displayed (NOT the precision) is stored in an int field in the number. As soon as you do anything other than add 0 or multiply by 1, since it is a machine number and Mathematica doesn't bother to keep track of its precision, the number of digits to be displayed is lost and it will display with the 6 digit default. In my opinion this convention is pretty much useless and it certainly leads to a great deal of confusion. Jerry B. Keiper Wolfram Research Inc. keiper@wri.com From @vmd.cso.uiuc.edu:WIESENEKKER@SARA.NL Sat Mar 24 17:31:27 1990 Received: from vmd.cso.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA13152; Sat, 24 Mar 90 17:31:25 -0600 Received: from HASARA5.BITNET by VMD.CSO.UIUC.EDU (IBM VM SMTP R1.2) with BSMTP id 1356; Sat, 24 Mar 90 17:30:06 CST Received: from VE1.LCN by SARA.NL for mathgroup@yoda.ncsa.uiuc.edu; 24 Mar 90 22:16 MET Message-Id: <$147986941S0116D19900323T104331.0001.Mail-VE> To: mathgroup@yoda.ncsa.uiuc.edu From: WIESENEKKER@sara.nl Subject: problem with solve Date: 23 MAR 90 11:56:31 Status: RO Subject: problem with solve Try the following with Mathematica for the MacII running on a MacIIci: Solve[x^2==0.0,x] Mathematica starts complaining about ComplexInfinities etc. Why? Drs. G. Wiesenekker WIESENEKKER@SARA.NL From gjc@mitech.com Sun Mar 25 16:59:23 1990 Received: from schizo.samsung.com by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA14088; Sun, 25 Mar 90 16:59:20 -0600 From: gjc@mitech.com Received: by schizo.samsung.com from mitech.UUCP via UUCP (vers 5.61+) for mathgroup@yoda.ncsa.uiuc.edu (from gjc@mitech.com) id ; Sun, 25 Mar 90 17:57:54 -0500 Message-Id: <9003252257.AA01694@schizo.samsung.com> Reply-To: Received: by mitech.com (DECUS UUCP w/Smail); Sun, 25 Mar 90 09:57:07 EDT Date: Sun, 25 Mar 90 09:57:07 EDT To: mathgroup@yoda.ncsa.uiuc.edu Subject: Mathematic mailing list forwarding X-Vms-Mail-To: uucp%"mathgroup@yoda.ncsa.uiuc.edu" Status: RO This is a test to see if mail to the list mathgroup at yoda.ncsa.uiuc.edu is realling being forwarded to sci.math.symbolic -gjc From jacobson@cello.hpl.hp.com Tue Mar 27 15:48:24 1990 Received: from hplms2.hpl.hp.com by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA00471; Tue, 27 Mar 90 15:48:21 -0600 Received: from cello.hpl.hp.com by hplms2.hpl.hp.com with SMTP (15.11.1.3/15.5+IOS 3.20) id AA21928; Tue, 27 Mar 90 13:47:18 pst Received: from localhost by cello.HPL.HP.COM; Tue, 27 Mar 90 13:47:13 pst To: mathgroup@yoda.ncsa.uiuc.edu Subject: GNU Emacs Mathematica mode Date: Tue, 27 Mar 90 13:47:11 PST Message-Id: <24831.638574431@cello> From: jacobson@cello.hpl.hp.com Status: RO Here is a GNU Emacs package for use with Mathematica. Its main features are: * Editing of multi-line "cells" before submission. * Limited error checking before submission * Copying of earlier cells by name or by pointing. * Go to the point of an error in a .m file. * On-line help * Symbol completion * Interrupts Installation: Check the $Path variable of your version of Mathematica. Edit the Mathematica-search-path variable (or just make make sure it is set before loading this) to match. Use nil for the current working directory. After loading, type M-X math to start a copy of Mathematica. Edit an input cell using normal editing commands, the submit with ESC-RET. If the input is does not form a complete statement, Mathematica will either hang waiting for more input or will type "^ ". If this happens, space down a couple of lines (so that there is a blank line above the cursor) and type ESC-RET. This will clear Mathematica's input buffer; then remove the new prompt, edit the input and resubmit. You can copy previous cells with C-c C-y. It will ask for what cell you want in the minibuffer. gives cell number . gives the cell the cursor is on gives the last cell. With a prefix this will back over incarnation boundaries of Mathematica. See the on-line help for math-copy-cell for more info. You can complete Mathematica symbols with ESC-TAB. C-c C-c interrupts Mathematica (as well is it can be interrupted). When it gives you the prompt, type your response followed by ESC-RET. C-c 9 is equivalent to kill -9 . If you have read in a .m file with "<<", and have gotten a response of the form ": : syntax error in ..." you can go directly to the point of the error by typing C-c C-e. This is very useful because the line numbers are almost always wrong. This function counts lines the way Mathematica does. Enjoy, -- David Jacobson ================================ ;; Copyright (c) 1990 Hewlett-Packard Company, all rights reserved. ;; ;; LEGAL NOTICE ;; ;; This math-mode package is experimental and HP shall have no obligation to ;; maintain or support it. HP makes no express or implied warranty of any ;; kind with respect to this software, and HP shall not be liable for any ;; direct, indirect, special, incidental or consequential damages (whether ;; based on contract, tort or any other legal theory) arising in any way from ;; use of the software. ;; ;; Everyone is granted permission to copy, modify and redistribute this ;; math-mode package, provided: ;; 1. All copies contain this copyright notice. ;; 2. All modified copies shall carry a prominant notice stating who ;; made the last modification and the date of such modification. ;; 3. No charge is made for this software or works derived from it. ;; This clause shall not be construed as constraining other software ;; distributed on the same medium as this software, nor is a ;; distribution fee considered a charge. ;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;; Portions of this package were adapted from GNU Emacs. ;; ;; Copyright (C) 1985, 1986, 1987, 1988 Free Software Foundation, Inc. ;; ;; GNU Emacs is distributed in the hope that it will be useful, ;; but WITHOUT ANY WARRANTY. No author or distributor ;; accepts responsibility to anyone for the consequences of using it ;; or for whether it serves any particular purpose or works at all, ;; unless he says so in writing. Refer to the GNU Emacs General Public ;; License for full details. ;; Everyone is granted permission to copy, modify and redistribute ;; GNU Emacs, but only under the conditions described in the ;; GNU Emacs General Public License. A copy of this license is ;; supposed to have been given to you along with GNU Emacs so you ;; can know your rights and responsibilities. It should be in a ;; file named COPYING. Among other things, the copyright notice ;; and this notice must be preserved on all copies. ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;; Author: David Jacobson ;; Experimental version of March 24, 1990 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; (require 'shell) (defvar Mathematica-search-path (list nil (getenv "HOME") "/usr/local/math/Init" "/usr/local/math/Packages") "*A list of directories in which to look for files. Use nil for the current directory.") (defconst math-process-string "/usr/local/bin/math" "A string to pass to the unix exec function to start Mathematica") (defconst math-header-re (concat "^" (regexp-quote "by S. Wolfram, D. Grayson, R. Maeder, H. Cejtin,")) "A regular expression that will match somewhere in Mathematica preamble") (defvar math-mode-map nil) (if math-mode-map nil (setq math-mode-map (deep-copy-keymap shell-mode-map)) (define-key math-mode-map "\C-m" 'newline) ; the global keymap maps to newline (define-key math-mode-map "\e\C-m" 'math-send-input) ; (define-key math-mode-map "\C-c\C-c" 'interrupt-math-proc) (define-key math-mode-map "\C-c9" 'kill-math-process) (define-key math-mode-map "\C-c\C-h" 'math-help); buffer specific C-h (define-key math-mode-map "\C-he" 'math-help) ; e-xpression in help menu (define-key math-mode-map "\C-hE" 'math-extra-help) ; E-xpression in help menu (define-key math-mode-map "\e\t" 'math-complete-symbol) (define-key math-mode-map "\C-c\C-y" 'math-copy-cell) (define-key math-mode-map "\C-c\C-e" 'find-math-error)) (defvar math-mode-syntax-table nil "Syntax table used while in math mode.") (if math-mode-syntax-table () (setq math-mode-syntax-table (make-syntax-table)) (modify-syntax-entry ?% "." math-mode-syntax-table) (modify-syntax-entry ?& "." math-mode-syntax-table) (modify-syntax-entry ?* ". 23" math-mode-syntax-table) ;allow for (* comment *) (modify-syntax-entry ?+ "." math-mode-syntax-table) (modify-syntax-entry ?- "." math-mode-syntax-table) (modify-syntax-entry ?/ "." math-mode-syntax-table) (modify-syntax-entry ?< "." math-mode-syntax-table) (modify-syntax-entry ?= "." math-mode-syntax-table) (modify-syntax-entry ?> "." math-mode-syntax-table) (modify-syntax-entry ?_ "." math-mode-syntax-table) (modify-syntax-entry ?\| "." math-mode-syntax-table) (modify-syntax-entry ?\` "_" math-mode-syntax-table) ; Mathematica context symbol (modify-syntax-entry ?\( "()1" math-mode-syntax-table) ;allow for (* comment *) (modify-syntax-entry ?\) ")(4" math-mode-syntax-table)) ;allow for (* comment *) (defun math-send-input () "Send input to subshell. At end of buffer, sends all text after last output as input to the subshell, including a newline inserted at the end. When not at end, copies current line to the end of the buffer and sends it, after first attempting to discard any prompt at the beginning of the line by matching the regexp that is the value of shell-prompt-pattern if possible. This regexp should start with \"^\"." (interactive) (or (get-buffer-process (current-buffer)) (error "Current buffer has no process")) ;; Stick on a newline if the current line is non-blank and ;; it's end is also the end of the buffer ;; In retrospect this seems stupid 3/21/90 (beginning-of-line) (if (looking-at "\\s *\\S .*\\'") (progn (end-of-line) (newline))) ;; Find beginning of "cell" (let* ((cellinfo (math-identify-cell (point))) (bpt (car cellinfo)) (ept (nth 1 cellinfo)) (query (nth 2 cellinfo)) copy) (if (not query) (check-math-syntax bpt ept)) ;; If we are \"near\" the end of the buffer, we don't copy the data down ;; there, but we kill excess white space. Otherwise, we go there and ;; copy the data. (goto-char ept) (forward-line 1) (if (not (bolp)) (newline)) (setq copy (buffer-substring bpt (point))) (if (looking-at "\\s *\\'") (replace-match "") (goto-char (point-max)) (forward-line 0) (if (or (eolp) (looking-at "^In\\[[0-9]+\\]:=\\s *$")) (end-of-line) (end-of-line) (newline)) (insert copy)) (if (= (length copy) 0) (setq copy "\n")) ; hack (let ((process (get-buffer-process (current-buffer)))) (set-process-filter process 'math-insert-blank-filter) (metered-process-send-string process copy) (set-marker (process-mark process) (point))))) (defun math-insert-blank-filter (proc string) ; force a blank line after input cell. (let ((cbuf (current-buffer)) (save-match-data (match-data))) (unwind-protect (progn (set-buffer (process-buffer proc)) (goto-char (point-max)) ;; Sometimes Mathematica's first line of output ;; contains white space characters before the ;; newline. We wish to treat that as an acceptable ;; blank line. ;; Zero testing is necessary to avoid matches on ;; subsequent lines. Zerop won't work since ;; it gives an error with a nil arg. (cond ((equal (string-match "^\\s *\n" string) 0) (set-process-filter proc nil)) ((equal (string-match "^\\s *$" string) 0)) ; do nothing (t (newline) (message "newline inserted by Emacs' math-mode"))) (insert-string string) (set-marker (process-mark proc) (point)) ; is this necessary? ) ; matches progn (set-process-filter proc nil) (set-buffer cbuf) (store-match-data save-match-data)))) (defun math-mode () "Major mode for interacting with Mathematica. \\[math] starts Mathematica. \\[math-send-input] tries to identify stuff following last \"In[...]:= \" or blank line and sends it. To clear out Mathmatica after an error occurs, move point two lines below last printing character and type \\[math-send-input] \\[math-help] gives help on a Mathematica symbol. C-u \\[math-help] or \\[math-extra-help] gives more verbose help. \\[math-complete-symbol] will complete the symbol near point. \\[math-copy-cell] will copy a previous cell to the end of the buffer. See its description for details. \\[find-math-error] when typed after < comment-depth 0) (re-search-forward "\\((\\*\\)\\|\\(\\*)\\)\\|\\(\n\\)" nil 1) ; (* or *) or newline (cond ((match-beginning 1) (setq comment-depth (1+ comment-depth))) ((match-beginning 2) (setq comment-depth (1- comment-depth))) ((match-beginning 3) (setq lineno (1+ lineno))))) (instring (re-search-forward "\\(\\\\\\\\\\)\\|\\(\\\\\042\\)\\|\\(\042\\)\\|\\(\\\\\n\\)\\|\\(\n\\)" nil 1) ; \\ or \quote or quote or \newline or newline (cond ((match-beginning 3) (setq instring nil)) ((match-beginning 4) (setq lineno (1+ lineno))) ((match-beginning 5) (setq lineno (+ 2 lineno))))) (t (re-search-forward "\\(\050\\*\\)\\|\\(\042\\)\\|\\(\n\\)" nil 1) ; left paren* or quote or newline (cond ((match-beginning 1) (setq comment-depth 1)) ((match-beginning 2) (setq instring t)) ((match-beginning 3) (setq lineno (1+ lineno)) (skip-over-white-lines)))))))) (defun find-math-error () "Searches for the last \"syntax error in\" message, then goes to the file and line indicated, where lines are counted as by Mathematica. It uses the symbol Mathematica-search-path rather than going to all the work to discover the real real search path." (interactive) (let (filename linenumber raw-filename (math-search-path Mathematica-search-path)) (save-excursion (re-search-backward "syntax error in") (forward-line 0) (if (not (looking-at "\\([^:]+\\): *\\([0-9]+\\):")) (error "Cannot parse error line")) (setq raw-filename (buffer-substring (match-beginning 1) (match-end 1))) (setq linenumber (string-to-int (buffer-substring (match-beginning 2) (match-end 2))))) (while (not filename) (setq filename (expand-file-name raw-filename (car math-search-path))) (if (not (file-readable-p filename)) (progn (setq filename nil) (setq math-search-path (cdr math-search-path)) (if (null math-search-path) (error "File %s not found" raw-file-name))))) (find-file-other-window filename) (goto-matherr-line linenumber))) From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Mar 29 17:53:24 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA03573; Thu, 29 Mar 90 17:53:23 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA13958; Thu, 29 Mar 90 17:49:01 CST Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA03505; Thu, 29 Mar 90 15:40:02 -0600 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA03501; Thu, 29 Mar 90 15:40:01 -0600 Message-Id: <9003292140.AA03501@yoda.ncsa.uiuc.edu> Date: Mon, 26 Mar 90 13:03:08 CST From: keiper@wri.UUCP (Jerry Keiper) To: mathgroup@yoda.ncsa.uiuc.edu Subject: precision and accuracy Status: RO uunet!renoir.Berkeley.EDU!fateman (Richard Fateman) writes: The notions of precision and accuracy as used in Mathematica are, in my view, wrong. I have argued at some length (and apparently with no effect) for a model in which a floating-point number's precision can be extended by adding 0's to its internal representation, if you wish. The mathematica model is (somewhat crudely) that if you write 0.5 you do not mean 0.500000... but any number between 0.450 and 0.5499.. . While this latter model may be reminiscent of a physics-lab approach of carrying significant figures in your measurements, it is not useful in computation. Numerical analysis texts talk about relative and absolute error, not precision and accuracy. I presume he is unhappy with Mathematica's use of significance arithmetic as opposed to fixed, but arbitrary precision arithmetic. These two models of arithmetic are indeed very different and they both have their advantages and disadvantages, but I have seen no convincing evidence that one is better than the other. Certainly significance arithmetic is very difficult to implement correctly and Mathematica has not yet achieved perfection in this matter, but the fact that most elementary numerical texts only discuss fixed precision arithmetic (note that they don't discuss arbitrary precision arithmetic either) is not a reason to reject significance arithmetic. As to increasing the precision of a number, Mathematica allows this to be done very simply using SetPrecision[] (likewise the accuracy can be increased with SetAccuracy[].) y = SetPrecision[x, prec] gives y a value such that y == x is True and such that the precision of y is prec. If the precision of y is greater than the precision of x the "missing" digits of x are filled in for y with 0's in binary. This does not mean that they will appear as 0's in decimal however. e.g. the decimal number 1.2 has a nonterminating binary expansion 1.0011001100110011001100... Clearly if we start with a finite approximation to this and attach 0's in binary we will not get the decimal expansion for 1.200000000... Since it is not possible to know what number a user has in mind when he wants to increase its precision it is not possible to give a better approximation; all that Mathematica can do is give another number with more digits in it. As to relative and absolute error vs. precision and accuracy, precision is a nonnegative integer and accuracy is an integer. Relative and absolute error are small numbers, sometimes complex, but they are never known exactly (if they were the approximate answer could be corrected.) I find it more convenient to deal with an accuracy of 27 rather than an absolute error of 0.000000000000000000000000001, but perhaps not everyone does. From @uxc.cso.uiuc.edu:keiper@wri.UUCP Mon Apr 2 18:07:13 1990 Received: from uxc.cso.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA01977; Mon, 2 Apr 90 18:07:12 -0500 Received: from wri.UUCP by uxc.cso.uiuc.edu with UUCP (5.61+/IDA-1.2.8) id AA08846; Mon, 2 Apr 90 17:26:17 -0500 Received: by WRI.com (3.2/SMI-3.0DEV3) id AA17550; Mon, 2 Apr 90 17:24:41 CDT Date: Mon, 2 Apr 90 17:24:41 CDT From: keiper@wri.UUCP (Jerry Keiper) Message-Id: <9004022224.AA17550@WRI.com> To: mathgroup@yoda.ncsa.uiuc.edu Subject: SetPrecision[] Status: RO Jeffrey P. Golden writes: >If the user types SetPrecision[1.2,30], I think it is pretty clear >that most users mean the same number that SetPrecision[12/10,30] >would mean, i.e. fill in with decimal 0's, which is not what >Mathematica does. Since that sort of functionality is in general impossible, I presume that the suggestion is only intended to make it more convenient to enter numbers precisely. But the 1.2 will have been converted to 1.001100110011... long before SetPrecision[] ever even gets to look at it. If the above functionality is desired one can do something like HighPrecision[x_, n_] := SetPrecision[Rationalize[x], n] then In[9]:= HighPrecision[1.2,40] Out[9]= 1.2 In[10]:= SetPrecision[%, 60] Out[10]= 1.19999999999999999999999999999999999999999999999917892668106 But this will only work for numbers that are essentially rational numbers with relatively small denominators with a small rounding error thrown in to allow it to be represented in binary. I do not think that overloading SetPrecision[] to have this functionality is appropriate. Jerry Keiper keiper@wri.com Wolfram Research Inc. From mathgroup-adm@yoda.ncsa.uiuc.edu Mon Apr 2 22:35:13 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA02069; Mon, 2 Apr 90 22:35:12 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA28148; Mon, 2 Apr 90 22:30:08 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA02054; Mon, 2 Apr 90 21:49:45 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA02050; Mon, 2 Apr 90 21:49:43 -0500 Message-Id: <9004030249.AA02050@yoda.ncsa.uiuc.edu> Date: Mon, 2 Apr 90 17:24:41 CDT From: keiper@wri.UUCP (Jerry Keiper) To: mathgroup@yoda.ncsa.uiuc.edu Subject: SetPrecision[] Status: RO Jeffrey P. Golden writes: >If the user types SetPrecision[1.2,30], I think it is pretty clear >that most users mean the same number that SetPrecision[12/10,30] >would mean, i.e. fill in with decimal 0's, which is not what >Mathematica does. Since that sort of functionality is in general impossible, I presume that the suggestion is only intended to make it more convenient to enter numbers precisely. But the 1.2 will have been converted to 1.001100110011... long before SetPrecision[] ever even gets to look at it. If the above functionality is desired one can do something like HighPrecision[x_, n_] := SetPrecision[Rationalize[x], n] then In[9]:= HighPrecision[1.2,40] Out[9]= 1.2 In[10]:= SetPrecision[%, 60] Out[10]= 1.19999999999999999999999999999999999999999999999917892668106 But this will only work for numbers that are essentially rational numbers with relatively small denominators with a small rounding error thrown in to allow it to be represented in binary. I do not think that overloading SetPrecision[] to have this functionality is appropriate. Jerry Keiper keiper@wri.com Wolfram Research Inc. From mathgroup-adm@yoda.ncsa.uiuc.edu Mon Apr 2 23:38:07 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA02106; Mon, 2 Apr 90 23:38:06 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA28299; Mon, 2 Apr 90 23:32:58 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA02048; Mon, 2 Apr 90 21:49:01 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA02044; Mon, 2 Apr 90 21:49:00 -0500 Message-Id: <9004030249.AA02044@yoda.ncsa.uiuc.edu> Date: Mon, 2 Apr 90 16:18 EDT From: Jeffrey P. Golden Subject: precision and accuracy To: mathgroup@yoda.ncsa.uiuc.edu Status: RO Date: Mon, 26 Mar 90 13:03:08 CST From: wri!keiper@yoda.ncsa.uiuc.edu (Jerry Keiper) [...] As to increasing the precision of a number, Mathematica allows this to be done very simply using SetPrecision[] (likewise the accuracy can be increased with SetAccuracy[].) y = SetPrecision[x, prec] gives y a value such that y == x is True and such that the precision of y is prec. If the precision of y is greater than the precision of x the "missing" digits of x are filled in for y with 0's in binary. This does not mean that they will appear as 0's in decimal however. e.g. the decimal number 1.2 has a nonterminating binary expansion 1.0011001100110011001100... Clearly if we start with a finite approximation to this and attach 0's in binary we will not get the decimal expansion for 1.200000000... Since it is not possible to know what number a user has in mind when he wants to increase its precision it is not possible to give a better approximation; all that Mathematica can do is give another number with more digits in it. If the user types SetPrecision[1.2,30], I think it is pretty clear that most users mean the same number that SetPrecision[12/10,30] would mean, i.e. fill in with decimal 0's, which is not what Mathematica does. As to relative and absolute error vs. precision and accuracy, precision is a nonnegative integer and accuracy is an integer. Relative and absolute error are small numbers, sometimes complex, but they are never known exactly (if they were the approximate answer could be corrected.) I find it more convenient to deal with an accuracy of 27 rather than an absolute error of 0.000000000000000000000000001, but perhaps not everyone does. I think no one finds it convenient to deal with 0.000000000000000000000000001 . That's why notations such as 1.0 10^-27 (or even 1.0e-27) were invented. (I can't tell whether you're trying to bias the situation or just so used to typing numbers such as 1.20000000000000000000000000000 to Mathematica to get the precision you need!-) From shore@KRAMDEN.ACF.NYU.EDU Tue Apr 3 00:26:48 1990 Received: from KRAMDEN.ACF.NYU.EDU by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA02830; Tue, 3 Apr 90 00:26:11 -0500 Received: by KRAMDEN.ACF.NYU.EDU (5.61/1.34) id AA29088; Tue, 3 Apr 90 01:26:28 -0400 Date: Tue, 3 Apr 90 01:26:28 -0400 From: shore@KRAMDEN.ACF.NYU.EDU (John Shore) Message-Id: <9004030526.AA29088@KRAMDEN.ACF.NYU.EDU> To: mathgroup-request@yoda.ncsa.uiuc.edu Subject: please add me to your list Status: RO please add shore@kramden.acf.nyu.edu to your mailing list. Thanks. John Shore New York University CIMS Academic Computing Facility From fateman@renoir.Berkeley.EDU Tue Apr 3 10:00:21 1990 Received: from renoir.Berkeley.EDU by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA03009; Tue, 3 Apr 90 10:00:13 -0500 Received: by renoir.Berkeley.EDU (5.61/1.29) id AA01543; Tue, 3 Apr 90 07:59:17 -0700 Date: Tue, 3 Apr 90 07:59:17 -0700 From: fateman@renoir.Berkeley.EDU (Richard Fateman) Message-Id: <9004031459.AA01543@renoir.Berkeley.EDU> To: mathgroup@yoda.ncsa.uiuc.edu, keiper@wri.UUCP Subject: Re: SetPrecision[] Status: RO Actually, SetPrecision[1.2,30] --> 1.2000000 <30 digits> IS possible, and here's how. Treat 1.2 as an input form, like RealNumber[1,2]. Don't convert it to machine precision until you do arithmetic on it. This is a total hack, and only serves to maintain the mistaken illusion that Mathematica does decimal arithmetic, and perpetuates the myth that there is something inherently correct about decimal input or output .... but, for example, I could easily put the hack above into my own Mathematica-like parser written in Common Lisp. -- Richard Fateman From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Apr 3 12:34:20 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA03107; Tue, 3 Apr 90 12:34:19 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA09972; Tue, 3 Apr 90 12:29:09 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA03073; Tue, 3 Apr 90 11:28:53 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA03069; Tue, 3 Apr 90 11:28:51 -0500 Message-Id: <9004031628.AA03069@yoda.ncsa.uiuc.edu> Date: Tue, 3 Apr 90 07:59:17 -0700 From: fateman@renoir.Berkeley.EDU (Richard Fateman) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: SetPrecision[] Status: RO Actually, SetPrecision[1.2,30] --> 1.2000000 <30 digits> IS possible, and here's how. Treat 1.2 as an input form, like RealNumber[1,2]. Don't convert it to machine precision until you do arithmetic on it. This is a total hack, and only serves to maintain the mistaken illusion that Mathematica does decimal arithmetic, and perpetuates the myth that there is something inherently correct about decimal input or output .... but, for example, I could easily put the hack above into my own Mathematica-like parser written in Common Lisp. -- Richard Fateman From jpg@ALLEGHENY.SCRC.Symbolics.COM Wed Apr 4 14:10:12 1990 Received: from [128.81.41.45] by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA04719; Wed, 4 Apr 90 14:10:08 -0500 Received: from SKUA.SCRC.Symbolics.COM by ALLEGHENY.SCRC.Symbolics.COM via CHAOS with CHAOS-MAIL id 180944; 4 Apr 90 15:08:42 EDT Date: Wed, 4 Apr 90 15:08 EDT From: Jeffrey P. Golden Subject: Re: SetPrecision[] To: fateman@renoir.Berkeley.EDU Cc: mathgroup@yoda.ncsa.uiuc.edu In-Reply-To: <9004031628.AA03069@yoda.ncsa.uiuc.edu> Message-Id: <19900404190827.8.JPG@SKUA.SCRC.Symbolics.COM> Status: RO Date: Tue, 3 Apr 90 07:59:17 -0700 From: fateman@renoir.Berkeley.EDU (Richard Fateman) Actually, SetPrecision[1.2,30] --> 1.2000000 <30 digits> IS possible, and here's how. Treat 1.2 as an input form, like RealNumber[1,2]. Don't convert it to machine precision until you do arithmetic on it. This is a total hack, and only serves to maintain the mistaken illusion that Mathematica does decimal arithmetic, and perpetuates the myth that there is something inherently correct about decimal input or output There's no myth here. There -is- something inherently correct (whatever that means) about decimal input or output - that's what most humans use most of the time. We build mathematical systems not only so that Apples and Suns can exchange bytes, but so that humans can feel comfortable using them. That SetPrecision[1.2,30] does not match most users' expectations for what should be in those 30 (decimal!) digits (decimal!) is just one example. There are many such examples in all our computer mathematical systems. That Mathematica converts 1.2 to a machine number too early to be useful for the job at hand may be an unfortunate fact of life for this undocumented (by the Mathematica book) function. .... but, for example, I could easily put the hack above into my own Mathematica-like parser written in Common Lisp. From mathgroup-adm@yoda.ncsa.uiuc.edu Sat Apr 7 02:08:29 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA01200; Sat, 7 Apr 90 02:08:28 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA21621; Sat, 7 Apr 90 02:03:54 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA01173; Sat, 7 Apr 90 01:04:14 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA01169; Sat, 7 Apr 90 01:04:12 -0500 Message-Id: <9004070604.AA01169@yoda.ncsa.uiuc.edu> Date: Fri, 6 Apr 90 16:16:49 EDT From: km@mathcs.emory.edu (Ken Mandelberg) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Mathematica Frontends Status: RO The promo on the Mathematica Journal says that frontends for versions besides Mac and NeXT will be coming in the "near future". Anyone know what this refers to? A Sun fontend using X is on my wishlist! km@mathcs.emory.edu (Ken Mandelberg) From mcdonald@quark.UMD.EDU Tue Apr 10 11:12:47 1990 Received: from quark.umd.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA05399; Tue, 10 Apr 90 11:12:44 -0500 Received: by quark.UMD.EDU (5.57/Ultrix3.0-C) id AA06082; Tue, 10 Apr 90 12:14:05 EDT Date: Tue, 10 Apr 90 12:14:05 EDT From: mcdonald@quark.umd.edu (Bill MacDonald) Message-Id: <9004101614.AA06082@quark.UMD.EDU> To: mathgroup@yoda.ncsa.uiuc.edu Subject: Format of Real Numbers in Mathematica Status: RO Apropos Richard Fateman's complaint that Mathematica interprets 5.0 as being uncertain to the range 4.5 to 5.4, I note that NumberForm[] insists in printing an exact 0.5 in a table of the sine function as 0.5, dropping all trailing zeroes, even when asked to output all numbers in the table to, say 5 decimal places. This is very annoying when I want to produce a good looking table, but it also is inconsistent with the assumption on INPUT that 0.5 has one significant decimal figure. I will also throw in my complaint that Mathematica labels the tics on graph figures in a nonuniform way, for example, as 1.5,2.,2.5,3. etc. when publication quality graphs require 1.5,2.0,2.5,3.0, etc. In short, Mathematica seems to be inconsistent in the way it relates trailing zeros to precision, or accuracy, or whatever. From mathgroup-adm@yoda.ncsa.uiuc.edu Mon Apr 16 02:54:17 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA11135; Mon, 16 Apr 90 02:54:16 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA22199; Mon, 16 Apr 90 02:49:54 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA10391; Sun, 15 Apr 90 22:54:18 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA10387; Sun, 15 Apr 90 22:54:16 -0500 Message-Id: <9004160354.AA10387@yoda.ncsa.uiuc.edu> Date: Fri, 13 Apr 90 16:05:23 PDT From: lacomb@sierra.Stanford.EDU (Lloyd J. Lacomb) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Mathematica and printing on the PC Status: RO I not a member of this newsgroup so pardon my ignorance if this has already be hashed out many times before. I have Mathematica running on an IBM PC-AT clone. The only printers I have available are an HP Laserjet and an HP Deskjet neither of which are able to print the postscript file output by Mathematica. Is there a piece of software out there somewhere that will transcribe postscript files to TIFF compatible files. The program can be freeware, shareware, commerical whatever. Is some way to have Mathematica output something other than postscript. I can't imagine that I'm the only person using an IBM so I'm hoping someone else has solved this problem. I don't subscribe to the newsgroup so please respond to me at lacomb@sierra.stanford.edu (internet or bitnet) Thanks in advance. Lloyd lacomb@sierra.stanford.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Mon Apr 16 04:24:31 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA11209; Mon, 16 Apr 90 04:24:30 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA23533; Mon, 16 Apr 90 04:20:05 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA10385; Sun, 15 Apr 90 22:53:49 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA10381; Sun, 15 Apr 90 22:53:48 -0500 Message-Id: <9004160353.AA10381@yoda.ncsa.uiuc.edu> Date: Fri, 13 Apr 90 18:01:33 EDT From: Jack To: mathgroup@yoda.ncsa.uiuc.edu Subject: Transformation Rules via AlgebraicRules Status: RO Can someone explain the following result. I thought I would get the same result using rule1 and rule2 below. rule1 = x->t^(3/2) rule2 = AlgebraicRules[x==t^(3/2),{x,t}] exp = x^(5/4) + x + x^2 + x^3 + x^4 (1) exp/.rule1 (2) exp/.rule2 (1) gives the desired result.... 3 15 9 - -- - 2 8 3 2 6 Out[184]= t + t + t + t + t while (2) gives 1 - 2 3 4 4 5 General::newv: x + x + x + x + `private`$AuxVar[x ] involves variables not among {x, `private`$AuxVar[Sqrt[t]], t}. 3 - 2 Replace::rep: {t -> t, x -> t } encountered where lhs->rhs expected. etc.,etc. From mathgroup-adm@yoda.ncsa.uiuc.edu Mon Apr 16 05:25:41 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA11258; Mon, 16 Apr 90 05:25:39 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA24308; Mon, 16 Apr 90 05:21:12 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA10379; Sun, 15 Apr 90 22:53:16 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA10375; Sun, 15 Apr 90 22:53:14 -0500 Message-Id: <9004160353.AA10375@yoda.ncsa.uiuc.edu> Date: Fri, 13 Apr 90 21:08:59 JST From: cai@icluna.kobe-u.ac.jp (Dong Sheng Cai) To: mathgroup@yoda.ncsa.uiuc.edu Subject: mathink. in NeXT Status: RO I have problem to use mathlink in NeXT (version 1.0). I want to link my own C program to Mathematica and evaluate my program as if it were a build-in function. However, it is almost impossible for me to use mathlink in NeXT system and link my C program to Mathematica. I am using mathlink.c and mathlink.h which are stored in the Sources subdirectory of the main Mathematica directory, and my program is named sample.c. Following is what is happening in my NeXT....... |NeXT> math |Mathematica 1.2 (August 30, 1989) [With pre-loaded data] |by S. Wolfram, D. Grayson, R. Maeder, H. Cejtin, | S. Omohundro, D. Ballman and J. Keiper |with I. Rivin and D. Withoff |Copyright 1988,1989 Wolfram Research Inc. | |CallProcess::cppdied: Process sample has died. | |In[1]:= Quit |NeXT> I also varied the Linking-options ( -l sys_s or -l NeXT_s ), but I cannot get expected result. My Makefile for mathlink.c and sample.c are as follows: |CPATH=-c -bsd |LPATH= -lNeXT_s # or -l sys_s | |sample: sample.o mathlink.o | cc $(LPATH) -o sample sample.o mathlink.o | |sample.o: sample.c mathlink.h Makefile | cc $(CPATH) sample.c | |mathlink.o: mathlink.c Makefile | cc $(CPATH) mathlink.c I also obtained warning messages which I don't understand as follows: |NeXT> make |cc -c -bsd sample.c |cc -c -bsd mathlink.c |mathlink.c: In function typelookup: |mathlink.c:166: warning: `typelookup' was declared implicitly `extern' |and later `static' |mathlink.c: In function service_loop: |mathlink.c:178: warning: `service_loop' was declared implicitly `extern' and later | `static' |mathlink.c: In function rcvpkt: |mathlink.c:205: warning: `rcvpkt' was declared implicitly `extern' and later |`static' |mathlink.c: In function sendbuf: |mathlink.c:215: warning: `sendbuf' was declared |implicitly `extern' and later `static' |mathlink.c: In function sendpkt: |mathlink.c:235: warning: `sendpkt' was declared |implicitly `extern' and later `static' |mathlink.c: In function docall: |mathlink.c:247: warning: `docall' was declared implicitly `extern' |and later `static' |mathlink.c: In function outtypename: |mathlink.c:533: warning: `outtypename' |was declared implicitly `extern' and later `static' |cc -lsys_s -o sample sample.o mathlink.o |NeXT> I also tried the same sample program appeared in the manual of the mathlink which I found in NeXT and I foundthat the same error is happening. Does anyone know how to use mathlink in NeXT? D. Cai From mathgroup-adm@yoda.ncsa.uiuc.edu Mon Apr 16 05:25:41 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA11258; Mon, 16 Apr 90 05:25:39 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA24308; Mon, 16 Apr 90 05:21:12 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA10379; Sun, 15 Apr 90 22:53:16 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA10375; Sun, 15 Apr 90 22:53:14 -0500 Message-Id: <9004160353.AA10375@yoda.ncsa.uiuc.edu> Date: Fri, 13 Apr 90 21:08:59 JST From: cai@icluna.kobe-u.ac.jp (Dong Sheng Cai) To: mathgroup@yoda.ncsa.uiuc.edu Subject: mathink. in NeXT Status: RO I have problem to use mathlink in NeXT (version 1.0). I want to link my own C program to Mathematica and evaluate my program as if it were a build-in function. However, it is almost impossible for me to use mathlink in NeXT system and link my C program to Mathematica. I am using mathlink.c and mathlink.h which are stored in the Sources subdirectory of the main Mathematica directory, and my program is named sample.c. Following is what is happening in my NeXT....... |NeXT> math |Mathematica 1.2 (August 30, 1989) [With pre-loaded data] |by S. Wolfram, D. Grayson, R. Maeder, H. Cejtin, | S. Omohundro, D. Ballman and J. Keiper |with I. Rivin and D. Withoff |Copyright 1988,1989 Wolfram Research Inc. | |CallProcess::cppdied: Process sample has died. | |In[1]:= Quit |NeXT> I also varied the Linking-options ( -l sys_s or -l NeXT_s ), but I cannot get expected result. My Makefile for mathlink.c and sample.c are as follows: |CPATH=-c -bsd |LPATH= -lNeXT_s # or -l sys_s | |sample: sample.o mathlink.o | cc $(LPATH) -o sample sample.o mathlink.o | |sample.o: sample.c mathlink.h Makefile | cc $(CPATH) sample.c | |mathlink.o: mathlink.c Makefile | cc $(CPATH) mathlink.c I also obtained warning messages which I don't understand as follows: |NeXT> make |cc -c -bsd sample.c |cc -c -bsd mathlink.c |mathlink.c: In function typelookup: |mathlink.c:166: warning: `typelookup' was declared implicitly `extern' |and later `static' |mathlink.c: In function service_loop: |mathlink.c:178: warning: `service_loop' was declared implicitly `extern' and later | `static' |mathlink.c: In function rcvpkt: |mathlink.c:205: warning: `rcvpkt' was declared implicitly `extern' and later |`static' |mathlink.c: In function sendbuf: |mathlink.c:215: warning: `sendbuf' was declared |implicitly `extern' and later `static' |mathlink.c: In function sendpkt: |mathlink.c:235: warning: `sendpkt' was declared |implicitly `extern' and later `static' |mathlink.c: In function docall: |mathlink.c:247: warning: `docall' was declared implicitly `extern' |and later `static' |mathlink.c: In function outtypename: |mathlink.c:533: warning: `outtypename' |was declared implicitly `extern' and later `static' |cc -lsys_s -o sample sample.o mathlink.o |NeXT> I also tried the same sample program appeared in the manual of the mathlink which I found in NeXT and I foundthat the same error is happening. Does anyone know how to use mathlink in NeXT? D. Cai From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Apr 17 14:13:48 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA12808; Tue, 17 Apr 90 14:13:47 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA08641; Tue, 17 Apr 90 14:08:57 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA12753; Tue, 17 Apr 90 13:03:05 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA12749; Tue, 17 Apr 90 13:03:03 -0500 Message-Id: <9004171803.AA12749@yoda.ncsa.uiuc.edu> Subject: Trigonometry expansions To: mathgroup@yoda.ncsa.uiuc.edu Date: Tue, 17 Apr 90 7:38:24 PDT From: Steven Warwick Status: RO Has anyone taken the time to define trigonometric simplifications of the form: Sin[ArcSin[x]] -> x Sin[ArcTan[x/y]] -> y/Sqrt[x^2+y^2] etc. that can be added to the Algebra/trigonometry package??? -- Steven Warwick Hewlett-Packard sdw@hpsad From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Apr 17 15:18:49 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA12840; Tue, 17 Apr 90 15:18:46 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA10431; Tue, 17 Apr 90 15:13:40 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA12759; Tue, 17 Apr 90 13:03:39 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA12755; Tue, 17 Apr 90 13:03:36 -0500 Message-Id: <9004171803.AA12755@yoda.ncsa.uiuc.edu> To: mathgroup@yoda.ncsa.uiuc.edu Subject: Math mode for GNU Emacs Date: Tue, 17 Apr 90 10:59:20 PDT From: jacobson@cello.hpl.hp.com Status: RO Here is a GNU Emacs package for use with Mathematica. Its main features are: * Editing of multi-line "cells" before submission. * Limited error checking before submission * Copying of earlier cells by name or by pointing. * Go to the point of an error in a .m file. * On-line help * Symbol completion * Interrupts Installation: Copy the stuff below the ======== line below to math.el in whatever directory you put emacs-lisp stuff in. (If you don't know, type go to the *scratch* buffer, type load-path C-u C-x C-e. If none of those directories are writable by you, ask an emacs expert to make you directory for your own private emacs stuff.) Check the $Path variable of your version of Mathematica. Edit the Mathematica-search-path variable, which is set in the 3rd line beyond the legalese (or just make make sure it is set before loading this) to match. Use nil for the current working directory. Also make sure that the emacs variable math-process-string (just below Mathematica-search-path) reflects the location of Mathematica on your system. When you want to use math-mode, first type M-x load-library RET math RET After loading, type M-x math to start a copy of Mathematica. Edit an input cell using normal editing commands, the submit with ESC-RET. If Mathematica detects a syntax error, it will be indicated with "^--error". Fix the error, cut out the "^--error", and resubmit. You can complete Mathematica symbols, in both the working buffer and in other math-mode buffers, with ESC-TAB. Do not try this when Mathematica is busy or chaos will result. You can get help on Mathematica symbols, in both the working buffer and in other math-mode buffers, with C-h e or C-h E (the latter is more verbose). Again, don't try this when Mathematica is busy. HP users, please note that C-h and DEL are usually reversed in most GNU Emacs installations. You can copy cells to the end of the buffer with C-c C-y. It will ask for what cell you want in the minibuffer. copies cell number copies the previous In cell if the cursor is after the last In[..], otherwise copies the cell the cursor is in. This latter case will copy an In cell, an Out cell containing no blank lines (especially useful with InputForm), or just any block of text. This also works from any math-mode buffer, but copies to the math process buffer (one with an active Mathematica process--normally *math*, but it be changed with set-math-process-buffer). With a prefix arg, the option will back over incarnation boundaries of Mathematica. See the on-line help for math-copy-cell for more info. C-c C-c interrupts Mathematica (as well is it can be interrupted). When it gives you the prompt, type your response followed by ESC-RET. C-c 9 is equivalent to kill -9 . If you have read in a .m file with "<<", and have gotten a response of the form ": : syntax error in ..." you can go directly to the point of the error by typing C-c C-e. This is very useful because the line numbers are almost always wrong. This function counts lines the way Mathematica does. (There are reports of this not working with older versions of Emacs.) C-h e, C-h E, (help commands), and ESC-TAB (math-complete-symbol) depend on a running Mathematica process. C-c C-y affects a buffer expected to have a running Mathematica process. These commands can all be used from a buffer that does not have a running Mathematica process, in which case they affect a buffer that does. The default is *math*, the buffer created by the math command, but the buffer can be changed with M-x set-math-process-buffer. Different buffers can have different associated math process buffers. Bugs/limitations: If the input is does not form a complete statement, Mathematica may hang waiting for more input. If this happens, type a RET to add a blank line, then ESC-RET to send an empty cell, which will clear Mathematica's input buffer. Cut away the new prompt, fix the cell and resubmit. Do not just fix the input and hit ESC-RET, as Mathematica will get the concatenation of both the first submission and the second. (You can demonstrate incomplete statements on the input "5+".) If you change Mathematica's $Path variable, C-c C-e may be unable to find the file (or may find the wrong file). A solution short of changing the Mathematica-search-path variable (using M-x set-variable) is to visit the file, then use M-x goto-matherr-line. The code that locates errors after typing ESC-RET depends on certain output being delevered from the process in complete chunks. Emacs documentation explicitly forbids relying on this property. Therefore this feature may be unreliable or non-portable. Fancy installation: You can avoid having to explicitly load the math package by putting the following lines in your .emacs file (autoload 'math "math" "Starts Mathematica in a separate buffer" t) (autoload 'math-mode "math" "A mode for running Mathematica or editing Mathematica source files." t) (autoload 'start-math "math" "Starts Mathematica in the current buffer" t) (setq auto-mode-alist (cons '("\\.m$" . math-mode) auto-mode-alist)) Math-mode will run faster if you "byte-compile" it. Type M-x byte-compile-file math.el (make sure the directory is right). Enjoy, -- David Jacobson ================================ ;; math.el, a mode package for Mathematica. ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;; Copyright (c) 1990 Hewlett-Packard Company, all rights reserved. ;; ;; LEGAL NOTICE ;; ;; This math-mode package is experimental and HP shall have no obligation to ;; maintain or support it. HP makes no express or implied warranty of any ;; kind with respect to this software, and HP shall not be liable for any ;; direct, indirect, special, incidental or consequential damages (whether ;; based on contract, tort or any other legal theory) arising in any way from ;; use of the software. ;; ;; Everyone is granted permission to copy, modify and redistribute this ;; math-mode package, provided: ;; 1. All copies contain this copyright notice. ;; 2. All modified copies shall carry a prominant notice stating who ;; made the last modification and the date of such modification. ;; 3. No charge is made for this software or works derived from it. ;; This clause shall not be construed as constraining other software ;; distributed on the same medium as this software, nor is a ;; distribution fee considered a charge. ;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;; Portions of this package were adapted from GNU Emacs. ;; ;; Copyright (C) 1985, 1986, 1987, 1988 Free Software Foundation, Inc. ;; ;; GNU Emacs is distributed in the hope that it will be useful, ;; but WITHOUT ANY WARRANTY. No author or distributor ;; accepts responsibility to anyone for the consequences of using it ;; or for whether it serves any particular purpose or works at all, ;; unless he says so in writing. Refer to the GNU Emacs General Public ;; License for full details. ;; Everyone is granted permission to copy, modify and redistribute ;; GNU Emacs, but only under the conditions described in the ;; GNU Emacs General Public License. A copy of this license is ;; supposed to have been given to you along with GNU Emacs so you ;; can know your rights and responsibilities. It should be in a ;; file named COPYING. Among other things, the copyright notice ;; and this notice must be preserved on all copies. ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;; Author: David Jacobson, jacobson@hplabs.hp.com ;; Experimental version of April 10, 1990 ;; Assumes GNU Emacs version 18.54 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; (require 'shell) (defvar Mathematica-search-path (list nil (getenv "HOME") "/usr/local/math/Init" "/usr/local/math/Packages") "*A list of directories in which to look for files. Use nil for the current directory.") (defconst math-process-string "/usr/local/bin/math" "A string to pass to the unix exec function to start Mathematica") (defvar math-process-buffer "*math*" "The buffer normally running Mathematica. Certain commands (e.g. math-complete-symbol) will go to this buffer to find a Mathematica process. This can be locally set with set-math-process-buffer.") (defconst math-header-re (concat "^" (regexp-quote "by S. Wolfram, D. Grayson, R. Maeder, H. Cejtin,")) "A regexp that will match somewhere in the Mathematica preamble") (defvar math-mode-map nil) ;;; deep-copy-keymap was written by Daniel LaLiberte. ;;; Some GNU Emacs systems already have this installed. If so ;;; comment out this function definition. (defun deep-copy-keymap (keymap) "Return a deep copy of KEYMAP. That is, all levels are copied, not just the top level." (if (not (keymapp keymap)) keymap (cond ((listp keymap) (let ((new-keymap (copy-alist keymap))) (setq keymap (cdr new-keymap)) (while keymap (let ((binding (car keymap))) (if (keymapp (cdr binding)) (setcdr binding (deep-copy-keymap (cdr binding)))) ) (setq keymap (cdr keymap)) ) new-keymap )) ((vectorp keymap) (let ((i 0) (n (length keymap)) (new-keymap (copy-sequence keymap))) (while (< i n) (if (keymapp (aref keymap i)) (aset new-keymap i (deep-copy-keymap (aref keymap i)))) (setq i (1+ i))) new-keymap ))))) (if math-mode-map nil (setq math-mode-map (deep-copy-keymap shell-mode-map)) (define-key math-mode-map "\C-m" 'newline) ; the global keymap maps to newline (define-key math-mode-map "\e\C-m" 'math-send-input) ;; \C-c\C-c is set to interrupt-shell-subjob in the shell-mode-mode ;; The name is deceptive; it sends a SIGINT signal (control C) to ;; whatever process is running in the current buffer (define-key math-mode-map "\C-c9" 'kill-9-process) (define-key math-mode-map "\C-c\C-h" 'math-help); buffer specific C-h (define-key math-mode-map "\C-he" 'math-help) ; e-xpression in help menu (define-key math-mode-map "\C-hE" 'math-extra-help) ; E-xpression in help menu (define-key math-mode-map "\e\t" 'math-complete-symbol) (define-key math-mode-map "\C-c\C-y" 'math-copy-cell) (define-key math-mode-map "\C-c\C-e" 'find-math-error) (define-key math-mode-map "\C-c\C-r" 'math-isearch-backward)) (defvar math-mode-syntax-table nil "Syntax table used while in math mode.") (if math-mode-syntax-table () (setq math-mode-syntax-table (make-syntax-table)) (modify-syntax-entry ?% "." math-mode-syntax-table) (modify-syntax-entry ?& "." math-mode-syntax-table) (modify-syntax-entry ?* ". 23" math-mode-syntax-table) ;allow for (* comment *) (modify-syntax-entry ?+ "." math-mode-syntax-table) (modify-syntax-entry ?- "." math-mode-syntax-table) (modify-syntax-entry ?/ "." math-mode-syntax-table) (modify-syntax-entry ?< "." math-mode-syntax-table) (modify-syntax-entry ?= "." math-mode-syntax-table) (modify-syntax-entry ?> "." math-mode-syntax-table) (modify-syntax-entry ?_ "." math-mode-syntax-table) (modify-syntax-entry ?\| "." math-mode-syntax-table) (modify-syntax-entry ?\` "_" math-mode-syntax-table) ; Mathematica context symbol (modify-syntax-entry ?\( "()1" math-mode-syntax-table) ;allow for (* comment *) (modify-syntax-entry ?\) ")(4" math-mode-syntax-table)) ;allow for (* comment *) ;;; math-send-input sends a chunk of text to Mathematica. It ;;; interacts tightly with math-send-filter using the buffer-specific ;;; variable math-send-state and synchronizes though sending output ;;; and the accept-process-output (but see below) command. ;;; The Emacs documentation ;;; claims that one cannot be sure how much output will be delivered ;;; in a chunk to the output filter. However we depend on chunks of ;;; up to one line after which Mathematica immediately does a read, ;;; arriving in a single chunk. A slightly more robust technique than ;;; doing string-match on the input string would be to put the input ;;; into the buffer and match there. ;;; If the Mathematica process does not send a prompt at all, the ;;; accept-process-output hangs and the only solution is to kill the ;;; mathexe process or Emacs. This can happen if you use an Input[""] ;;; (a rather perverse thing to do). An alternative is to replace ;;; (accept-process-output process) with (sleep-for 10). It appears that ;;; arrival of any output causes Emacs to pop immediately out of a ;;; sleep-for. But this could mess up if you have more than one active ;;; process running at a time or if you strke a key. ;;; Of course, we could use a while loop and have the filter set ;;; math-send-state to another value when it has actually gotten ;;; something. I tried this but ran into unknown trouble and have ;;; not followed up on it. ;;; The variable math-send-state has the following interpretatons: ;;; non-last-line We are in the middle of sending a ;;; multi-line input. Watch for ;;; errors and output other than indent ;;; cookies. ;;; ;;; last-line The last line has been sent, still watch ;;; for syntax error messages. Also insert ;;; a blank like (and warn about it) if the ;;; output contained any non-whitespace ;;; characters before a newline. ;;; ;;; throw-away-prompt A syntax error has been detected and a ;;; newline sent to Mathematica to flush its ;;; input buffer. Normally it will come ;;; back with a new prompt. If the next ;;; input looks like a prompt, throw it ;;; away and give a syntax error message. ;;; Otherwise display that discarded ;;; material as a warning. ;;; ;;; normal Just post the output. Actually I think ;;; everything that sets the mode to normal ;;; also sets the filter to nil, so this is ;;; hardly used. (But see the exit clause of ;;; the unwind-protect.) (defun math-send-input () "Send input to Mathematica. At end of buffer, sends last \"cell\" to Mathematica. When not at end, copies current \"cell\" to the end of the buffer and sends it. Also sends input for interrupt and Input[]. Warning: A multi-line input to Input[\"\"] will cause deadlock." (interactive "*") (let ((process (or (get-buffer-process (current-buffer)) (error "Current buffer has no process"))) bpt2 ept2 begpkt endpkt copy ) ;; Find beginning of "cell" (let* ((cellinfo (math-identify-cell (point) (process-mark process))) (bpt (car cellinfo)) (ept (nth 1 cellinfo)) ) (check-math-syntax bpt ept) (goto-char ept) ;; Move to line beyond cell, adding newline if necessary. (forward-line 1) (if (or (not (bolp)) (= (point) bpt)) ; make null cells contain a newline (newline)) (setq copy (buffer-substring bpt (point))) ;; If we are \"near\" the end of the buffer, we don't copy the data down ;; there, but we kill excess white space. Otherwise, we go there and ;; copy the data. (if (looking-at "\\s *\\'") (progn (replace-match "") (setq bpt2 bpt) (setq ept2 (point))) (goto-char (point-max)) (forward-line 0) (if (or (eolp) (looking-at "^In\\[[0-9]+\\]:=\\s *$")) (end-of-line) (end-of-line) (newline)) (setq bpt2 (point)) (insert copy) (setq ept2 (point))) (goto-char bpt2) ;; indentstring is a global variable ;; indentstring is a the string Mathematica would have indented ;; the user's start point by if we were talking to it directly. (setq math-indent-string "") (set-process-filter process 'math-send-filter) ;; math-send-state is a global variable (setq math-send-state 'non-last-line) (setq begpkt bpt2) ; point (message "*") (unwind-protect (while (eq math-send-state 'non-last-line) (goto-char begpkt) (forward-line 1) (setq endpkt (point)) (if (= endpkt ept2) (setq math-send-state 'last-line)) (metered-process-send-string process (buffer-substring begpkt endpkt)) (if (eq math-send-state 'non-last-line) ;; See discussion above. (accept-process-output process) ;;(sleep-for 10) ) (cond ((eq math-send-state 'premature-output) (setq math-send-state 'normal) ; for sake of unwind protect (set-process-filter process nil) (error "Unexpected output; part of cell discarded")) ) (setq begpkt endpkt) ; advance to next line ) ; end while ;; unwind protect tail (if (memq math-send-state '(last-line normal)) () (set-process-filter process nil)))))) (defun math-send-filter (proc string) (let ((cbuf (current-buffer)) (save-match-data (match-data))) (unwind-protect (progn (set-buffer (process-buffer proc)) (cond ;; a ((and (memq math-send-state '(non-last-line last-line)) (string-match "\\`\\([ \t]*\\)\\^ " string)) (let ((tpt (point)) error-column indent-column (tail-string (substring string (match-end 0)))) (goto-char tpt) (insert (substring string 0 (match-end 1))) (setq error-column (current-column)) (delete-region tpt (point)) (insert math-indent-string) (setq indent-column (current-column)) (delete-region tpt (point)) (indent-to-column (- error-column indent-column)) (insert "^--error\n") (backward-char 9) (previous-line 1) ;; Display any unexpected output. I don't know how to ;; test this code. (if (string-match "\\S " tail-string) (save-excursion (goto-char (point-max)) (insert tail-string)))) ; end of let (setq math-send-state 'throw-away-prompt) (message "Syntax error") ; live dangerously here, but sometimes we ; don't get a prompt back from ; Mathematica (process-send-string proc "\n")) ;; snarf up indent strings ((and (eq math-send-state 'non-last-line) (string-match "\\`[ \t]+\\'" string)) (setq math-indent-string string)) ;; unexpected output ((eq math-send-state 'non-last-line) (insert "-------- Unexpected output appeared here; rest of cell not sent --------\n" ) (goto-char (point-max)) (insert string) (set-marker (process-mark proc) (point)) (setq math-send-state 'premature-output) (message "")) ;; throw away unwanted prompt ((eq math-send-state 'throw-away-prompt) (setq math-send-state 'normal) (set-process-filter proc nil) (if (string-match "\\`In\\[[0-9]+\\]:= \\'" string) (message "Syntax error") (message "Syntax error, discarding prompt(?): %s" string))) ((eq math-send-state 'last-line) (goto-char (point-max)) (cond ((and (string-match "\\`[ \t]*\\S " string) (not (string-match "\\`In\\[[0-9]+\\]:=" string))) (newline) (insert string) (set-marker (process-mark proc) (point)) (setq math-send-state 'normal) (message "newline inserted by Emacs' math-mode")) ((string-match "\\`[ \t]*\n" string) (setq math-send-state 'normal) (insert string) (set-marker (process-mark proc) (point)) (message "")) ((string-match "\\S " string) (insert string) (set-marker (process-mark proc) (point)) (message "")) (t ; just white space (insert string) (message "Incomplete cell? (Clear with RET ESC RET)")))) (t (setq math-send-state 'normal) (goto-char (point-max)) (insert string) (set-marker (process-mark proc) (point))) )) ; finishes up cond and progn ;; safely exit the filter (set-buffer cbuf) (store-match-data save-match-data)))) (defun math-mode () "Major mode for interacting with Mathematica and editing .m files. \\[math] starts Mathematica. \\[math-send-input] tries to identify stuff following last \"In[...]:= \" or blank line or the last output and sends it. To clear out Mathmatica after an error occurs, move point two lines below last printing character and type \\[math-send-input]. Warning: do not use Input[\"\"], and type in a mult-line reply; deadlock results. \\[math-help] gives help on a Mathematica symbol. \\[math-extra-help] or C-u \\[math-help] gives more verbose help. \\[math-complete-symbol] will complete the symbol near point. \\[math-copy-cell] will copy a previous cell to the end of the buffer. See its description for details. \\[math-isearch-backward] does a backward regexp i-search, initialized to find In[...]. \\[find-math-error] when typed after <] to the end of the buffer. With CELLNUMBER of empty string and point at or after last In[...]:= copies previous In cell to end of buffer. With point before last In[...]:= copies cell near point (In, Out, or just a block of text) to end of buffer. With an explicit CELLNUMBER, a prefix arg will skip back prefix arg incarnations before searching for In[]. C-u's count in unary. When called from a program, CELLNUMBER must be a string, second arg is INCARNATIONS back and third is POINT to begin search at." (interactive "*sCell number (default is cell near point): \nP\nd") (cond ((zerop (length numberstring)) (goto-char (point-max)) (if (and (re-search-backward "^In\\[[0-9]+\\]:=" nil t) (>= pt (point))) (progn (re-search-backward "^In\\[[0-9]+\\]:=") ; back up to previous one (while (and (not (bobp)) (or (looking-at ; reject ones without any useful text "^In\\[[0-9]+\\]:=\\s *\\(\\'\\|\n\\s *$\\)"))) (re-search-backward "^In\\[[0-9]+\\]:="))) (goto-char pt))) ; do current cell (t (goto-char (point-max)) (backward-incarnations incarnations) (re-search-backward (concat "^In\\[" numberstring "\\]:=")))) (if (interactive-p) (push-mark)) (let* ((cellinfo (math-identify-cell (point) nil t)) (copy (buffer-substring (car cellinfo) (nth 1 cellinfo)))) (if (not (equal (get-buffer math-process-buffer) (current-buffer))) (pop-to-buffer math-process-buffer)) (goto-char (point-max)) (re-search-backward "\\S ") (forward-line 0) (if (looking-at "^In\\[[0-9]+\\]:=\\s *$") (end-of-line) (goto-char (point-max))) (insert copy))) (defun math-isearch-backward () "Does a backward regexp i-search, initialized to find In[...]:=" (interactive) (setq search-last-regexp "^In\\[[0-9]+\\]:=\\s *") (setq unread-command-char search-reverse-char) (isearch-backward-regexp)) (defun math-identify-cell (pt &optional procmark out-ok) "Finds cell around POS. Optional second arg PROCMARK (normally the process-mark) will bound the search if the boundary otherwise would be a blank line (or the beginning of the buffer) and POS >= PROCMARK. Optional 3rd arg OUT-OK will allow acceptance of Out cells as well as In cells. Returns a list of the buffer position of the beginning and end of the cell." (save-excursion (goto-char pt) ;; back up at most one blank line looking for input (end-of-line) (re-search-backward (if out-ok "\\(^In\\[[0-9]+\\]:= ?\\)\\|\\(^\\s *\n\\)\\|\\(^Out\\[[0-9]+\\]\\(//[^=]*\\)?= ?\\)" "\\(^In\\[[0-9]+\\]:= ?\\)\\|\\(^\\s *\n\\)") nil 1) (goto-char (cond ((match-end 1)) ((and out-ok (match-end 3))) ((and procmark (>= pt procmark)) (max procmark (or (match-end 2) (point-min) ))) ((match-end 2)) ((point-min)))) (let ((bpt (point)) ept ) (if (re-search-forward "^\\s *$\\|^Out\\[[0-9]+\\][^=\n]*=\\|^In\\[[0-9]+\\]:=" nil 1) ;; If it matches, we have found the beginning of a line ;; following the cell. Back up one character. ;; If it doesn't match we are at eob and end of cell. (goto-char (max (- (match-beginning 0) 1) bpt))) (setq ept (point)) (list bpt ept)))) (defun get-math-completion (prefix) "Returns string to insert to complete a Mathematica symbol Designed to be called as in (insert (get-math-completion word))" (let ((cbuf (current-buffer))) (unwind-protect (progn (set-buffer " Mathwork") (goto-char (point-min)) (let (alist) (while (looking-at "\\S +") (setq alist (cons (list (buffer-substring (match-beginning 0) (match-end 0))) alist)) (forward-line 1)) (set-buffer cbuf) (let ((t-c-result (and alist (try-completion prefix alist)))) ; try-completion barfs on a nil alist, so we help it out (cond ((eq t-c-result t) (message "%s is complete" prefix) "") ((eq t-c-result nil) (message "No match found") "") ((not (string= prefix t-c-result)) (substring t-c-result (length prefix))) (t (with-output-to-temp-buffer "*Help*" (display-completion-list (all-completions prefix alist)) (print-help-return-message)) "")))))))) (defun kill-9-process () "Kills the process in the current buffer as in kill -9." (interactive) (kill-process (get-buffer-process (current-buffer)))) (defun metered-process-send-string (process string) "The same semantics as process-send-string, except the string is broken into small enough chunks to not mess up emacs." (let ((p 0) (len (length string))) (while (< p len) (process-send-string process (substring string p (setq p (min len (+ p 80)))))))) (defun skip-over-white-lines () ;; it might be possible to do this with ;; (re-search-forward "\\(^\\s *\n\\)*") ;; but this works. (while (and (not (eobp)) (looking-at "^\\s *$") ; blank line (zerop (forward-line))))) ;;; Mathematica counts lines wrong. The following is what really happens. ;;; Blank lines, other than the first line are not counted (unless inside ;;; quotes or comments). Unescaped newlines inside strings count double. (defun goto-matherr-line (argline) "Goes to the line intended by Mathematica error messages" (interactive "ngoto Mathematica line number: ") (let ((lineno 1) (comment-depth 0) instring) (goto-char (point-min)) (if (looking-at "^\s *$") (progn (setq lineno 2) (skip-over-white-lines))) (while (and (not (eobp)) (< lineno argline)) (cond ((> comment-depth 0) (re-search-forward "\\((\\*\\)\\|\\(\\*)\\)\\|\\(\n\\)" nil 1) ; (* or *) or newline (cond ((match-beginning 1) (setq comment-depth (1+ comment-depth))) ((match-beginning 2) (setq comment-depth (1- comment-depth))) ((match-beginning 3) (setq lineno (1+ lineno))))) (instring (re-search-forward "\\(\\\\\\\\\\)\\|\\(\\\\\042\\)\\|\\(\042\\)\\|\\(\\\\\n\\)\\|\\(\n\\)" nil 1) ;; \\ or \quote or quote or \newline or newline ;; \042 is a double quote. ;; Using the octal form keeps Emacs from getting lost. (cond ((match-beginning 3) (setq instring nil)) ((match-beginning 4) (setq lineno (1+ lineno))) ((match-beginning 5) (setq lineno (+ 2 lineno))))) (t (re-search-forward "\\(\050\\*\\)\\|\\(\042\\)\\|\\(\n\\)" nil 1) ; left paren* or quote or newline (cond ((match-beginning 1) (setq comment-depth 1)) ((match-beginning 2) (setq instring t)) ((match-beginning 3) (setq lineno (1+ lineno)) (skip-over-white-lines)))))))) (defun find-math-error () "Searches for the last \"syntax error in\" message; goes to indicated line in the indicated file. It uses the symbol Mathematica-search-path rather than going to all the work to discover the real real search path." (interactive) (let (filename linenumber raw-filename (math-search-path Mathematica-search-path)) (save-excursion (re-search-backward "syntax error in") (forward-line 0) (if (not (looking-at "\\([^:]+\\): *\\([0-9]+\\):")) (error "Cannot parse error line")) (setq raw-filename (buffer-substring (match-beginning 1) (match-end 1))) (setq linenumber (string-to-int (buffer-substring (match-beginning 2) (match-end 2))))) (while (not filename) (setq filename (expand-file-name raw-filename (car math-search-path))) (if (not (file-readable-p filename)) (progn (setq filename nil) (setq math-search-path (cdr math-search-path)) (if (null math-search-path) (error "File %s not found" raw-filename))))) (find-file-other-window filename) (goto-matherr-line linenumber))) (defun set-math-process-buffer (buffer) "Sets the buffer in/to which to evaluate/copy Mathematica code. (You only need to use this function if you want a buffer other than *math*.)" (interactive "bMathematica buffer: ") (make-local-variable 'math-process-buffer) ;; The following trick will use the buffer itself if ;; it is defined. That way if the user eventually ;; changes the name, say by writing it out, this local ;; math-process-buffer will still point to the right place. ;; But if the buffer does not yet exist, it will still work. (setq math-process-buffer (or (get-buffer buffer) buffer))) From kmorriso@data.acs.calpoly.edu Wed Apr 18 18:04:04 1990 Received: from data.ACS.CalPoly.EDU by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA14542; Wed, 18 Apr 90 18:04:00 -0500 Received: from worf.acs.calpoly.edu (worf) by data.acs.calpoly.edu (NeXT-1.0 (From Sendmail 5.52)/NeXT-1.0) id AA15341; Wed, 18 Apr 90 16:02:37 GMT-0800 Message-Id: <9004190002.AA15341@ data.acs.calpoly.edu > Received: by worf.acs.calpoly.edu (NeXT-1.0 (From Sendmail 5.52)/NeXT-1.0) id AA00641; Wed, 18 Apr 90 16:04:27 GMT-0800 Date: Wed, 18 Apr 90 16:04:27 GMT-0800 From: kmorriso@data.acs.calpoly.edu To: mathgroup@yoda.ncsa.uiuc.edu Subject: Different NeXT versions? Cc: jdelany@data.acs.calpoly.edu Status: RO We have version 1.2 (Aug. 1989) running on NeXTs. At the Redwood City conference in January 1990 there were some things working differently on the NeXT, but it was still version 1.2. Two examples: Integrate and NIntegrate were listable in Redwood City so that one could integrate vector valued functions without extra effort. In the Aug. 1989 version that does not work. Second, an integrand such as Sqrt[x^2 +y^2] leads to messages about insufficient accuracy after seven recursive subdivisions, using NIntegrate. But in Redwood City the computations proceeded without a hitch. Are we running the same version? Are there files or packages that need loading? From shdavis@marsh.rice.edu Wed Apr 18 18:06:51 1990 Received: from marsh.rice.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA14551; Wed, 18 Apr 90 18:06:48 -0500 Received: from piranha.rice.edu by marsh.rice.edu (AA25510); Wed, 18 Apr 90 18:05:38 CDT Received: by piranha.rice.edu (AA01852); Wed, 18 Apr 90 18:05:46 CDT Date: Wed, 18 Apr 90 18:05:46 CDT From: Sam H. Davis Message-Id: <9004182305.AA01852@piranha.rice.edu> To: mathgroup@yoda.ncsa.uiuc.edu Subject: Mathematica Simplify problem Status: RO In trying to demonstrate how to find a conjugate harmonic function, I ran into a problem with Simplify: In[1]:= u=Exp[x^2-y^2] Cos[2 x y] 2 2 x - y Out[1]= E Cos[2 x y] In[2]:= ux=D[u,x] 2 2 2 2 x - y x - y Out[2]= 2 E x Cos[2 x y] - 2 E y Sin[2 x y] In[3]:= v=Integrate[ux,y] -I I -- - 2 2 Out[3]= ------------ + ----------- 2 2 (-I x + y) (I x + y) E E In[4]:= Simplify[v] 2 -2 I x y - y 4 I x y E (I + -I E ) Out[4]= -------------------------------- 2 Somehow Exp(x^2) got lost in this last step. Is there a way around this? Sam Davis shdavis@rice.edu From phil@einstein.tamu.edu Thu Apr 19 14:55:39 1990 Received: from TAMU.EDU by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA15471; Thu, 19 Apr 90 14:55:24 -0500 Received: from einstein.tamu.edu by TAMU.EDU (AA06574); Thu, 19 Apr 90 14:54:20 CDT Received: by einstein.tamu.edu (4.0/SMI-4.0) id AA21783; Thu, 19 Apr 90 14:52:47 CDT Date: Thu, 19 Apr 90 14:52:47 CDT From: phil@einstein.tamu.edu (Philip B. Yasskin) Message-Id: <9004191952.AA21783@einstein.tamu.edu> To: rsarava@splash.princeton.edu Subject: Re: supressing argument evaluation by function Part Cc: mathgroup@yoda.ncsa.uiuc.edu, phil@einstein.tamu.edu Status: RO The reason you get error messages from lhs = { { -(k^2 + lamsq[[n]]), lamsq[[n]] }, { lamsq[[n]], -(k^2 + lamsq[[n]]) } } rhs = { { -(k^2 + lamsq[[n]]) u1[[n]], lamsq[[n]] u1[[n]] }, { lamsq[[n]] u2[[n]], -(k^2 + lamsq[[n]]) u2[[n]] } } cmatrix[k_,n_] = Inverse[lhs] . rhs is that n is not defined as a number when you define lhs and rhs. The errors should dissappear if you insert the expressions for lhs and rhs into the formula for cmatrix. However, the following should be much faster since you don't have to recompute the n-th component repeatedly: In[1]:= cmatrix[k_,n_] := Block[{lamsqn=lamsq[[n]], u1n=u1[[n]], u2n=u2[[n]]}, lhs = { { -(k^2 + lamsqn), lamsqn }, { lamsqn, -(k^2 + lamsqn) } }; rhs = { { -(k^2 + lamsqn) u1n, lamsqn u1n }, { lamsqn u2n, -(k^2 + lamsqn) u2n } }; Inverse[lhs] . rhs ] In[2]:= lamsq = {1,2,3,4} Out[2]= {1, 2, 3, 4} In[3]:= u1 = {2,4,6,8} Out[3]= {2, 4, 6, 8} In[4]:= u2 = {1,3,5,7} Out[4]= {1, 3, 5, 7} In[5]:= cmatrix[1,2] 24 6 6 11 Out[5]= {{--, -(-)}, {-, --}} 5 5 5 5 Phil Yasskin phil@einstein.tamu.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Sat Apr 21 01:26:39 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA17705; Sat, 21 Apr 90 01:26:38 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA21342; Sat, 21 Apr 90 01:21:33 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA16996; Fri, 20 Apr 90 22:17:54 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA16992; Fri, 20 Apr 90 22:17:52 -0500 Message-Id: <9004210317.AA16992@yoda.ncsa.uiuc.edu> Date: Thu, 19 Apr 90 14:52:47 CDT From: phil@einstein.tamu.edu (Philip B. Yasskin) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: supressing argument evaluation by function Part Status: RO The reason you get error messages from lhs = { { -(k^2 + lamsq[[n]]), lamsq[[n]] }, { lamsq[[n]], -(k^2 + lamsq[[n]]) } } rhs = { { -(k^2 + lamsq[[n]]) u1[[n]], lamsq[[n]] u1[[n]] }, { lamsq[[n]] u2[[n]], -(k^2 + lamsq[[n]]) u2[[n]] } } cmatrix[k_,n_] = Inverse[lhs] . rhs is that n is not defined as a number when you define lhs and rhs. The errors should dissappear if you insert the expressions for lhs and rhs into the formula for cmatrix. However, the following should be much faster since you don't have to recompute the n-th component repeatedly: In[1]:= cmatrix[k_,n_] := Block[{lamsqn=lamsq[[n]], u1n=u1[[n]], u2n=u2[[n]]}, lhs = { { -(k^2 + lamsqn), lamsqn }, { lamsqn, -(k^2 + lamsqn) } }; rhs = { { -(k^2 + lamsqn) u1n, lamsqn u1n }, { lamsqn u2n, -(k^2 + lamsqn) u2n } }; Inverse[lhs] . rhs ] In[2]:= lamsq = {1,2,3,4} Out[2]= {1, 2, 3, 4} In[3]:= u1 = {2,4,6,8} Out[3]= {2, 4, 6, 8} In[4]:= u2 = {1,3,5,7} Out[4]= {1, 3, 5, 7} In[5]:= cmatrix[1,2] 24 6 6 11 Out[5]= {{--, -(-)}, {-, --}} 5 5 5 5 Phil Yasskin phil@einstein.tamu.edu From jpg@ALLEGHENY.SCRC.Symbolics.COM Mon Apr 2 16:01:13 1990 Received: from [128.81.41.45] by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA01874; Mon, 2 Apr 90 16:01:06 -0500 Received: from SKUA.SCRC.Symbolics.COM by ALLEGHENY.SCRC.Symbolics.COM via CHAOS with CHAOS-MAIL id 180586; 2 Apr 90 16:18:53 EDT Date: Mon, 2 Apr 90 16:18 EDT From: Jeffrey P. Golden Subject: precision and accuracy To: keiper@wri.UUCP Cc: mathgroup@yoda.ncsa.uiuc.edu, jpg@ALLEGHENY.SCRC.Symbolics.COM In-Reply-To: <9003292140.AA03501@yoda.ncsa.uiuc.edu> Message-Id: <19900402201819.8.JPG@SKUA.SCRC.Symbolics.COM> Status: RO Date: Mon, 26 Mar 90 13:03:08 CST From: wri!keiper@yoda.ncsa.uiuc.edu (Jerry Keiper) [...] As to increasing the precision of a number, Mathematica allows this to be done very simply using SetPrecision[] (likewise the accuracy can be increased with SetAccuracy[].) y = SetPrecision[x, prec] gives y a value such that y == x is True and such that the precision of y is prec. If the precision of y is greater than the precision of x the "missing" digits of x are filled in for y with 0's in binary. This does not mean that they will appear as 0's in decimal however. e.g. the decimal number 1.2 has a nonterminating binary expansion 1.0011001100110011001100... Clearly if we start with a finite approximation to this and attach 0's in binary we will not get the decimal expansion for 1.200000000... Since it is not possible to know what number a user has in mind when he wants to increase its precision it is not possible to give a better approximation; all that Mathematica can do is give another number with more digits in it. If the user types SetPrecision[1.2,30], I think it is pretty clear that most users mean the same number that SetPrecision[12/10,30] would mean, i.e. fill in with decimal 0's, which is not what Mathematica does. As to relative and absolute error vs. precision and accuracy, precision is a nonnegative integer and accuracy is an integer. Relative and absolute error are small numbers, sometimes complex, but they are never known exactly (if they were the approximate answer could be corrected.) I find it more convenient to deal with an accuracy of 27 rather than an absolute error of 0.000000000000000000000000001, but perhaps not everyone does. I think no one finds it convenient to deal with 0.000000000000000000000000001 . That's why notations such as 1.0 10^-27 (or even 1.0e-27) were invented. (I can't tell whether you're trying to bias the situation or just so used to typing numbers such as 1.20000000000000000000000000000 to Mathematica to get the precision you need!-) From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Apr 24 12:19:17 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA21230; Tue, 24 Apr 90 12:19:16 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA01547; Tue, 24 Apr 90 12:14:12 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA21033; Tue, 24 Apr 90 11:16:25 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA21029; Tue, 24 Apr 90 11:16:24 -0500 Message-Id: <9004241616.AA21029@yoda.ncsa.uiuc.edu> Date: Mon, 23 Apr 90 14:05:54 EDT From: Jim_Wendel@ub.cc.umich.edu To: mathgroup-adm@yoda.ncsa.uiuc.edu Subject: Re: Transformation Rules via Algebraic Rules Status: RO This is in reply to "Transformation Rules via Algebraic Rules" posted 4/13 by ???. It doesn't completely solve the problem, however. Type rule1, you'll see x->t^(3/2). Type rule2, you'll see {x->t^(3/2)}, apparently just rule1 surrounded by braces. Define rule3={x->t^(3/2)}. Type rule3, see apparently same as rule2 gave. But if you request InputForm of these rules you will see that they are very different; 1 & 3 are just the actual inputs, but rule2 is a complicated thing that makes reference to an undocumented function AlgebraicRulesData, known to users only as Protected. Jim_Wendel@ub.cc.umich.edu. From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Apr 27 11:53:43 1990 To: mathgroup@yoda.ncsa.uiuc.edu Subject: deferred evaluation question Status: RO There are functions in Mma that do not defer evaluation when their arguments are undefined symbols, for example N and Mod: In[1]:= N[x] Out[1]= x In[2]:= Mod[m, 7] Out[2]= m Question: is it possible, through rule definition or some other clever artifice, to make functions N and Mod defer evaluation with the input above, i.e., evaluate to N[x] and Mod[m, 7]? Constraints: the artifice should have no disastrous side effects on the normal operation of N and Mod or on evaluation generally, and it should be substantially less complex than rebuilding Mathematica in Mathematica. - Bill MacGregor From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Apr 27 12:53:44 1990 Subject: NumberQ To: mathgroup@yoda.ncsa.uiuc.edu Status: RO I am trying to define some numeric functions. If I make definitions like myfun[x_Real] := thing1 myfun[x_Integer] := thing2 myfun[x_Number] := thing3 myfun[x_Rational] := thing4 my function does not get evaluated for myfun[Sqrt[3]]. What type is Sqrt[3]? I note that NumberQ[Sqrt[3]] returns False. E. Neely Atkinson AN123651 at UTHVM1.BITNET neely@mdaali.cancer.utexas.edu From lsf@astrosun.TN.CORNELL.EDU Fri Apr 27 13:17:41 1990 To: stevec@yoda.ncsa.uiuc.edu Subject: Re: NumberQ Status: RO Steve: Do you think that you could fix the mathgroup mailheader so that the From: line indicates either the true originator of the message or mathgroup? Right now, they all come from you. Thanks, From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Apr 27 13:36:26 1990 To: mathgroup@yoda.ncsa.uiuc.edu Subject: High precision floating point considered hazardous Status: RO Suppose that I double a floating point number then subtract off the original number. I ought to get the original number back, with maybe the LSB being trashed. If I do this N times, the introduced error should be at most N times the weight of the LSB. Well, Mathematica's high precision floating point numbers don't work that way! In fact, the way they work is downright hazardous, as I found out. In[1]:= a=1.1111111111111111 Out[1]= 1.1111111111111111 In[2]:= Do[a=2a-a,{55}] In[3]:= a Out[3]= 0. Wow, just 55 iterations got a zero, not a 1.111... with some error. Furthermore that zero is a black hole: In[4]:= a+1 Out[4]= 0. Everything works fine if we use a machine float instead of a big float: In[5]:= b=1.111111111 Out[5]= 1.111111111 In[6]:= Do[b=2b-b,{1000}] In[7]:= b Out[7]= 1.11111 In[8]:= b-%5 Out[8]= 0. The problem is that each iteration ratchets down the precision by one until it eventually gets to zero. Although it is less serious, there are also constructs that ratchet up the precision, which, by the way, indicates that the precision calculation cannot be quite correct. In[35]:= p=N[Pi,20] Out[35]= 3.1415926535897932385 In[36]:= Do[p=(p+p)/2,{100}] In[37]:= p Out[37]= 3.1415926535897932384626445913472373472822072149898 In[39]:= Precision[p] Out[39]= 50 In[40]:= N[Pi,50] Out[40]= 3.1415926535897932384626433832795028841971693993751 You might think that you never use big floats, so you don't have to worry. That's what I thought, too. Unfortunately, the function Fit sometimes outputs a function with coefficients that are big floats, even when only passed machine floats in the input: In[24]:= Fit[{0., 0.00694444, 0.0165094, 0.0278869},{x^3, x^2,x,1},x] 2 Out[24]= -0.00351594 + 0.0015323633333333 x + 0.00211823999999999 x - 3 > 0.00013466333333333 x (Those are the actual numbers that caused the problem that I ran into.) The ratcheting up of precision may be a performance problem, but the ratcheting down of precision is downright disastrous. I can suggest two approaches: either take care to avoid big floats altogether in calculations where each iteration uses the results of the previous iteration, or if you really need higher precision, figure out in advance what precision you want, then restore the precision of every variable at the end of each iteration with something like x = SetPrecision[x,desiredPrecision] The immediate problem arises from the way Mathematica computes the precision/accuracy of the result of an addition: it seems to make the accuracy of the result be the accuracy of the least accurate addend. Now for some opinions: There are at least 3 different notions of precision. 1. A bound on the error introduced in each computation (including conversion to floating point) leading up to the present value. Thus a precision of 16 digits (53 bits) means the result is as accurate/precise as could have been expected if 53 bit mantissas had been used in all calculations leading to the number. This says nothing about how close the number represented is to the ideal number that would have occurred if all arithmetic in an entire computation were exact; rather, it says that in each individual computation at most so much error is introduced by the arithmetic and by forcing results back into variables of this much "precision". 2. An upper bound on the relative difference between the number actually represented and that which would have occurred if each computation were exact. Thus 1.6453 with a precision of 4 means that, had all arithmetic been exact, the result would have been in the range 1.6453 +/- .00016453. 3. An estimate of the uncertainty of the output of a calculation based on the uncertainty of measured values. This is commonly used in physics labs. (The mumblefoo distance was 76.2 +/- .1 cm.) Thus if from an experiment computing the acceleration of gravity, the calculation yields 9.81 with a precision of 3, the true acceleration of gravity lies in the range 9.815 +/- .009815, assuming there are no systematic errors in the experiment. Mathematica seems to be trying for meaning two. (Although the policy of making the precision of a literal be the number of digits typed in shows vestiges of meaning 3.) As evidence for this claim note that the precision of a result of a subtraction is less than either argument: In[41]:= q = 1.11111111111111111111111111111 Out[41]= 1.11111111111111111111111111111 In[42]:= 1025 q - 1024 q Out[42]= 1.11111111111111111111111111 Also N[] reduces but never increases precision, presumably based on the idea that it shouldn't give the illusion of precision that isn't already there. Now the question is, what ought Mathematica to provide? (Disclaimer, I'm no expert in this stuff. Other people have undoubtedly written entire dissertations on the topic.) It ought to be useful, free of ratcheting, either up or down, and reasonable to implement. It also ought to have an appealingly simple definition, and handle exact numbers (numbers with a precision of Infinity) without any ugly special cases that break the spirit of the definition. I'll dispose of definition 3 (propagation of input uncertainty to output) right off: it should be done by the user, possibly with the help of a Mathematica package. I believe that correctly implementing a system based on definition 2 is virtually impossible. While it is can be done locally for each operation, the composite precision for an entire computation fails to give the right answer. To see this, suppose that x is some variable, and in the early stages an error of epsilon was introduced, so we have x = x' + epsilon, where x' is the ideal value. Then we compute y=x, then eventually y-x. We ought to get a true zero. But since the system does not know that the error in x is always the same as the error in y, it must assume the worst case, namely that they could be of opposite sign, and indicate the result to be 0 +/- 2 epsilon. As the example involving Pi indicates, Mathematica doesn't even always get the calculated precision right. (I also conjecture that even getting it locally right requires that the accuracy be carried to several significant bits, but I'll skip that discussion.) What the user really wants is to ensure that his/her calculations are done with enough precision (definition 1 sense) that errors introduced by arithmetic and by forcing numbers into some representation are negligible for his/her application. But since Mathematica is not a compiled language with declarations for every variable (and since in any case there are still intermediate results that need to be represented), we want a reasonable precision to be automatically generated for every operation. I suggest that a good definition of "precision" is roughly definition 1. (Admittedly, its not really a property of a number, but of a computation. Perhaps we need a different word.) Intuitively a number has a certain precision, P, if it is as accurate/precise as one could have expected had P bits of mantissa been used in all computations/conversions leading up to it. (It may be convenient to display/accept precision in decimal digits, but in this discussion we are using bits.) We need rules for the precision of the results of the various operations. I suggest the following. When converting to a float, the precision is the number of bits the mantissa is truncated to. The precision of the output of the basic arithmetic opertions is the minimum of the precision of the operands. The basic defintion is obviously satisfied, since the reported precision is the minimum of all the precisions involved in the entire calculation. What properties does this have? 1. Operations on a pair of numbers of the same precision leaves the precision unchanged. 2. The precision can never ratchet up or down. 3. There is no special case for exact numbers. The can be converted to the precision of the other operand and the operation can proceed. 4. If input is always converted to at least the precision of machine floats, then machine floats are in no way a special case. If some big float or exact number is to be combined with a machine float, just convert it to a machine float and proceed with the two machine floats. -- David Jacobson Postscript: I spent many hours working on an alternate set of rules for addition and subtraction. This set of rules would have allowed an addition as shown in the example below to keep the precision of the large, high precision number. (The picture shows the addition of the mantissas after shifting. A "d" indicates a bit actually available in the data.) 1ddddddddddddddddddddd 1dddddddd Unfortunately, proving that it satisfied the basic definition required that doing a calculation to N digits, then truncating down to a smaller M, be considered equivalent to having done the calculation in M digits all along---something I know is false. If there is any interest in this topic, someone just send mail directly to me and I'll post the idea. From @vmd.cso.uiuc.edu:USERCLEL@UALTAMTS.BITNET Fri Apr 27 14:38:12 1990 Subject: your equations in Mathematica To: stevec@YODA.NCSA.UIUC.EDU Status: RO Thank you for your message. It nust have contained a number of symbols that cannot be printed on the screen or on our printer. They are replaced by interrogation points. The message is therefore not quite readable. Could you send it, please, by mail? My address is: Clement Leibovitz University Computing Systems GBS 372 University of Alberta Edmonton, Alberta, Canada. T6G 2E1 With thanks. Clement From testgroup-adm@yoda.ncsa.uiuc.edu Fri Apr 27 14:25:15 1990 To: stevec@yoda.ncsa.uiuc.edu Subject: Re: NumberQ Status: RO try this myfun[x_Sqrt] := thing5 ie. the tag after the underscore can be any expression "head". Mathematica does have numeric types: Real, Integer etc. But, symbolic results such as Sqrt[3] can either be considered to belong to the general expression type which will match: myfun[x_] := thing or specifically matched by the name of the outermost function. check out page 228 in Wolframs text Dave skankman@ux1.lbl.gov From mathgroup-adm@yoda.ncsa.uiuc.edu Sat Apr 28 14:55:05 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA00236; Sat, 28 Apr 90 14:55:04 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA29164; Sat, 28 Apr 90 14:50:33 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA01372; Fri, 27 Apr 90 15:29:18 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA01368; Fri, 27 Apr 90 15:29:16 -0500 Date: Fri, 27 Apr 90 15:29:16 -0500 Message-Id: <9004272029.AA01368@yoda.ncsa.uiuc.edu> From: skankman@ux1.lbl.gov.Fri.Apr.27.14:02:16.1990 To: stevec@yoda.ncsa.uiuc.edu Subject: Re: NumberQ Status: RO try this myfun[x_Sqrt] := thing5 ie. the tag after the underscore can be any expression "head". Mathematica does have numeric types: Real, Integer etc. But, symbolic results such as Sqrt[3] can either be considered to belong to the general expression type which will match: myfun[x_] := thing or specifically matched by the name of the outermost function. check out page 228 in Wolframs text Dave skankman@ux1.lbl.gov From jacobson@cello.hpl.hp.com Sat Apr 28 14:59:16 1990 Received: from bardeen.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA00308; Sat, 28 Apr 90 14:59:04 -0500 Received: from newton.ncsa.uiuc.edu by bardeen.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA18143; Fri, 27 Apr 90 19:21:48 CDT Return-Path: Received: from hplms2.hpl.hp.com ([15.255.176.66]) by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA11247; Fri, 27 Apr 90 19:21:46 CDT Received: from cello.hpl.hp.com by hplms2.hpl.hp.com with SMTP (15.11.1.3/15.5+IOS 3.20) id AA25884; Fri, 27 Apr 90 17:20:19 pdt Received: from localhost by cello.HPL.HP.COM; Fri, 27 Apr 90 17:20:14 pdt To: mathgroup@yoda.ncsa.uiuc.edu Cc: neely@mdaali.cancer.utexas.edu Subject: Re: NumberQ In-Reply-To: Your message of "Fri, 27 Apr 90 09:27:16 CDT." <9004271602.AA00467@yoda.ncsa.uiuc.edu> Date: Fri, 27 Apr 90 17:20:11 PDT Message-Id: <443.641262011@cello> From: jacobson@cello.hpl.hp.com Status: RO > I am trying to define some numeric functions. If I make definitions > like > myfun[x_Real] := thing1 > myfun[x_Integer] := thing2 > myfun[x_Number] := thing3 > myfun[x_Rational] := thing4 > my function does not get evaluated for myfun[Sqrt[3]]. What type is > Sqrt[3]? I note that NumberQ[Sqrt[3]] returns False. The simplest approach if real, integer, rational, and number are all the other cases is to just use myfun[x_] := thing5 If you want to recognize all things that are non-simple goodies, this will work: myfun[x_?(!AtomQ[#]&)] := thing5a To recognize all non-numbers myfun[x_?(!NumberQ[#]&)] := thing5b To recognize symbols myfun[x_Symbol] := thing6 To recognize specific constructs, e.g. to differentiate between Sqrt and Log myfun[x:Sqrt[_]] := thing7 myfun[x:Log[_]] := thing8 -- David Jacobson From @uunet.UU.NET:paul@wri.UUCP Sat Apr 28 14:57:40 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA00268; Sat, 28 Apr 90 14:57:38 -0500 Return-Path: Received: from uunet.uu.net by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA10025; Fri, 27 Apr 90 17:56:53 CDT Received: from wri.UUCP by uunet.uu.net (5.61/1.14) with UUCP id AA06275; Fri, 27 Apr 90 18:56:47 -0400 Received: by WRI.com (3.2/SMI-3.0DEV3) id AA02561; Fri, 27 Apr 90 13:27:04 CDT Date: Fri, 27 Apr 90 13:27:04 CDT From: paul@wri.UUCP (Paul Abbott) Message-Id: <9004271827.AA02561@WRI.com> To: wester@ghostwheel.unm.edu Subject: Determinant and Eigenvalue routines in Mathematica Cc: rivin@uunet.UU.NET, stevec@ncsa.uiuc.edu Status: RO Dear Michael: Hope that the following answers some of your questions: Eigenvalues and Eigenvectors: same as EISPAK; see numerous references for the latter for details. For the symbolic (and exact) cases, we do it the hard way by solving the characteristic polynomial, etc. Determinants: Symbolic: Expansion by minors Exact Integers: Modular reduction followed by Gauss Elimination. Floats: LU decomposition. From mathgroup-adm@yoda.ncsa.uiuc.edu Mon Apr 30 14:06:50 1990 To: mathgroup-adm@yoda.ncsa.uiuc.edu Subject: Re: NumberQ Status: RO Try myfun[Sqrt[3.0]]. jim_wendel@ub.cc.umich.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Mon Apr 30 14:45:36 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA03075; Mon, 30 Apr 90 14:45:34 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA25809; Mon, 30 Apr 90 14:40:49 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA02594; Mon, 30 Apr 90 12:18:45 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA02590; Mon, 30 Apr 90 12:18:43 -0500 Date: Mon, 30 Apr 90 12:18:43 -0500 Message-Id: <9004301718.AA02590@yoda.ncsa.uiuc.edu> From: jack@sun.udel.edu.Mon.Apr.30.11:15:11.1990 To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: High precision floating point considered hazardous Status: RO I tried this problem.... a = 1.1111111111111111 Do[a=2a-a,{55}] on versions 1.1 and 1.2. I did obtain 0 on version 1.2, but there was no error on 1.1..i.e., I did not obtain 0! Seems like a bug in version 1.2. From mathgroup-adm@yoda.ncsa.uiuc.edu Tue May 1 16:46:30 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA04699; Tue, 1 May 90 16:46:28 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA15025; Tue, 1 May 90 16:41:52 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA04622; Tue, 1 May 90 16:05:00 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA04618; Tue, 1 May 90 16:04:59 -0500 Date: Tue, 1 May 90 16:04:59 -0500 Message-Id: <9005012104.AA04618@yoda.ncsa.uiuc.edu> From: knutj@idt.unit.no.Tue.May.1.07:04:07.1990 To: mathgroup@yoda.ncsa.uiuc.edu Subject: Plots and scientific notation Status: RO I have a (simple ?) question : Is it possible to tell Mathematica to _automatically_ format real numbers using scientific notation ? Or more specific, to use scientific notation on all or one of the axes on 2-D and 3-D plots ? In my case I will be very happy if it is possible to use scientific notation on the z-axis of 3-D plots. It looks rather ugly with 0.0000002, 0.0000004, etc. And even worse when Mathematica (must) use a variable number of digits, e.g. 0.000015, 0.00002, 0.000025. I could use other tools but Mathematica is the only one available that let me specify a function as a numerical integral. Any suggestions ? Knut Johannessen Dept. Computer Science and Telematics Norwegian Institute of Technology N-7034 Trondheim, Norway email: knutj@idt.unit.no From jacobson@hplred.hpl.hp.com Tue May 1 18:26:20 1990 Received: from hplms2.hpl.hp.com by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA04826; Tue, 1 May 90 18:26:17 -0500 Received: from hplred.hpl.hp.com by hplms2.hpl.hp.com with SMTP (15.11.1.3/15.5+IOS 3.20) id AA21804; Tue, 1 May 90 16:25:23 pdt Received: by hplred.HPL.HP.COM; Tue, 1 May 90 16:24:59 pdt Date: Tue, 1 May 90 16:24:59 pdt From: David M. Jacobson Message-Id: <9005012324.AA17394@hplred.HPL.HP.COM> To: mathgroup@yoda.ncsa.uiuc.edu Status: RO Here is *starter*. When I did this, the labels on the ticks of a plot came out looking like scientific notation, but the graph was tiny on my screen. It obviously messes something else up. Also, you'll need to do something about zeros, as this will take the Log of zero. In[14]:= Unprotect[Real] In[15]:= Format[x_Real] := Block[{exp=Floor[Log[10,x]],mant}, mant=Round[x/10^(exp-3)]; StringJoin[ToString[Floor[mant/1000]],".",ToString[Mod[mant,1000]], " 10^",ToString[exp]]] In[16]:= Protect[Real] There's got to be a better solution. -- David Jacobson From mathgroup-adm@yoda.ncsa.uiuc.edu Tue May 1 20:13:48 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA04908; Tue, 1 May 90 20:13:47 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA18424; Tue, 1 May 90 20:09:14 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA04850; Tue, 1 May 90 18:29:37 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA04846; Tue, 1 May 90 18:29:36 -0500 Message-Id: <9005012329.AA04846@yoda.ncsa.uiuc.edu> Date: Tue, 1 May 90 16:24:59 pdt From: David M. Jacobson Subject: Re: Plots and scientific notation To: mathgroup@yoda.ncsa.uiuc.edu Status: RO Here is *starter*. When I did this, the labels on the ticks of a plot came out looking like scientific notation, but the graph was tiny on my screen. It obviously messes something else up. Also, you'll need to do something about zeros, as this will take the Log of zero. In[14]:= Unprotect[Real] In[15]:= Format[x_Real] := Block[{exp=Floor[Log[10,x]],mant}, mant=Round[x/10^(exp-3)]; StringJoin[ToString[Floor[mant/1000]],".",ToString[Mod[mant,1000]], " 10^",ToString[exp]]] In[16]:= Protect[Real] There's got to be a better solution. -- David Jacobson From nb@Sunburn.Stanford.EDU Fri May 4 19:25:03 1990 Received: from Sunburn.Stanford.EDU by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA09012; Fri, 4 May 90 19:25:01 -0500 Received: by Sunburn.Stanford.EDU with SMTP (5.61+IDA/25-eef) id AA12403; Fri, 4 May 90 17:24:05 -0700 Message-Id: <9005050024.AA12403@Sunburn.Stanford.EDU> To: stevec@yoda.ncsa.uiuc.edu Subject: An improved posting Date: Fri, 04 May 90 17:24:05 PDT From: nb@Sunburn.Stanford.EDU Status: RO Steve, If you have not already posted the message I sent you earlier today, I would appreciate you posting this note instead. Thank, Nancy ----------------------------------------------------------------------------- Variable Symbols, Inc. offers training, consulting, and reference materials for people who use or plan to use Mathematica. PRODUCTS Variable Symbols, Inc. has developed two help facilities: Mathematica Reference Cards and a Mathematica Help Stack based on HyperCard. THE MATHEMATICA HELP STACK makes it simple to find information about functions, and commands in Mathematica. It categorizes each of them and offers a visual representation for some. Demonstrations copies of this stack are available. THE MATHEMATICA REFERENCE CARDS provide a summary of the functions in Mathematica. One laminated four-card set describes Mathematica's built-in objects and lists all functions, options, variables, aliases, and special forms available in Version 1.2. The second set, made up of five double-sided pages, lists all objects defined in the packages distributed with Mathematica and includes a cross reference. If you know the name of a function, you can lookup the name of the folder/directory in which it is contained. Nancy Blachman Tel. 415 486-8073 AppleLink: VSI Email: nb@cs.stanford.edu Variable Symbols, Inc. * P.O. Box 9013 * Berkeley, CA 94709-0013 * 415 486 8073 Order form follows. _______________________________________________________________________________ Variable Symbols, Inc. Order Form Name___________________________________________________________________________ Job title or occupation________________________________________________________ Organization____________________________________________________________________ Street address_________________________________________________________________ City, state zip (postal) code, country_________________________________________ Electronic mail address__________________________________ Fax ________________ Telephone______________________________________________________________________ ORDER INFORMATION Description Price Quantity Total Laminated Reference Cards Mathematica Built-in Objects $9.95 ________ $________ California residents include 7.25% sales tax $________ Postage and handling $2.00 $________ ($4 for foreign orders) Total $________ Make your check payable to Variable Symbols, Inc. __ Send me a reference card for the packages distributed with Mathematica. We are developing a Mathematica Help HyperCard stack. __ Send me a demonstration copy of the Mathematica Help Stack. __ Contacted when the full release of the Mathematica Help Stack is available. We are developing additional Mathematica reference material. Are you interested in? __ Reference cards containing examples __ Other reference material, please specify___________________________________ Would you be interested in? __ On-site training __ Video tapes __ Notification of Workshops in your area __ Off-site training __ On-line tutorials __ Consulting __ WYSIWYG Front End to Mathematica What level of training courses would be of interest to you? __ Introductory __ Intermediate __ Advanced On which computer systems do you use Mathematica? _____________________________ Do you use Mathematica as part of your job? __ Yes __ No How many people in your department or organization use Mathematica? __ 1 __ 2-5 __ 6-10 __ 11-20 __ Over 20 Where did you hear about Variable Symbols, Inc.? ______________________________ _______________________________________________________________________________ Variable Symbols, Inc. * P.O. Box 9013 * Berkeley, CA 94709-0013 * 415 486 8073 Nancy Blachman Tel. 415 486-8073 AppleLink: VSI Email: nb@cs.stanford.edu From myers@helios.TN.CORNELL.EDU Sat May 5 11:58:46 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA09857; Sat, 5 May 90 11:58:45 -0500 Return-Path: Received: from devvax.TN.CORNELL.EDU by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA28636; Sat, 5 May 90 11:57:54 CDT Received: from ARTEMIS.TN.CORNELL.EDU by devvax.TN.CORNELL.EDU (5.59-1.12/1.3-Cornell-Theory-Center) id AA22768; Sat, 5 May 90 12:57:43 EDT Received: from localhost by artemis.TN.CORNELL.EDU (3.2/1.1nn-Cornell-LASSP) id AA01418; Sat, 5 May 90 12:57:42 EDT Message-Id: <9005051657.AA01418@artemis.TN.CORNELL.EDU> To: steve@ncsa.uiuc.edu Subject: Passing variables to FindMinimum[] Date: Sat, 05 May 90 12:57:41 -0400 From: myers@helios.TN.CORNELL.EDU Status: RO I have a Mathematica question regarding the use of FindMinimum[]. If there is more than one variational parameter, the correct syntax is FindMinimum[f, {x[1], x0[1]}, {x[2], x0[2]}, ..., {x[n], x0[n]}], where f is the function to be minimized, x[i] are the variational parameters and the x0[i] are starting guesses for the x[i]. I am trying to construct a routine that will minimize with respect to a variable number (n) of variational parameters, as suggested by my example above. The first approach that came to mind was something of the form FindMinimum[f, Table[{x[i], x0[i]}, {i,1,n}]], but the problem with this is that Table[] produces an extra set of {}, resulting in FindMinimum[f, {{x[1], x0[1]}, {x[2], x0[2]}, ..., {x[n], x0[n]}}]. Somehow the outer set of brackets needs to be stripped, but trying to use Apply[] in a roundabout way to put FindMinimum at the head of the list has not been fruitful. Any ideas, comments, or suggestions would be appreciated. Chris Myers myers@helios.tn.cornell.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Sat May 5 15:28:45 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA10085; Sat, 5 May 90 15:28:44 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA01663; Sat, 5 May 90 15:24:16 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA09917; Sat, 5 May 90 13:41:32 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA09913; Sat, 5 May 90 13:41:31 -0500 Message-Id: <9005051841.AA09913@yoda.ncsa.uiuc.edu> To: steve@ncsa.uiuc.edu Subject: Passing variables to FindMinimum[] Date: Sat, 05 May 90 12:57:41 -0400 From: myers@helios.TN.CORNELL.EDU Status: RO I have a Mathematica question regarding the use of FindMinimum[]. If there is more than one variational parameter, the correct syntax is FindMinimum[f, {x[1], x0[1]}, {x[2], x0[2]}, ..., {x[n], x0[n]}], where f is the function to be minimized, x[i] are the variational parameters and the x0[i] are starting guesses for the x[i]. I am trying to construct a routine that will minimize with respect to a variable number (n) of variational parameters, as suggested by my example above. The first approach that came to mind was something of the form FindMinimum[f, Table[{x[i], x0[i]}, {i,1,n}]], but the problem with this is that Table[] produces an extra set of {}, resulting in FindMinimum[f, {{x[1], x0[1]}, {x[2], x0[2]}, ..., {x[n], x0[n]}}]. Somehow the outer set of brackets needs to be stripped, but trying to use Apply[] in a roundabout way to put FindMinimum at the head of the list has not been fruitful. Any ideas, comments, or suggestions would be appreciated. Chris Myers myers@helios.tn.cornell.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Sat May 5 17:33:13 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA10251; Sat, 5 May 90 17:33:12 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA03360; Sat, 5 May 90 17:28:42 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA09904; Sat, 5 May 90 13:34:57 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA09900; Sat, 5 May 90 13:34:55 -0500 Message-Id: <9005051834.AA09900@yoda.ncsa.uiuc.edu> To: stevec@yoda.ncsa.uiuc.edu Subject: An improved posting Date: Fri, 04 May 90 17:24:05 PDT From: nb@Sunburn.Stanford.EDU Status: RO ----------------------------------------------------------------------------- Variable Symbols, Inc. offers training, consulting, and reference materials for people who use or plan to use Mathematica. PRODUCTS Variable Symbols, Inc. has developed two help facilities: Mathematica Reference Cards and a Mathematica Help Stack based on HyperCard. THE MATHEMATICA HELP STACK makes it simple to find information about functions, and commands in Mathematica. It categorizes each of them and offers a visual representation for some. Demonstrations copies of this stack are available. THE MATHEMATICA REFERENCE CARDS provide a summary of the functions in Mathematica. One laminated four-card set describes Mathematica's built-in objects and lists all functions, options, variables, aliases, and special forms available in Version 1.2. The second set, made up of five double-sided pages, lists all objects defined in the packages distributed with Mathematica and includes a cross reference. If you know the name of a function, you can lookup the name of the folder/directory in which it is contained. Nancy Blachman Tel. 415 486-8073 AppleLink: VSI Email: nb@cs.stanford.edu Variable Symbols, Inc. * P.O. Box 9013 * Berkeley, CA 94709-0013 * 415 486 8073 Order form follows. _______________________________________________________________________________ Variable Symbols, Inc. Order Form Name___________________________________________________________________________ Job title or occupation________________________________________________________ Organization____________________________________________________________________ Street address_________________________________________________________________ City, state zip (postal) code, country_________________________________________ Electronic mail address__________________________________ Fax ________________ Telephone______________________________________________________________________ ORDER INFORMATION Description Price Quantity Total Laminated Reference Cards Mathematica Built-in Objects $9.95 ________ $________ California residents include 7.25% sales tax $________ Postage and handling $2.00 $________ ($4 for foreign orders) Total $________ Make your check payable to Variable Symbols, Inc. __ Send me a reference card for the packages distributed with Mathematica. We are developing a Mathematica Help HyperCard stack. __ Send me a demonstration copy of the Mathematica Help Stack. __ Contacted when the full release of the Mathematica Help Stack is available. We are developing additional Mathematica reference material. Are you interested in? __ Reference cards containing examples __ Other reference material, please specify___________________________________ Would you be interested in? __ On-site training __ Video tapes __ Notification of Workshops in your area __ Off-site training __ On-line tutorials __ Consulting __ WYSIWYG Front End to Mathematica What level of training courses would be of interest to you? __ Introductory __ Intermediate __ Advanced On which computer systems do you use Mathematica? _____________________________ Do you use Mathematica as part of your job? __ Yes __ No How many people in your department or organization use Mathematica? __ 1 __ 2-5 __ 6-10 __ 11-20 __ Over 20 Where did you hear about Variable Symbols, Inc.? ______________________________ _______________________________________________________________________________ Variable Symbols, Inc. * P.O. Box 9013 * Berkeley, CA 94709-0013 * 415 486 8073 Nancy Blachman Tel. 415 486-8073 AppleLink: VSI Email: nb@cs.stanford.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Sat May 5 16:30:11 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA10166; Sat, 5 May 90 16:30:09 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA02520; Sat, 5 May 90 16:25:42 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA09923; Sat, 5 May 90 13:42:11 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA09919; Sat, 5 May 90 13:42:10 -0500 Message-Id: <9005051842.AA09919@yoda.ncsa.uiuc.edu> Date: Sat, 5 May 90 10:18:55 -0700 From: stewart@sdsu.edu (Kris Stewart) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Differential Equation Solutions Status: RO I'm a new Mathematica user. I was hoping for a strong differential equation solving facility in Mathematica. I don't know whether I'm not using it correctly yet, or what. I started with a simple initial value problem, y''= -y, y(0)=0, y'(0)=1, and I expected the solution, y(x)=sin(x). Instead the solution was in the equivalent, but complicated, complex exponential form still. Is there a easy to simplification package that I haven't found out about? I would like to attempt more elaborate DEs, but would solutions returned in as straight forward a form as possible. Please advise. (Note, I ran this example with Maple and got precisely the results I expected. Did I purchase the wrong symbolic package?) In[3]:= DSolve[{y'[x]==w[x],w'[x]==-y[x],y[0]==0,w[0]==1},{y[x],w[x]},x] -I x 2 I x -I x 2 I x E (-I + I E ) E (1 + E ) Out[3]= {{y[x] -> ---------------------, w[x] -> ------------------}} 2 2 Thanks, in advance, for any community help I receive. Kris Stewart stewart@cs.sdsu.edu From testgroup-adm@yoda.ncsa.uiuc.edu Mon May 7 10:22:16 1990 To: Steve Christensen Subject: Reference Material for Mathematica Users Status: RO ----------------------------------------------------------------------------- To: MathGroup Subject: Reference Material for Mathematica Users Variable Symbols, Inc. offers training, consulting, and reference materials for people who use or plan to use Mathematica. PRODUCTS Variable Symbols, Inc. has developed two help facilities: Mathematica Reference Cards and a Mathematica Help Stack based on HyperCard. THE MATHEMATICA HELP STACK makes it simple to find information about functions, and commands in Mathematica. It categorizes each of them and offers a visual representation for some. Demonstrations copies of this stack are available. THE MATHEMATICA REFERENCE CARDS provide a summary of the functions in Mathematica. One laminated four-card set describes Mathematica's built-in objects and lists all functions, options, variables, aliases, and special forms available in Version 1.2. The second set, made up of five double-sided pages, lists all objects defined in the packages distributed with Mathematica and includes a cross reference. If you know the name of a function, you can lookup the name of the folder/directory in which it is contained. Nancy Blachman Tel. 415 486-8073 AppleLink: VSI Email: nb@cs.stanford.edu Variable Symbols, Inc. * P.O. Box 9013 * Berkeley, CA 94709-0013 * 415 486 8073 Order form follows. _______________________________________________________________________________ Variable Symbols, Inc. Order Form Name___________________________________________________________________________ Job title or occupation________________________________________________________ Organization___________________________________________________________________ Street address_________________________________________________________________ City, state zip (postal) code, country_________________________________________ Electronic mail address__________________________________ Fax ________________ Telephone______________________________________________________________________ ORDER INFORMATION Description Price Quantity Total Laminated Reference Cards Mathematica Built-in Objects $9.95 ________ $________ California residents include 7.25% sales tax $________ Postage and handling $2.00 $________ ($4 for foreign orders) Total $________ Make your check payable to Variable Symbols, Inc. __ Send me a reference card for the packages distributed with Mathematica. We are developing a Mathematica Help HyperCard stack. __ Send me a demonstration copy of the Mathematica Help Stack. __ Contacted when the full release of the Mathematica Help Stack is available. We are developing additional Mathematica reference material. Are you interested in? __ Reference cards containing examples __ Other reference material, please specify___________________________________ Would you be interested in? __ On-site training __ Video tapes __ Notification of Workshops in your area __ Off-site training __ On-line tutorials __ Consulting __ WYSIWYG Front End to Mathematica What level of training courses would be of interest to you? __ Introductory __ Intermediate __ Advanced On which computer systems do you use Mathematica? _____________________________ Do you use Mathematica as part of your job? __ Yes __ No How many people in your department or organization use Mathematica? __ 1 __ 2-5 __ 6-10 __ 11-20 __ Over 20 Where did you hear about Variable Symbols, Inc.? ______________________________ _______________________________________________________________________________ Variable Symbols, Inc. * P.O. Box 9013 * Berkeley, CA 94709-0013 * 415 486 8073 Nancy Blachman Tel. 415 486-8073 AppleLink: VSI Email: nb@cs.stanford.edu From jacobson@cello.hpl.hp.com Mon May 7 11:05:00 1990 To: myers@helios.TN.CORNELL.EDU, mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Passing variables to FindMinimum[] In-Reply-To: Your message of "Sat, 05 May 90 12:57:41 EDT." <9005051841.AA09913@yoda.ncsa.uiuc.edu> Status: RO Chris Myers writes: > I have a Mathematica question regarding the use of FindMinimum[]. If there > is more than one variational parameter, the correct syntax is > > FindMinimum[f, {x[1], x0[1]}, {x[2], x0[2]}, ..., {x[n], x0[n]}], > > where f is the function to be minimized, x[i] are the variational parameters > and the x0[i] are starting guesses for the x[i]. I am trying to construct > a routine that will minimize with respect to a variable number (n) of > variational parameters, as suggested by my example above. ... Here is a construct that I think will do what you want. Apply[FindMinimum,Prepend[Table[{x[i], x0[i]}, {i,1,n}],f]] -- David Jacobson From @vmd.cso.uiuc.edu:AN123651@UTHVM1.BITNET Mon May 7 11:52:05 1990 Received: from vmd.cso.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA13179; Mon, 7 May 90 11:52:04 -0500 Message-Id: <9005071652.AA13179@yoda.ncsa.uiuc.edu> Received: from UTHVM1.BITNET by VMD.CSO.UIUC.EDU (IBM VM SMTP R1.2) with BSMTP id 7778; Mon, 07 May 90 11:51:26 CDT Received: from UTHVM1 (AN123651) by UTHVM1.BITNET (Mailer R2.05) with BSMTP id 3120; Mon, 07 May 90 11:50:09 CST Date: Mon, 07 May 90 11:47:53 CST From: "E. Neely Atkinson" Subject: Simplification of powers To: mathgroup@yoda.ncsa.uiuc.edu Status: RO Is there a way to get Mathematica to simplify 4^(1/3) / (2 2^(1/3)) to 2^(-2/3) or is this actually a hard problem? E. Neely Atkinson AN123651 at UTHVM1.BITNET neely@mdaali.cancer.utexas.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Mon May 7 13:58:27 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA13479; Mon, 7 May 90 13:58:26 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA17573; Mon, 7 May 90 13:53:56 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA13160; Mon, 7 May 90 11:32:13 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA13156; Mon, 7 May 90 11:32:12 -0500 Message-Id: <9005071632.AA13156@yoda.ncsa.uiuc.edu> From: jacobson@cello.hpl.hp.com Date: Mon May 7 11:05:00 1990 To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Passing variables to FindMinimum[] Status: RO Chris Myers writes: > I have a Mathematica question regarding the use of FindMinimum[]. If there > is more than one variational parameter, the correct syntax is > > FindMinimum[f, {x[1], x0[1]}, {x[2], x0[2]}, ..., {x[n], x0[n]}], > > where f is the function to be minimized, x[i] are the variational parameters > and the x0[i] are starting guesses for the x[i]. I am trying to construct > a routine that will minimize with respect to a variable number (n) of > variational parameters, as suggested by my example above. ... Here is a construct that I think will do what you want. Apply[FindMinimum,Prepend[Table[{x[i], x0[i]}, {i,1,n}],f]] -- David Jacobson From mathgroup-adm@yoda.ncsa.uiuc.edu Mon May 7 14:43:09 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA13632; Mon, 7 May 90 14:43:08 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA18760; Mon, 7 May 90 14:38:35 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA13154; Mon, 7 May 90 11:31:30 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA13150; Mon, 7 May 90 11:31:28 -0500 Message-Id: <9005071631.AA13150@yoda.ncsa.uiuc.edu> From: nb@Sunburn.Stanford.EDU Date: Mon May 7 03:06:52 1990 To: Steve Christensen Subject: Reference Material for Mathematica Users Status: RO ----------------------------------------------------------------------------- To: MathGroup Subject: Reference Material for Mathematica Users Variable Symbols, Inc. offers training, consulting, and reference materials for people who use or plan to use Mathematica. PRODUCTS Variable Symbols, Inc. has developed two help facilities: Mathematica Reference Cards and a Mathematica Help Stack based on HyperCard. THE MATHEMATICA HELP STACK makes it simple to find information about functions, and commands in Mathematica. It categorizes each of them and offers a visual representation for some. Demonstrations copies of this stack are available. THE MATHEMATICA REFERENCE CARDS provide a summary of the functions in Mathematica. One laminated four-card set describes Mathematica's built-in objects and lists all functions, options, variables, aliases, and special forms available in Version 1.2. The second set, made up of five double-sided pages, lists all objects defined in the packages distributed with Mathematica and includes a cross reference. If you know the name of a function, you can lookup the name of the folder/directory in which it is contained. Nancy Blachman Tel. 415 486-8073 AppleLink: VSI Email: nb@cs.stanford.edu Variable Symbols, Inc. * P.O. Box 9013 * Berkeley, CA 94709-0013 * 415 486 8073 Order form follows. _______________________________________________________________________________ Variable Symbols, Inc. Order Form Name___________________________________________________________________________ Job title or occupation________________________________________________________ Organization___________________________________________________________________ Street address_________________________________________________________________ City, state zip (postal) code, country_________________________________________ Electronic mail address__________________________________ Fax ________________ Telephone______________________________________________________________________ ORDER INFORMATION Description Price Quantity Total Laminated Reference Cards Mathematica Built-in Objects $9.95 ________ $________ California residents include 7.25% sales tax $________ Postage and handling $2.00 $________ ($4 for foreign orders) Total $________ Make your check payable to Variable Symbols, Inc. __ Send me a reference card for the packages distributed with Mathematica. We are developing a Mathematica Help HyperCard stack. __ Send me a demonstration copy of the Mathematica Help Stack. __ Contacted when the full release of the Mathematica Help Stack is available. We are developing additional Mathematica reference material. Are you interested in? __ Reference cards containing examples __ Other reference material, please specify___________________________________ Would you be interested in? __ On-site training __ Video tapes __ Notification of Workshops in your area __ Off-site training __ On-line tutorials __ Consulting __ WYSIWYG Front End to Mathematica What level of training courses would be of interest to you? __ Introductory __ Intermediate __ Advanced On which computer systems do you use Mathematica? _____________________________ Do you use Mathematica as part of your job? __ Yes __ No How many people in your department or organization use Mathematica? __ 1 __ 2-5 __ 6-10 __ 11-20 __ Over 20 Where did you hear about Variable Symbols, Inc.? ______________________________ _______________________________________________________________________________ Variable Symbols, Inc. * P.O. Box 9013 * Berkeley, CA 94709-0013 * 415 486 8073 Nancy Blachman Tel. 415 486-8073 AppleLink: VSI Email: nb@cs.stanford.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Mon May 7 15:39:41 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA13788; Mon, 7 May 90 15:39:40 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA20113; Mon, 7 May 90 15:35:09 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA13231; Mon, 7 May 90 12:38:42 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA13227; Mon, 7 May 90 12:38:41 -0500 Message-Id: <9005071738.AA13227@yoda.ncsa.uiuc.edu> Date: Mon, 07 May 90 11:47:53 CST From: "E. Neely Atkinson" Subject: Simplification of powers To: mathgroup@yoda.ncsa.uiuc.edu Status: RO Is there a way to get Mathematica to simplify 4^(1/3) / (2 2^(1/3)) to 2^(-2/3) or is this actually a hard problem? E. Neely Atkinson AN123651 at UTHVM1.BITNET neely@mdaali.cancer.utexas.edu From myers@helios.TN.CORNELL.EDU Tue May 8 16:40:08 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA15654; Tue, 8 May 90 16:40:07 -0500 Return-Path: Received: from devvax.TN.CORNELL.EDU by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA22750; Tue, 8 May 90 16:39:19 CDT Received: from artemis.tn.cornell.edu by devvax.TN.CORNELL.EDU (5.59-1.12/1.3-Cornell-Theory-Center) id AA00335; Mon, 7 May 90 19:49:06 EDT Received: from localhost by artemis.TN.CORNELL.EDU (3.2/1.1nn-Cornell-LASSP) id AA04558; Mon, 7 May 90 19:49:04 EDT Message-Id: <9005072349.AA04558@artemis.TN.CORNELL.EDU> To: steve@ncsa.uiuc.edu Subject: Re: Passing variables to FindMinimum[] Date: Mon, 07 May 90 19:49:02 -0400 From: myers@helios.TN.CORNELL.EDU Status: RO To the mathgroup -- I received many responses to my query regarding how to pass an undetermined number of variables to FindMinimum[]. I thank everyone who took the time to share their tricks. For those who didn't know how to answer my question, I'll pass along some of the more popular responses. The first involves constructing a secondary list which folds together the function to be minimized and the set of variational parameters. Apply [FindMinimum, Prepend[Table[{x[i],x0[i]},{i,1,2}],f]] The second takes advantage of the apparently undocumented command Sequence to strip the outer brackets of the nested list. FindMinimum[ f, Sequence @@ Table[...]] The third, and to me the most appealing, is to apply FindMinimum[f] to the list of variables. I had tried this approach, but with only a single # instead of the required ##; using a single # results in an application to only the first element of the Table, whereas ## applies to all arguments. ((FindMinimum[f, ##])&) @@ Table[{x[i], x0[i]}, {i,1,n}] Once again, thanks for the help. Chris Myers myers@helios.tn.cornell.edu From sdw@hpsadsdw.hp.com Tue May 8 18:04:52 1990 Received: from hp-sde.sde.hp.com by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA15737; Tue, 8 May 90 18:04:50 -0500 Received: from hpcea.ce.hp.com by hp-sde.sde.hp.com with SMTP (16.2A/15.5+IOS 3.13) id AA23062; Tue, 8 May 90 16:03:55 -0700 Received: from hpsadsdw.HP.COM by hpcea ; Tue, 8 May 90 16:03:22 pdt Received: by hpsadsdw.HP.COM; Tue, 8 May 90 16:02:02 pdt Message-Id: <9005082302.AA06926@hpsadsdw.HP.COM> Subject: log plots To: mathgroup@yoda.ncsa.uiuc.edu (mathgroup for mathematica) Date: Tue, 8 May 90 16:01:59 PDT From: Steven Warwick Organization: Hewlett-Packard Phone: 1-794-3198 Address: 1212 Valley House Drive, Rohnert Park, Ca 94928-4999 Mailer: Elm [revision: 64.9] Status: RO OK friends, how about a method of making plots where instead of tic marks, we get a full grid, like on log-log and log-lin paper! perhaps even thinner lines for the grid than the actual data... -- Steven Warwick Hewlett-Packard sdw@hpsad From mathgroup-adm@yoda.ncsa.uiuc.edu Tue May 8 19:51:34 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA16067; Tue, 8 May 90 19:51:33 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA25629; Tue, 8 May 90 19:47:10 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA15767; Tue, 8 May 90 18:16:47 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA15763; Tue, 8 May 90 18:16:46 -0500 Message-Id: <9005082316.AA15763@yoda.ncsa.uiuc.edu> Subject: log plots To: mathgroup@yoda.ncsa.uiuc.edu (mathgroup for mathematica) Date: Tue, 8 May 90 16:01:59 PDT From: sdw@hpsadsdw.hp.com Status: RO OK friends, how about a method of making plots where instead of tic marks, we get a full grid, like on log-log and log-lin paper! perhaps even thinner lines for the grid than the actual data... -- Steven Warwick Hewlett-Packard sdw@hpsad From mathgroup-adm@yoda.ncsa.uiuc.edu Tue May 8 20:51:18 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA16217; Tue, 8 May 90 20:51:17 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA26504; Tue, 8 May 90 20:46:54 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA15754; Tue, 8 May 90 18:15:21 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA15750; Tue, 8 May 90 18:15:20 -0500 Message-Id: <9005082315.AA15750@yoda.ncsa.uiuc.edu> To: steve@ncsa.uiuc.edu Subject: Re: Passing variables to FindMinimum[] Date: Mon, 07 May 90 19:49:02 -0400 From: myers@helios.TN.CORNELL.EDU Status: RO To the mathgroup -- I received many responses to my query regarding how to pass an undetermined number of variables to FindMinimum[]. I thank everyone who took the time to share their tricks. For those who didn't know how to answer my question, I'll pass along some of the more popular responses. The first involves constructing a secondary list which folds together the function to be minimized and the set of variational parameters. Apply [FindMinimum, Prepend[Table[{x[i],x0[i]},{i,1,2}],f]] The second takes advantage of the apparently undocumented command Sequence to strip the outer brackets of the nested list. FindMinimum[ f, Sequence @@ Table[...]] The third, and to me the most appealing, is to apply FindMinimum[f] to the list of variables. I had tried this approach, but with only a single # instead of the required ##; using a single # results in an application to only the first element of the Table, whereas ## applies to all arguments. ((FindMinimum[f, ##])&) @@ Table[{x[i], x0[i]}, {i,1,n}] Once again, thanks for the help. Chris Myers myers@helios.tn.cornell.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Tue May 8 22:50:30 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA16364; Tue, 8 May 90 22:50:29 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA28155; Tue, 8 May 90 22:46:04 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA16287; Tue, 8 May 90 21:25:19 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA16283; Tue, 8 May 90 21:25:17 -0500 Message-Id: <9005090225.AA16283@yoda.ncsa.uiuc.edu> To: steve@ncsa.uiuc.edu Subject: Re: Passing variables to FindMinimum[] Date: Mon, 07 May 90 19:49:02 -0400 From: myers@helios.TN.CORNELL.EDU Status: RO To the mathgroup -- I received many responses to my query regarding how to pass an undetermined number of variables to FindMinimum[]. I thank everyone who took the time to share their tricks. For those who didn't know how to answer my question, I'll pass along some of the more popular responses. The first involves constructing a secondary list which folds together the function to be minimized and the set of variational parameters. Apply [FindMinimum, Prepend[Table[{x[i],x0[i]},{i,1,2}],f]] The second takes advantage of the apparently undocumented command Sequence to strip the outer brackets of the nested list. FindMinimum[ f, Sequence @@ Table[...]] The third, and to me the most appealing, is to apply FindMinimum[f] to the list of variables. I had tried this approach, but with only a single # instead of the required ##; using a single # results in an application to only the first element of the Table, whereas ## applies to all arguments. ((FindMinimum[f, ##])&) @@ Table[{x[i], x0[i]}, {i,1,n}] Once again, thanks for the help. Chris Myers myers@helios.tn.cornell.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Wed May 9 03:38:58 1990 Received: from lth.se by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA17150; Wed, 9 May 90 03:38:39 -0500 Received: from Valhall.dna.lth.se by lth.se (5.61-bind 1.5+ida/LTH-4-NS); Wed, 9 May 90 10:03:24 +0200 (MET) Received: from sunic.sunet.se by DNA.LTH.Se (5.61-bind 1.4+ida/DNA 4-Dan); Wed, 9 May 90 10:05:10 +0200 (MET) Received: from mcsun.eu.net by sunic.sunet.se (5.61+IDA/KTH/LTH/1.135) id AAsunic14231; Wed, 9 May 90 10:04:53 +0200 Received: by mcsun.EU.net via EUnet; Wed, 9 May 90 02:54:44 +0200 (MET) Received: from uiucuxc.UUCP by uunet.uu.net (5.61/1.14) with UUCP id AA10895; Tue, 8 May 90 20:49:43 -0400 Received: from yoda.ncsa.uiuc.edu by uxc.cso.uiuc.edu with SMTP (5.62+/IDA-1.2.8) id AA10174; Tue, 8 May 90 19:33:24 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA15767; Tue, 8 May 90 18:16:47 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA15763; Tue, 8 May 90 18:16:46 -0500 Message-Id: <9005082316.AA15763@yoda.ncsa.uiuc.edu> Subject: log plots To: mathgroup@yoda.ncsa.uiuc.edu (mathgroup for mathematica) Date: Tue, 8 May 90 16:01:59 PDT From: sdw@hpsadsdw.hp.com Status: RO OK friends, how about a method of making plots where instead of tic marks, we get a full grid, like on log-log and log-lin paper! perhaps even thinner lines for the grid than the actual data... -- Steven Warwick Hewlett-Packard sdw@hpsad From mathgroup-adm@yoda.ncsa.uiuc.edu Fri May 11 00:32:43 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA02213; Fri, 11 May 90 00:32:42 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA10012; Fri, 11 May 90 00:28:34 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA01467; Thu, 10 May 90 23:11:27 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA01463; Thu, 10 May 90 23:11:25 -0500 Message-Id: <9005110411.AA01463@yoda.ncsa.uiuc.edu> Date: Thu, 10 May 90 23:09:09 -0500 From: Steve Christensen To: mathgroup@yoda.ncsa.uiuc.edu Subject: Combinatorica (Discrete Mathematics Package) Status: RO I have just placed the new Mathematica package Combinatorica.m in the Symbolic/Mathematica/Packages/SKIENA directory on the NCSA anonymous ftp server (128.174.20.50). Here are two files from that directory and a contact address for Steve Skiena, the author. This is a Beta release. Steve Christensen ====================================================================== (* Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica Version 0.5 5/8/90 Beta Release Copyright (c) 1990 by Steven S. Skiena This package contains all the programs from the book, "Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica" by Steven S. Skiena, Addison-Wesley Publishing Co., Advanced Book Program, 350 Bridge Parkway, Redwood City CA 94065. ISBN 0-201-50943-1. For ordering information, call 1-800-447-2226. This package is copyright 1990 by Steven S. Skiena. It may be copied in its entirety for nonprofit purposes only. Sale, other than for the direct cost of the media, is prohibited. This copyright notice must accompany all copies. These programs can be obtained on Macintosh and MS-DOS disks by sending $15.00 to Discrete Mathematics Disk, Wolfram Research Inc., PO Box 6059, Champaign, IL 61826-9905. (217)-398-0700. The author, Wolfram research, and Addison-Wesley Publishing Company, Inc. make no representations, express or implied, with respond to this documentation, of the software it describes and contains, including without limitations, any implied warranties of mechantability or fitness for a particular purpose, all of which are expressly disclaimed. The author, Wolfram Research, or Addison-Wesley, their licensees, distributors and dealers shall in no event be liable for any indirect, incidental, or consequential damages. This beta release is designed to run under Version 1.2 of Mathematica. Any comments, bug reports, or requests to get on the Combinatorica mailing list should be forwarded to: Steven Skiena Department of Computer Science State University of New York Stony Brook, NY 11794 skiena@sbcs.sunysb.edu (516)-632-9026 / 8470 *) ======================================================================= The Combinatorial Mathematica package contains all the programs from the book, "Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica" by Steven S. Skiena, Addison-Wesley Publishing Co., Advanced Book Program, 350 Bridge Parkway, Redwood City CA 94065. ISBN 0-201-50943-1. For ordering information, call 1-800-447-2226. Combinatorial Mathematica currently consists of one file, Combinatorica.m. It is a 100K ASCII file, and so should be easy to ftp. Since some mailers choke on files this large, we have also prepared a distribution of three smaller files, Part01, Part02, and Part03. ------------------------------------------------------------------ (0) A General Public License for Combinatorial Mathematica is in the file COPYING. (1) To execute Combinatorial Mathematica, enter Mathematica and load the package (< Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA04871; Fri, 11 May 90 18:00:23 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA03133; Fri, 11 May 90 17:09:10 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA03129; Fri, 11 May 90 17:09:08 -0500 Date: Fri, 11 May 90 17:09:08 -0500 Message-Id: <9005112209.AA03129@yoda.ncsa.uiuc.edu> From: GALANG@bcvms.bitnet Subject: Mathematica and the vax To: mathgroup@yoda.ncsa.uiuc.edu Status: RO Hi there, I was told that someone there would be able to tell me of user/s that are using Mathematica on a Apple Mac/VAX setup with either VMS or Ultrix running. I am very interested in knowing how well it works and the ease of implementation. If someone could help me out I would be very greatful. Roy D. Galang Boston College Galang@BCVAX2 From macg@SLCS.SLB.COM Tue May 15 09:05:37 1990 Received: from SLCS.SLB.COM by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA07325; Tue, 15 May 90 09:05:35 -0500 Received: from frank.SLCS.SLB.COM by SLCS.SLB.COM (4.1/SLCS Mailhost 3.2) id AA18545; Tue, 15 May 90 09:05:56 CDT From: macg@SLCS.SLB.COM (Bill Macgregor) Received: by frank.SLCS.SLB.COM (4.1/SLCS Subsidiary 1.6) id AA03074; Tue, 15 May 90 09:05:52 CDT Date: Tue, 15 May 90 09:05:52 CDT Message-Id: <9005151405.AA03074.macg@frank.SLCS.SLB.COM> To: mathgroup@yoda.ncsa.uiuc.edu Subject: Mathematica 2.0? Status: RO WRI discussed plans for Mma 2.0 at the Mathematica conference in January. Several possible additions to Mma are very desirable--a pseudocode compiler for numerical functions, alternation in pattern matching, expression typesetting (maybe by way of a TeXForm interpreter?), and numerical functions defined by interpolation on discrete sample sets, for example. Can anyone provide us with an update/progress report on Mma 2.0? Does it still look like release in 1990? Any major additions/ deletions for the planned enhancements? If someone can speak with authority, a quick review of the entire plan (e.g., new Packages?) would be appreciated by the mailing list. Thanks for any help in advance, - Bill MacGregor From mathgroup-adm@yoda.ncsa.uiuc.edu Tue May 15 11:00:01 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA07459; Tue, 15 May 90 11:00:00 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA04467; Tue, 15 May 90 10:55:28 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA07365; Tue, 15 May 90 10:24:28 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA07361; Tue, 15 May 90 10:24:27 -0500 Message-Id: <9005151524.AA07361@yoda.ncsa.uiuc.edu> From: macg@SLCS.SLB.COM (Bill Macgregor) Date: Tue, 15 May 90 09:05:52 CDT To: mathgroup@yoda.ncsa.uiuc.edu Subject: Mathematica 2.0? Status: RO WRI discussed plans for Mma 2.0 at the Mathematica conference in January. Several possible additions to Mma are very desirable--a pseudocode compiler for numerical functions, alternation in pattern matching, expression typesetting (maybe by way of a TeXForm interpreter?), and numerical functions defined by interpolation on discrete sample sets, for example. Can anyone provide us with an update/progress report on Mma 2.0? Does it still look like release in 1990? Any major additions/ deletions for the planned enhancements? If someone can speak with authority, a quick review of the entire plan (e.g., new Packages?) would be appreciated by the mailing list. Thanks for any help in advance, - Bill MacGregor From @uunet.UU.NET:ebneter@wri.UUCP Wed May 16 14:31:00 1990 Received: from uunet.UU.NET by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA08838; Wed, 16 May 90 14:30:58 -0500 Received: from wri.UUCP by uunet.uu.net (5.61/1.14) with UUCP id AA10711; Wed, 16 May 90 15:30:53 -0400 Received: by WRI.com (3.2/SMI-3.0DEV3) id AA02106; Wed, 16 May 90 14:24:26 CDT Date: Wed, 16 May 90 14:24:26 CDT From: ebneter@wri.UUCP (Kate Ebneter) Message-Id: <9005161924.AA02106@WRI.com> To: stevec@yoda.ncsa.uiuc.edu Status: RO Steve, Attached below is a reply to Stefan Mueller's article roasting us over the Together bug. It states our policy fairly well, I hope, as well as pointing out that we *did* send out upgrades to fix the bug. (I don't know how we missed him...I sure wish we hadn't!) Could you send this out? If there are any problems with it, please let me know, and we'll fix 'em. Thanks! (And thanks for alerting us to this ... he posted it to info-mac also, from where it went out worldwide over usenet. Yikes!) Kate Ebneter -------------------------------------------------------------------------------- A recent posting to the mathgroup by Dr. Stefan Mueller raises some valid questions about bugs in Mathematica. As the manager of the Software Quality Assurance Department at Wolfram Research, I would like to address these issues. There was indeed a bug, as described by Dr. Mueller, in early versions of Mathematica 1.2 on all platforms. The bug was actually in the Together function, and was due to a fairly subtle logic error. This bug caused Together to give incorrect answers for expressions involving both integer and rational powers of the same subexpression. A very simple example of this problem: In[2]:= Together[(a + b x)/(1 + Sqrt[a + b x])] Sqrt[a + b x] Out[2]= ----------------- 1 + Sqrt[a + b x] ... which of course should give: a + b x Out[2]= ----------------- 1 + Sqrt[a + b x] ... which is what the current versions of Mathematica do indeed give. Because Simplify calls Together (as do many other functions in our algebraic simplifi- cation system), this bug was manifested in Simplify as well, as shown by Dr. Mueller's example. As soon as this bug was discovered, a fix was made and a free upgrade was sent to all of our registered users. We sent out several thousand "fix" disks to our Macintosh customers. This was the first time in the history of Mathematica that Wolfram Research has had to send out upgrades of this kind, as this was the first time that a bug of this severity was uncovered in a released version of the program. Unfortunately, as Dr. Mueller's case demonstrates, some of our users did not receive their upgrade disks. We are currently investigating how and why this happened, and are taking steps to ensure that it does not happen again should such an occasion arise in the future. The policy of Wolfram Research is that if a bug is found that causes a function to give incorrect answers, and it is in a function used by most or all of our users, we will send out free upgrades to all of our registered users. If the bug is in a more specialized function, which does not affect other functions, free upgrades will be sent to registered users who request it. The letters accompanying any future such upgrades will explicitly state which functions are affected by the upgrade. Note, however, the importance of registering your copy of Mathematica: We cannot notify you of upgrades or send you bug fixes if your copy is not registered. More importantly, we are taking significant steps to ensure that such bugs do not appear in released versions of Mathematica. We have a very ambitious program for testing Mathematica, and we are always interested in hearing suggestions for further tests. For example, in recent months we have been comparing the output of Mathematica's special functions with the tables in Abramowitz and Stegun. (We found a couple of typographical errors in Abramowitz and Stegun; we didn't find any new bugs in Mathematica. I won't say anything about old bugs! ;-) ) We have a very intensive testing effort scheduled for this summer; the SQA department has hired seven additional summer interns to test various aspects of the program. Of course, testing can only find bugs; it cannot prove that there are no bugs. Although we try to keep the program bug-free, in a system of the size and complexity of Mathematica, some errors are inevitable. If you do find a bug in Mathematica, please send us a bug report by email to bugs@wri.com, by fax at (217) 398-0747 (to the attention of the SQA Department), or by snail mail to Software Quality Assurance, Wolfram Research, Inc., P.O. Box 6059, Champaign, IL 61826-6059. We can't fix them if we don't know about them! Your bug report will be acknowledged and you will be given a bug-tracking number which you may use if you wish to inquire about the status of the bug. If you have any general concerns or comments about the quality of Mathematica, please contact me by email at sqa@wri.com, or by fax or mail as above. Kate Ebneter Software Quality Assurance Manager Wolfram Research, Inc. From mathgroup-adm@yoda.ncsa.uiuc.edu Wed May 16 21:02:05 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA09345; Wed, 16 May 90 21:02:04 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA16665; Wed, 16 May 90 20:58:24 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA09028; Wed, 16 May 90 18:42:38 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA09024; Wed, 16 May 90 18:42:37 -0500 Message-Id: <9005162342.AA09024@yoda.ncsa.uiuc.edu> Date: Wed, 16 May 90 14:24:26 CDT From: ebneter@wri.UUCP (Kate Ebneter) To: mathgroup@yoda.ncsa.uiuc.edu Status: RO [This is the response by Wolfram Research to the two previous messages. -- Steve Christensen.] -------------------------------------------------------------------------------- A recent posting to the mathgroup by Dr. Stefan Mueller raises some valid questions about bugs in Mathematica. As the manager of the Software Quality Assurance Department at Wolfram Research, I would like to address these issues. There was indeed a bug, as described by Dr. Mueller, in early versions of Mathematica 1.2 on all platforms. The bug was actually in the Together function, and was due to a fairly subtle logic error. This bug caused Together to give incorrect answers for expressions involving both integer and rational powers of the same subexpression. A very simple example of this problem: In[2]:= Together[(a + b x)/(1 + Sqrt[a + b x])] Sqrt[a + b x] Out[2]= ----------------- 1 + Sqrt[a + b x] ... which of course should give: a + b x Out[2]= ----------------- 1 + Sqrt[a + b x] ... which is what the current versions of Mathematica do indeed give. Because Simplify calls Together (as do many other functions in our algebraic simplifi- cation system), this bug was manifested in Simplify as well, as shown by Dr. Mueller's example. As soon as this bug was discovered, a fix was made and a free upgrade was sent to all of our registered users. We sent out several thousand "fix" disks to our Macintosh customers. This was the first time in the history of Mathematica that Wolfram Research has had to send out upgrades of this kind, as this was the first time that a bug of this severity was uncovered in a released version of the program. Unfortunately, as Dr. Mueller's case demonstrates, some of our users did not receive their upgrade disks. We are currently investigating how and why this happened, and are taking steps to ensure that it does not happen again should such an occasion arise in the future. The policy of Wolfram Research is that if a bug is found that causes a function to give incorrect answers, and it is in a function used by most or all of our users, we will send out free upgrades to all of our registered users. If the bug is in a more specialized function, which does not affect other functions, free upgrades will be sent to registered users who request it. The letters accompanying any future such upgrades will explicitly state which functions are affected by the upgrade. Note, however, the importance of registering your copy of Mathematica: We cannot notify you of upgrades or send you bug fixes if your copy is not registered. More importantly, we are taking significant steps to ensure that such bugs do not appear in released versions of Mathematica. We have a very ambitious program for testing Mathematica, and we are always interested in hearing suggestions for further tests. For example, in recent months we have been comparing the output of Mathematica's special functions with the tables in Abramowitz and Stegun. (We found a couple of typographical errors in Abramowitz and Stegun; we didn't find any new bugs in Mathematica. I won't say anything about old bugs! ;-) ) We have a very intensive testing effort scheduled for this summer; the SQA department has hired seven additional summer interns to test various aspects of the program. Of course, testing can only find bugs; it cannot prove that there are no bugs. Although we try to keep the program bug-free, in a system of the size and complexity of Mathematica, some errors are inevitable. If you do find a bug in Mathematica, please send us a bug report by email to bugs@wri.com, by fax at (217) 398-0747 (to the attention of the SQA Department), or by snail mail to Software Quality Assurance, Wolfram Research, Inc., P.O. Box 6059, Champaign, IL 61826-6059. We can't fix them if we don't know about them! Your bug report will be acknowledged and you will be given a bug-tracking number which you may use if you wish to inquire about the status of the bug. If you have any general concerns or comments about the quality of Mathematica, please contact me by email at sqa@wri.com, or by fax or mail as above. Kate Ebneter Software Quality Assurance Manager Wolfram Research, Inc. From mathgroup-adm@yoda.ncsa.uiuc.edu Wed May 16 20:17:16 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA09098; Wed, 16 May 90 20:17:14 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA15425; Wed, 16 May 90 20:13:32 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA09014; Wed, 16 May 90 18:40:41 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA09010; Wed, 16 May 90 18:40:39 -0500 Date: Wed, 16 May 90 18:40:39 -0500 Message-Id: <9005162340.AA09010@yoda.ncsa.uiuc.edu> To: mathgroup@yoda.ncsa.uiuc.edu From: ONM010@de0hrz1a.bitnet Subject: Bug in Mathematica 1.2 for the Macintosh and for the SUN 4 Status: RO [Note: This note and the next one were sent to me for posting to the MathGroup mailing list. After checking with the author I decided to ask Wolfram Research to prepare a response. The third mailing is from WRI. -- Steve Christensen] Re.: Bug in Mathematica 1.2 for the Macintosh and for the SUN 4 There is a serious bug in the original version 1.2 of Mathematica for the Macintosh and the SUN 4: In certain situations the results of calculations may be wrong when symbolic expressions are simplified using the "Simplify" command. I discovered this when a calculation, which had a reasonable result before, gave a (physically unrealizable) negative answer after symbolic simplification of the expression. I was able to isolate the following example from the more complicated original term: Simplify[ (r^2 + z^2)^(1/2)*(2 + (r^2 + z^2)^(1/2))*Log[2] ] gives: 3*(r^2 + z^2)^(1/2)*Log[2] This (wrong) simplification does not occur when the factor of Log[2] is taken out of the above expression. This very worrisome behavior of Mathematica 1.2 could be observed on a Macintosh SE/30 (enhanced version of Mathematica) and on a SUN 4 workstation. Therefore, I strongly encourage users of Mathematica 1.2 on Macintosh and SUN systems to carefully check their results when "Simplify" is invoked in the course of a calculation. There is a free upgrade of Mathematica for the Macintosh (version 1.2.1), which was mailed to me by Wolfram Research after I notified them about this bug a few days ago. This new version gives a correct result for the above example. The modification date in all files of version 1.2.1 is December 21, 1989, therefore, Wolfram Research must have been aware of this problem for about 6 month. Nevertheless, they did not notify their registered Macintosh customers about this serious problem. The release notes for version 1.2.1 explicitly describe a number of other bug fixes but they obviously put the above problem in the category of "A variety of other minor and cosmetic bugs have been fixed"! As far as I know, at least a few users of the SUN 4 version of Mathematica 1.2 were informed only a few days ago that a free upgrade which "fixes a minor but annoying problem with the simplification system" is available. For me, bugs which lead to incorrect results are the most serious problem mathematical software can have. I am appalled that Wolfram Research is playing this down to a mere nuisance instead of warning the registered customers immediately and sending them the improved version as soon as it becomes available. I believe that this policy of Wolfram Research endangers the reputation of Mathematica as a reliable tool. We should demand a notification system which ensures timely warning about all bugs which lead to erroneous results. Stefan ================================================================= Dr. Stefan P. Mueller, Nuklearmedizin, Universitaetsklinikum, Hufelandstr. 55, D-4300 Essen 1, Federal Republic of Germany, e-mail: ONM010@DE0HRZ1A on BITNET, FAX +49/ (201) 723-4694, phone: +49/ (201) 723-2080 or 2081 or 2032 ================================================================= From mathgroup-adm@yoda.ncsa.uiuc.edu Wed May 16 22:11:25 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA09795; Wed, 16 May 90 22:11:24 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA18521; Wed, 16 May 90 22:07:40 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA09022; Wed, 16 May 90 18:42:01 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA09018; Wed, 16 May 90 18:41:59 -0500 Message-Id: <9005162341.AA09018@yoda.ncsa.uiuc.edu> Date: Sun, 13 May 90 15:21:02 MEZ To: stevec@ncsa.uiuc.edu From: ONM010@de0hrz1a.bitnet Subject: Mathematica bug Status: RO [Note: This note and the previous one were sent to me for posting to the MathGroup mailing list. After checking with the author I decided to ask Wolfram Research to prepare a response. The third mailing is from WRI. -- Steve Christensen] Dear Steven, thank you for including mye subscription to your mailing list. You probably noticed that I am on a BITNET node, is there a possibility to access the files through BITNET (or INTERNET)? It is practically impossible to logon via modem over the bad international (and our institutional) phone lines. Please also let me know whether you prefer being contacted via INTERNET or BITNET. Thank you for also contacting Wolfram. My intention in publicizing this problem is not vindictive. I believe that software like Mathematica has to be extremely reliable. It will be used mainly where calculations are too complex to be done by hand, therefore, errors in the symbolic calculations - unlike bugs in the layout or printing modules - are not always easily recognizable. Of course, bugs will occur in the developement of any software product of this complexity (just as e.g. occasional mistakes will happen in medical practice or pharmaceuticals will exhibit serious side effects after their approval). It is of utmost importance, however, that such errors not are covered up to avoid further damage. I believe that this is the only way to ensure trust in the results of Mathematica, just as it has been successful in the other ares mentioned above. It is up to us to influence the way problems like this will be handled in the future. I would be happy about your support in this cause. To give you some more information about my "case" I am including the cover letter which came with the software upgrade and my letter to Wolfram Research (sent by air mail). Stefan ================================================================= Dr. Stefan P. Mueller, Nuklearmedizin, Universitaetsklinikum, Hufelandstr. 55, D-4300 Essen 1, Federal Republic of Germany, e-mail: ONM010@DE0HRZ1A on BITNET, FAX +49/ (201) 723-4694, phone: +49/ (201) 723-2080 or 2081 or 2032 ================================================================= enclosures: ************************************************************************* Letter from Wolfram's technical support: April 27, 1990 Dear Dr. Mueller: We received notice from you on 26th April that your version of Mathematica was simplifying expressions improperly. The upgrade to the fixed version is of course free of charge, and I have gone ahead and ordered the upgrade for you immediately. It will be sent under separate cover early next week. I hope that you receive it in time for your presentation. I apologize for any inconvenience this bug in the software may have caused you. Thank you for your interest in Mathematica. Sincerely yours, Paul Katula Technical Support ************************************************************************* My letter to Wolfram: May 11, 1990 Re.: Erroneous results with Simplify in Mathematica 1.2 (my FAX from April 26, 1990) Dear Madam or Sir, yesterday I received the Mathematica upgrade version 1.2.1 for the Macintosh; I really appreciate that you ordered itright after my bug report. It was a very sobering moment, however, when I looked at the file modification dates of the new version and read the release notes. The fact that the improved version - which fixes the reported bug in the Simplify module - was last modified in December 1989 implies that Wolfram Research must have been aware of the problem in Simplify for at least half a year, however, other registered users of Mathematica for the Macintosh or myself were never informed about the potentially dangerous consequences of using "Simplify". Furthermore, the release notes for version 1.2.1 describe several bug-fixes since version 1.2, the problem in the simplification system - which caused wrong results, not just misprinted registration marks - was not mentioned at all. It was obviously put under the last item "A variety of other minor and cosmetic bugs have been fixed". For the SUN system my coworker from Harvard Medical School was informed only a few days ago that a free upgrade which "fixes a minor but annoying problem with the simplification system" is available - after she reported the problem to Wolfram Research. Everybody knows that errors are bound to occur in programming, especially in a highly complex system like Mathematica. I believe however, that the attempt to cover up or to play down serious problems is detrimental to the reputation of Wolfram Research. I would have appreciated a warning about the erroneous behavior of Simplify. I could have avoided becoming a victim of this problem. Furthermore, a timely warning and the announcement of a bug fix version would have been a sign of your uncompromized commitment to ensure the highest possible reliability of Mathematica. I would like to suggest the announcement of a notification system which ensures a timely warning about all bugs which lead to erroneous results. Similar policies exist in many countries for e.g. serious side effects of pharmaceuticals. This would ensure high confidence in the accuracy of results obtained with Mathematica. Truly Yours Dr. Stefan P. Mller From jacobson@cello.hpl.hp.com Thu May 17 13:03:28 1990 Received: from hplms2.hpl.hp.com by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA11771; Thu, 17 May 90 13:03:26 -0500 Received: from cello.hpl.hp.com by hplms2.hpl.hp.com with SMTP (15.11.1.3/15.5+IOS 3.20) id AA23464; Thu, 17 May 90 11:03:43 pdt Received: from localhost by cello.HPL.HP.COM; Thu, 17 May 90 11:03:21 pdt To: stevec@yoda.ncsa.uiuc.edu Subject: Simplify/Together bug Date: Thu, 17 May 90 11:03:18 PDT Message-Id: <19893.642967398@cello> From: jacobson@cello.hpl.hp.com Status: RO NOT FOR PUBLICATION ON THE NET. But feel free to use this information in making summaries, etc. Here at HP Labs I know of 3 instances of Mathematica. For HP 9000/840, Mathematica Version 1.2 (August 22, 1989). It has the bug and WE HAVE NOT GOTTEN AN UPDATE. For HP 9000/???, Mathematica Version 1.2 (November 7, 1989). It does not have the bug. For the Macintosh, Mathematica Version 1.2 (July 17, 1989). It does not have the bug. Moral 1: WRI has not sent updates to everyone affected. Moral 2: Just the version number is insufficient to identify what kernel you have. -- David From @VM.BYU.EDU:smithw@mathnx.byu.edu Thu May 17 10:19:41 1990 Received: from vm.byu.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA11608; Thu, 17 May 90 10:19:38 -0500 Received: from mathnx.byu.edu.byu.edu by VM.BYU.EDU (IBM VM SMTP R1.2.1) with TCP; Thu, 17 May 90 09:19:37 MDT Received: by mathnx.byu.edu.byu.edu (NeXT-1.0 (From Sendmail 5.52)/NeXT-1.0) id AA02400; Thu, 17 May 90 09:17:04 GMT-0700 Date: Thu, 17 May 90 09:17:04 GMT-0700 From: smithw@mathnx.byu.edu (William V. Smith) Message-Id: <9005171617.AA02400@ mathnx.byu.edu.byu.edu > To: mathgroup-adm@yoda.ncsa.uiuc.edu Subject: Mathematica bug on NeXT Status: RO The "Together" bug also exists in the NeXT release of mathematica (1.0 opsys). Any word on how or when this will be fixed? From lsf@astrosun.TN.CORNELL.EDU Thu May 17 08:28:50 1990 Received: from ASTROSUN.TN.CORNELL.EDU by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA11364; Thu, 17 May 90 08:28:48 -0500 Received: from supernova.TN.CORNELL.EDU by astrosun.TN.CORNELL.EDU (4.1/1.1nn-Cornell Astronomy Dept) id AA22651; Thu, 17 May 90 09:28:27 EDT Date: Thu, 17 May 90 09:28:27 EDT From: lsf@astrosun.TN.CORNELL.EDU (Sam Finn) Message-Id: <9005171328.AA22651@astrosun.TN.CORNELL.EDU> To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Bug in Mathematica 1.2 for the Macintosh and for the SUN 4 Status: RO >For me, bugs which lead to incorrect results are the most serious >problem mathematical software can have. I am appalled that Wolfram >Research is playing this down to a mere nuisance instead of warning >the registered customers immediately and sending them the improved >version as soon as it becomes available. I believe that this policy of >Wolfram Research endangers the reputation of Mathematica as a reliable >tool. We should demand a notification system which ensures timely >warning about all bugs which lead to erroneous results. I agree wholeheartedly. Unfortunately, what we are seeing is, to a large extent, the same problems and attitudes that we saw with SMP years ago. There is the hype (which, if anything, is worse this time around) and (a new twist) the refusal to discuss algorithms or present some other means of validating performance. Now, as you rightly point out, incorrect results are seen by WRI as ``cosmetic details.'' Well, I suppose that is consistent, since mostly Mathematica is a glitzy (though indisputably useful) frontend. Just think how useful such a thing would be on, say, Maple or Macsyma . . . From @RELAY.CS.NET:sp@umb.edu Thu May 17 21:23:47 1990 Received: from relay.cs.net by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA13431; Thu, 17 May 90 21:23:44 -0500 Message-Id: <9005180223.AA13431@yoda.ncsa.uiuc.edu> Received: from relay2.cs.net by RELAY.CS.NET id aa08052; 17 May 90 22:22 EDT Received: from umb.edu by RELAY.CS.NET id ad20265; 17 May 90 22:13 EDT Received: by umb.umb.edu (5.51/5.17) id AA27641; Thu, 17 May 90 20:56:19 EDT Date: Thu, 17 May 90 20:56:19 EDT From: Steve Parrott To: mathgroup@yoda.ncsa.uiuc.edu Subject: Wolfram's policy on notifying users of bugs Cc: sp@umb.edu Status: RO In a May 16 posting, Kate Ebneter, the Software Quality Assurance Manager of Wolfram Research, Inc. explains Wolfram's policies on dealing with known bugs in Mathematica: > ... > The policy of Wolfram Research is that if a bug is found that causes a > function to give incorrect answers, and it is in a function used by most or > all of our users, we will send out free upgrades to all of our registered > users. If the bug is in a more specialized function, which does not > affect other functions, free upgrades will be sent to registered users who > request it. The letters accompanying any future such upgrades > will explicitly state which functions are affected by the upgrade. > ... _____________________________________________________________________ Nothing is said about notifying registered users of known bugs in specialized functions. Does this mean that if a user happens to find a bug in a specialized function he can obtain a free upgrade on request, but that it is his obligation to first discover the bug? I hope that this is not to be Wolfram's policy. It seems to me that they will have serious problems with customer confidence and satisfaction if they do not periodically notify users of known bugs. It is understandable that they would not want to send out upgrades every time an error is discovered in a specialized function, but a user who writes a program using such functions should be able to conveniently find out for which he should request upgrades. He shouldn't have to discover that his program doesn't work properly, laboriously trace the problem to a particular function, notify Wolfram, and finally receive the upgrade. From SIILI@CSC.FI Fri May 18 10:48:17 1990 Received: from router.funet.fi by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA15410; Fri, 18 May 90 10:48:05 -0500 Message-Id: <9005181548.AA15410@yoda.ncsa.uiuc.edu> Received: from CSC.FI by router.funet.fi; Fri, 18 May 90 13:55 EET Date: Fri, 18 May 90 13:57 EET From: Tero Siili Subject: Add to Mathematica users group To: mathgroup@yoda.ncsa.uiuc.edu X-Vms-To: IN%"mathgroup@yoda.ncsa.uiuc.edu" Status: RO Please add me to the Mathematica mailing list with my Internet address siili@csc.fi. Thank you. Tero Siili -------------------------------------------------------------------- Finnish Meteorological Institute Tel: +358-0-1929676 Department of Geophysics FAX: +358-0-1929539 P.O. Box 503 Internet: siili@csc.fi SF-00101 Helsinki EARN/BITNET: siili@finfun Finland SPAN: 21905::opmvax::siili From mathgroup-adm@yoda.ncsa.uiuc.edu Sun May 20 06:05:11 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA17680; Sun, 20 May 90 06:05:11 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA15355; Sun, 20 May 90 06:01:33 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA17533; Sun, 20 May 90 03:01:35 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA17529; Sun, 20 May 90 03:01:34 -0500 Message-Id: <9005200801.AA17529@yoda.ncsa.uiuc.edu> Date: Thu, 17 May 90 20:56:19 EDT From: sp@umb.edu To: mathgroup@yoda.ncsa.uiuc.edu Subject: Wolfram's policy on notifying users of bugs Status: RO In a May 16 posting, Kate Ebneter, the Software Quality Assurance Manager of Wolfram Research, Inc. explains Wolfram's policies on dealing with known bugs in Mathematica: > ... > The policy of Wolfram Research is that if a bug is found that causes a > function to give incorrect answers, and it is in a function used by most or > all of our users, we will send out free upgrades to all of our registered > users. If the bug is in a more specialized function, which does not > affect other functions, free upgrades will be sent to registered users who > request it. The letters accompanying any future such upgrades > will explicitly state which functions are affected by the upgrade. > ... _____________________________________________________________________ Nothing is said about notifying registered users of known bugs in specialized functions. Does this mean that if a user happens to find a bug in a specialized function he can obtain a free upgrade on request, but that it is his obligation to first discover the bug? I hope that this is not to be Wolfram's policy. It seems to me that they will have serious problems with customer confidence and satisfaction if they do not periodically notify users of known bugs. It is understandable that they would not want to send out upgrades every time an error is discovered in a specialized function, but a user who writes a program using such functions should be able to conveniently find out for which he should request upgrades. He shouldn't have to discover that his program doesn't work properly, laboriously trace the problem to a particular function, notify Wolfram, and finally receive the upgrade. Steve Parrott From mathgroup-adm@yoda.ncsa.uiuc.edu Sun May 20 05:05:27 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA17604; Sun, 20 May 90 05:05:26 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA14599; Sun, 20 May 90 05:01:48 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA17527; Sun, 20 May 90 02:59:38 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA17523; Sun, 20 May 90 02:59:37 -0500 Message-Id: <9005200759.AA17523@yoda.ncsa.uiuc.edu> Date: Thu, 17 May 90 09:28:27 EDT From: lsf@astrosun.TN.CORNELL.EDU (Sam Finn) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Bug in Mathematica 1.2 for the Macintosh and for the SUN 4 Status: RO >For me, bugs which lead to incorrect results are the most serious >problem mathematical software can have. I am appalled that Wolfram >Research is playing this down to a mere nuisance instead of warning >the registered customers immediately and sending them the improved >version as soon as it becomes available. I believe that this policy of >Wolfram Research endangers the reputation of Mathematica as a reliable >tool. We should demand a notification system which ensures timely >warning about all bugs which lead to erroneous results. I agree wholeheartedly. Unfortunately, what we are seeing is, to a large extent, the same problems and attitudes that we saw with SMP years ago. There is the hype (which, if anything, is worse this time around) and (a new twist) the refusal to discuss algorithms or present some other means of validating performance. Now, as you rightly point out, incorrect results are seen by WRI as ``cosmetic details.'' Well, I suppose that is consistent, since mostly Mathematica is a glitzy (though indisputably useful) frontend. Just think how useful such a thing would be on, say, Maple or Macsyma . . . From mathgroup-adm@yoda.ncsa.uiuc.edu Sun May 20 04:18:04 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA17564; Sun, 20 May 90 04:18:03 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA13858; Sun, 20 May 90 04:14:12 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA17520; Sun, 20 May 90 02:58:43 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA17516; Sun, 20 May 90 02:58:41 -0500 Message-Id: <9005200758.AA17516@yoda.ncsa.uiuc.edu> Date: Thu, 17 May 90 09:17:04 GMT-0700 From: smithw@mathnx.byu.edu (William V. Smith) To: mathgroup-adm@yoda.ncsa.uiuc.edu Subject: Mathematica bug on NeXT Status: RO The "Together" bug also exists in the NeXT release of mathematica (1.0 opsys). Any word on how or when this will be fixed? From mathgroup-adm@yoda.ncsa.uiuc.edu Mon May 21 10:01:16 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA19342; Mon, 21 May 90 10:01:15 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA15745; Mon, 21 May 90 09:57:37 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA19290; Mon, 21 May 90 09:27:55 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA19286; Mon, 21 May 90 09:27:53 -0500 Message-Id: <9005211427.AA19286@yoda.ncsa.uiuc.edu> From: macg@SLCS.SLB.COM (Bill Macgregor) Date: Mon, 21 May 90 09:22:26 CDT To: mathgroup@yoda.ncsa.uiuc.edu Subject: Should WRI publish a software defect list? Status: RO Several recent messages to the mailing list have addressed WRI's policies wrt. the announcement of software defects ("bugs") in Mathematica. The central point seems to be that WRI might have knowledge of defects in Mma, with potentially serious consequences for users, but decide not to announce the presence of the defects in order to protect Mma's reputation in the marketplace, and/or reduce the cost to WRI of interim releases. A strong argument can be made this this policy is, in fact, counterproductive for WRI. Publication of a software defect list would provide a strong incentive for WRI to improve the quality of their product, with a corresponding improvement in marketability. It would also generate feedback to WRI to help prioritize efforts at quality improvement. And although I am certainly not qualified to give a legal opinion, there is a possibility that the announcement of software defects would actually lessen WRI's liability in the event of serious consequences to life or property. Most important, perhaps, publication of software defects is one way for WRI to demonstrate respect for its customers. Could I propose a straw vote? Two issues: (1) How many readers of the mailing list believe WRI should, in the interests of good faith with its customers, make public a list of "known Mma kernel defects"? (2) Would it be sufficient for WRI to make such a list available on an internet file server? Please reply to me directly to avoid burdening the mailing list; I'll be happy to summarize and report. - Bill MacGregor macgregor@slcs.slb.com From Patti_Carlson@qmail.ncsa.uiuc.edu Mon May 21 10:13:27 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA19365; Mon, 21 May 90 10:13:25 -0500 Return-Path: Received: from qmail.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA16128; Mon, 21 May 90 10:13:27 CDT Message-Id: <9005211513.AA16128@newton.ncsa.uiuc.edu> Date: 21 May 90 10:16:27 From: Patti Carlson Subject: WRI To: steve@ncsa.uiuc.edu Status: RO GatorMail-Q WRI I sent mail to Marketing at WRI, telling them to answer this Mathgroup mail about publicizing bugs. It's getting pretty intense. (I agree with the expressed opinion that WRI should notify users of bugs, instead of making them BEG for an upgrade.) From walt%keynes@ucsd.edu Mon May 21 11:48:02 1990 Received: from ucsd.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA19611; Mon, 21 May 90 11:48:00 -0500 Received: from keynes.ucsd.edu by ucsd.edu; id AA24439 sendmail 5.61/UCSD-2.0-sun via SMTP Mon, 21 May 90 09:47:59 -0700 for mathgroup-adm@yoda.ncsa.uiuc.edu Received: by keynes.ucsd.edu (15.11/UCSDGENERIC.2) id AA18423 to mathgroup-adm@yoda.ncsa.uiuc.edu; Mon, 21 May 90 09:47:33 pdt Date: Mon, 21 May 90 09:47:33 pdt From: walt%keynes@ucsd.edu (Walt Heller) Message-Id: <9005211647.AA18423@keynes.ucsd.edu> To: mathgroup-adm@yoda.ncsa.uiuc.edu Subject: Re: Should WRI publish a software defect list? Status: RO WRI should not only publish known bugs ti the mailing list immediately, it should provide a quarterly "bug report" to all users by regular mail. Walter P. Heller From mathgroup-adm@yoda.ncsa.uiuc.edu Mon May 21 13:20:43 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA19717; Mon, 21 May 90 13:20:42 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA19859; Mon, 21 May 90 13:17:05 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA19661; Mon, 21 May 90 12:05:12 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA19657; Mon, 21 May 90 12:05:10 -0500 Message-Id: <9005211705.AA19657@yoda.ncsa.uiuc.edu> Date: Mon, 21 May 90 09:47:33 pdt From: walt%keynes@ucsd.edu (Walt Heller) To: mathgroup-adm@yoda.ncsa.uiuc.edu Subject: Re: Should WRI publish a software defect list? Status: RO WRI should not only publish known bugs ti the mailing list immediately, it should provide a quarterly "bug report" to all users by regular mail. Walter P. Heller From barry@playfair.stanford.edu Mon May 21 14:12:31 1990 Received: from Playfair.Stanford.EDU by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA19812; Mon, 21 May 90 14:12:28 -0500 Message-Id: <9005211912.AA19812@yoda.ncsa.uiuc.edu> Received: by playfair.stanford.edu; Mon, 21 May 90 12:11:13 PDT Date: Mon, 21 May 90 12:11:13 PDT From: Barrett P. Eynon Subject: Re: Should WRI publish a software defect list? To: macg@slcs.slb.com, mathgroup@yoda.ncsa.uiuc.edu Status: RO Yes, I think they should make a defects list public. At the least they should keep a current list available on an internet server, and major bugs should be widely publicized. -Barry Eynon From mdeale@sargas.acs.calpoly.edu Tue May 22 12:09:59 1990 Received: from cosmos-gw.ACS.CalPoly.EDU by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA21202; Tue, 22 May 90 12:09:56 -0500 Received: from sargas.acs.calpoly.edu by cosmos.acs.calpoly.edu (4.1/1.881115) id AA03982; Tue, 22 May 90 10:09:52 PDT Received: by sargas.acs.calpoly.edu (4.1/SMI-4.0) id AA09001; Tue, 22 May 90 10:09:25 PDT Date: Tue, 22 May 90 10:09:25 PDT From: mdeale@sargas.ACS.CalPoly.EDU (Myron Deale) Message-Id: <9005221709.AA09001@sargas.acs.calpoly.edu> To: mathgroup@yoda.ncsa.uiuc.edu Subject: Limit[] trouble Status: RO Hello, I'm not sure I've seen any discussion on defects with the Limit[] function, so here goes. Upon trying "Limit[ Cos[1/x^2]^(x^4), x->Infinity]" either a Bus Error (on a NeXT) or a Segmentation Fault (on a Sun) is the result. Anyone run into this before? Is this another "known" defect? -Myron // mdeale@cosmos.acs.calpoly.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Tue May 22 12:55:15 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA21289; Tue, 22 May 90 12:55:14 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA10331; Tue, 22 May 90 12:51:34 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA21228; Tue, 22 May 90 12:11:48 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA21224; Tue, 22 May 90 12:11:46 -0500 Message-Id: <9005221711.AA21224@yoda.ncsa.uiuc.edu> Date: Tue, 22 May 90 10:09:25 PDT From: mdeale@sargas.ACS.CalPoly.EDU (Myron Deale) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Limit[] trouble Status: RO Hello, I'm not sure I've seen any discussion on defects with the Limit[] function, so here goes. Upon trying "Limit[ Cos[1/x^2]^(x^4), x->Infinity]" either a Bus Error (on a NeXT) or a Segmentation Fault (on a Sun) is the result. Anyone run into this before? Is this another "known" defect? -Myron // mdeale@cosmos.acs.calpoly.edu From sdw@hpsadsdw.hp.com Tue May 22 13:15:01 1990 Received: from hp-sde.sde.hp.com by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA21333; Tue, 22 May 90 13:14:58 -0500 Received: from hpcea.ce.hp.com by hp-sde.sde.hp.com with SMTP (16.2A/15.5+IOS 3.13) id AA22749; Tue, 22 May 90 10:51:24 -0700 Received: from hpsadsdw.HP.COM by hpcea ; Tue, 22 May 90 11:15:36 pdt Received: by hpsadsdw.HP.COM; Tue, 22 May 90 11:14:17 pdt Date: Tue, 22 May 90 11:14:17 pdt From: Steve Warwick Message-Id: <9005221814.AA04361@hpsadsdw.HP.COM> To: mathgroup@yoda.ncsa.uiuc.edu Status: RO Mathematica seems to have problems with the simplifications of perfect squares - I have had problems finding the "Correct" simplification of such expressions and have tracked it down to the following problem: In[8]:= f1 = a-b Out[8]= a - b In[9]:= f2 = b-a Out[9]= -a + b In[10]:= Simplify[Sqrt[Expand[f1^2]]] Out[10]= a - b In[11]:= Simplify[Sqrt[Expand[f2^2]]] Out[11]= a - b a,b,f1,f2 were undefined before trying this... It seems that such simplifications should return multiple results, and for more complex formula with multiple roots of squares, should return a list of the possible simplifications, culling out duplicate results. Comments?? -- Steven Warwick From @vmd.cso.uiuc.edu,@VM.BYU.EDU:smithw@mathnx.byu.edu Mon May 21 15:13:22 1990 Received: from vmd.cso.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA19896; Mon, 21 May 90 15:13:20 -0500 Received: from VM.BYU.EDU by VMD.CSO.UIUC.EDU (IBM VM SMTP R1.2) with BSMTP id 8235; Mon, 21 May 90 15:13:28 CDT Received: from BYUVM by VM.BYU.EDU (Mailer R2.05) with BSMTP id 9951; Mon, 21 May 90 14:06:45 MDT Received: from mathnx.byu.edu.byu.edu by VM.BYU.EDU (IBM VM SMTP R1.2.1) with TCP; Mon, 21 May 90 14:06:44 MDT Received: by mathnx.byu.edu.byu.edu (NeXT-1.0 (From Sendmail 5.52)/NeXT-1.0) id AA03816; Mon, 21 May 90 14:03:59 GMT-0700 Date: Mon, 21 May 90 14:03:59 GMT-0700 From: smithw@mathnx.byu.edu (William V. Smith) Message-Id: <9005212103.AA03816@ mathnx.byu.edu.byu.edu > To: mathgroup@yoda.ncsa.uiuc.edu Subject: Mathematica bug on NeXT fix Status: RO There is a fix for the mathematica bug (together function) on the NeXT. I sent email to our area rep (in Denver) and he got back to me the same day saying that he was putting an OD in the mail with the fix on it. Nice work NeXT . . . From mathgroup-adm@yoda.ncsa.uiuc.edu Tue May 22 13:53:36 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA21493; Tue, 22 May 90 13:53:35 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA11530; Tue, 22 May 90 13:49:53 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA21355; Tue, 22 May 90 13:16:25 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA21351; Tue, 22 May 90 13:16:23 -0500 Message-Id: <9005221816.AA21351@yoda.ncsa.uiuc.edu> Date: Tue, 22 May 90 11:14:17 pdt From: Steve Warwick To: mathgroup@yoda.ncsa.uiuc.edu Status: RO Mathematica seems to have problems with the simplifications of perfect squares - I have had problems finding the "Correct" simplification of such expressions and have tracked it down to the following problem: In[8]:= f1 = a-b Out[8]= a - b In[9]:= f2 = b-a Out[9]= -a + b In[10]:= Simplify[Sqrt[Expand[f1^2]]] Out[10]= a - b In[11]:= Simplify[Sqrt[Expand[f2^2]]] Out[11]= a - b a,b,f1,f2 were undefined before trying this... It seems that such simplifications should return multiple results, and for more complex formula with multiple roots of squares, should return a list of the possible simplifications, culling out duplicate results. Comments?? -- Steven Warwick From mcdonald@quark.UMD.EDU Tue May 22 15:56:26 1990 Received: from quark.umd.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA21749; Tue, 22 May 90 15:56:24 -0500 Received: by quark.UMD.EDU (5.57/Ultrix3.0-C) id AA05134; Tue, 22 May 90 16:52:29 EDT Date: Tue, 22 May 90 16:52:29 EDT From: mcdonald@quark.umd.edu (Bill MacDonald) Message-Id: <9005222052.AA05134@quark.UMD.EDU> To: mathgroup@yoda.ncsa.uiuc.edu Subject: Square root of squares Status: RO The following Mathematica command will return f1 or f2 as appropriate. Solve[c==f1^2,c] Solve[c==f2^2,c] If your suggestion were followed, Mathematica could never do the simplest calculation involving square roots without getting hung up by delivering two or more roots every time Sqrt[] was requested. If you want multiple roots of an expression, treat it as you would an equation. From mathgroup-adm@yoda.ncsa.uiuc.edu Tue May 22 16:02:19 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA21755; Tue, 22 May 90 16:02:18 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA14042; Tue, 22 May 90 15:58:39 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA21669; Tue, 22 May 90 15:20:39 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA21665; Tue, 22 May 90 15:20:38 -0500 Message-Id: <9005222020.AA21665@yoda.ncsa.uiuc.edu> Date: Tue, 22 May 90 15:12:55 -0400 From: jack@sun.udel.edu To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Limit[] trouble Status: RO When running the problem, Limit[ Cos[1/x^2]^(x^4), x->Infinity] on a Sun, using Mathmatica 1.2, I also obtained a Sementation Fault. However, using Mathematica 1.1, I obtain... In[1]:= Limit[ Cos[1/x^2]^(x^4), x->Infinity] Limit::nlm: Could not find definite limit. 4 -2 x Out[1]= Limit[Cos[x ] , x -> Infinity] From macg@SLCS.SLB.COM Tue May 22 16:03:44 1990 Received: from SLCS.SLB.COM by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA21761; Tue, 22 May 90 16:03:33 -0500 Received: from frank.SLCS.SLB.COM by SLCS.SLB.COM (4.1/SLCS Mailhost 3.2) id AA27002; Tue, 22 May 90 16:03:30 CDT From: macg@SLCS.SLB.COM (Bill Macgregor) Received: by frank.SLCS.SLB.COM (4.1/SLCS Subsidiary 1.6) id AA08169; Tue, 22 May 90 16:03:22 CDT Date: Tue, 22 May 90 16:03:22 CDT Message-Id: <9005222103.AA08169.macg@frank.SLCS.SLB.COM> To: mathgroup@yoda.ncsa.uiuc.edu Subject: SUMMARY-software defect list poll Cc: macgregor@yoda.ncsa.uiuc.edu Status: RO In a message to the mailing list yesterday, I asked the questions: (1) How many readers of the mailing list believe WRI should, in the interests of good faith with its customers, make public a list of "known Mma kernel defects"? (2) Would it be sufficient for WRI to make such a list available on an internet file server? I received 46 responses. All were positive regarding question (1), the desirability of a published Mma defect list. Most were positive regarding (2), although a substantial minority felt that publication via internet file server would not reach enough of the Mathematica user community. One respondent made the point that the wording of the questions hardly permitted a negative response. I can only hope that WRI agrees. The number of responses and the comments that accompanied them are more significant than the tally. 46 people felt strongly enough about the issue to take time to respond, and a number of the responses were emphatic. We are justified, I believe, in hypothesizing that this is an important issue for the Mma user community at large. Here is an unordered summary of the comments I found to be most interesting and/or most often repeated: * Collectively, users waste a great deal of time rediscovering known defects and reinventing workarounds. * It is in WRI's interests to publish a software defect list, rather than to allow a third party to do so. * WRI's policy of providing updates to registered users when critical defects are found is commendable. * Availability of a software defect list to the internet- accessible users is a good start, but leaves out many Mma users. What about publication of the list in the Mma Journal? Or a technical newsletter, by subscription, if necessary, to cover costs? * WRI should verify errors before publishing them (keep the noise level down). * A software defect list could contain a statement of the problem, a description of workarounds, and a predicted disposition (e.g., fixed in next release, update available by request, update mailed to registered users). * Workarounds and package updates could be made available via anonymous ftp (possibly from ncsa?). Using the netlib software would allow access to the repository via email from any reachable network. * The registration form should include a "preferred contact method" for update information, e.g., an email address or paper mail, or maybe fax. * Could WRI keep documentation updates online, accessible via ftp? Maybe the entire Reference Guide? Could users get a file via ftp to update the local Information database? * Just providing a software defect list on paper, available on request to WRI, would be a big help. Sending incremental change notices to the mathgroup mailing list would be a good idea, too. Thanks to all of you who took the time to respond. - Bill MacGregor From mbp@lakisis.umd.edu Tue May 22 16:03:53 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA21766; Tue, 22 May 90 16:03:50 -0500 Return-Path: Received: from lakisis.umd.edu ([128.8.134.19]) by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA14147; Tue, 22 May 90 16:03:48 CDT Date: Tue, 22 May 90 17:04:10 EDT From: "Mark Phillips" Message-Id: <9005222104.AA02043@lakisis.umd.edu> Received: by lakisis.umd.edu; Tue, 22 May 90 17:04:10 EDT To: stevec@ncsa.uiuc.edu Subject: archive 8 -- last one Status: RO Steve, Below is Archive8, which will have to be my last one, at least for a while. I won't be here much this summer, and as I mentioned earlier I won't be on the Internet this fall (at least not at first). --Mark ---- cut here ---- cut here ---- cut here ---- cut here ---- cut here ---- Mathematica Notes from sci.math.symbolic, sci.math, and comp.sys.next Archive 8: 8 April 1990 -- 22 May 1990 Editor: Mark Phillips mbp@lakisis.umd.edu Subjects: Serious Mathematica Bug Laplace Transforms for Mathematica Combinatorica (Discrete Mathematic Re: Problem14 Combinatorica, etc... Re: Problem14 Solving equations in Mathematica Comparative review of Symbolic Math Software Re: Solving equations in Mathematica (eqn fmt) Riemann Surface of Algebraic Function in Mathematica Notebooks on Economics Why the complex root? plasma dispersion function in mathematica Digital Filter Design Packages for Mathematica Mathematica Integration Mathematica and Simplify (*======================================================================*) From: phd_ivo@gsbacd.uchicago.edu Subject: Serious Mathematica Bug Date: 17 May 90 23:35:55 GMT Newsgroups: comp.sys.next Here is the description of a very serious bug in the Simplify[] function. I would suggest that noone uses this function any longer without checking the results. It appears to me that this greatly reduces the value of Mathematica. When will the next OS version come out? /ivo welch ivo@next.agsm.ucla Excerpt of a "public" message: This bug caused Together to give incorrect answers for expressions involving both integerand rational powers of the same subexpression. A very simple example ofthis problem: In[2]:= Together[(a + b x)/(1 + Sqrt[a + b x])] Sqrt[a + b x] Out[2]= ----------------- 1 + Sqrt[a + b x] .. which of course should give: a + b x Out[2]= ----------------- 1 + Sqrt[a + b x] .. which is what the current versions of Mathematica do indeed give. Because Simplify calls Together (as do many other functions in our algebraic simplifi- cation system), this bug was manifested in Simplify as well, as shown by Dr. Mueller's example. As soon as this bug was discovered, a fix was made and a free upgrade was sent to all of our registered users. .. Kate Ebneter Software Quality Assurance Manager Wolfram Research, Inc. (*----------------------------------------------------------------------*) From: jweiss@cgdra.cgd.ucar.edu (Jeffrey Weiss) Subject: Laplace Transforms for Mathematica Date: 10 May 90 17:50:54 GMT Newsgroups: sci.math.symbolic Does anyone have a package that does Laplace transforms and inverse Laplace transforms for Mathematica? We have a package that we read in that does only the most elementary transforms and no inverse transforms. -- Jeff jweiss@ncar.ucar.edu (*----------------------------------------------------------------------*) From: chrstnsn@ux1.cso.uiuc.edu Subject: Combinatorica (Discrete Mathematic Date: 11 May 90 04:19:00 GMT Newsgroups: sci.math.symbolic I have just placed the new Mathematica package Combinatorica.m in the Symbolic/Mathematica/Packages/SKIENA directory on the anonymous ftp server (128.174.20.50). Here are two files from that directory and a contact address for Steve Skiena, the author. This is a Beta release. Steve Christensen ====================================================================== (* Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica Version 0.5 5/8/90 Beta Release Copyright (c) 1990 by Steven S. Skiena This package contains all the programs from the book, "Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica" by Steven S. Skiena, Addison-Wesley Publishing Co., Advanced Book Program, 350 Bridge Parkway, Redwood City CA 94065. ISBN 0-201-50943-1. For ordering information, call 1-800-447-2226. This package is copyright 1990 by Steven S. Skiena. It may be copied in its entirety for nonprofit purposes only. Sale, other than for the direct cost of the media, is prohibited. This copyright notice must accompany all copies. These programs can be obtained on Macintosh and MS-DOS disks. Contact Discrete Mathematics Disk, Wolfram Research Inc., PO Box 6059, Champaign, IL 61826-9905. (217)-398-0700. The author, Wolfram research, and Addison-Wesley Publishing Company, Inc. make no representations, express or implied, with respond to this documentation, of the software it describes and contains, including without limitations, any implied warranties of mechantability or fitness for a particular purpose, all of which are expressly disclaimed. The author, Wolfram Research, or Addison-Wesley, their licensees, distributors and dealers shall in no event be liable for any indirect, incidental, or consequential damages. This beta release is designed to run under Version 1.2 of Mathematica. Any comments, bug reports, or requests to get on the Combinatorica mailing list should be forwarded to: Steven Skiena Department of Computer Science State University of New York Stony Brook, NY 11794 skiena@sbcs.sunysb.edu (516)-632-9026 / 8470 *) ======================================================================= The Combinatorial Mathematica package contains all the programs from the book, "Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica" by Steven S. Skiena, Addison-Wesley Publishing Co., Advanced Book Program, 350 Bridge Parkway, Redwood City CA 94065. ISBN 0-201-50943-1. For ordering information, call 1-800-447-2226. Combinatorial Mathematica currently consists of one file, Combinatorica.m. It is a 100K ASCII file, and so should be easy to ftp. Since some mailers choke on files this large, we have also prepared a distribution of three smaller files, Part01, Part02, and Part03. ------------------------------------------------------------------ (0) A General Public License for Combinatorial Mathematica is in the file COPYING. (1) To execute Combinatorial Mathematica, enter Mathematica and load the package (< From: rp@XN.LL.MIT.EDU (Richard Pavelle) > Subject: Problem14 > Keywords: A difficult matrix inversion and simplification > > I encountered a problem this week which makes a good candidate > for the 14th entry in the series I am submitting to the > group. The problem arises in photon scattering and involves > little more than inverting a particular 4x4 matrix. But owing > to the nature of the matrix the components of the inverse are > huge. It therefore creates an unusually difficult matrix > inversion problem for my MACSYMA. (all following timings are with Mathematica 1.2 on a Sun 4/330) Well, the inversion is no problem, it takes about 14 seconds to compute it, but trying to print the result is next to impossible. Canceling common terms in the numerators and denominators brings the output down to reasonable size, however (this takes about 25 min.). Max memory used was about 4.5MB. In[1]:= s={ {(er^2+ei^2)/(4*w^2+g^2+2*er^2+2*ei^2), -(er^2+ei^2)*(2*p1+g)/((p1+g)*(2*er*w+2*ei*w+2*er*p1-2*ei*p1+er*g-ei*g)), -(er^2+ei^2)*(2*p2+g)/((p2+g)*(2*er*w+2*ei*w+2*er*p2-2*ei*p2+er*g-ei*g)), -(er^2+ei^2)*(2*p3+g)/((p3+g)*(2*er*w+2*ei*w+2*er*p3-2*ei*p3+er*g-ei*g))}, {-(2*er*w-ei*g)/(4*w^2+g^2+2*er^2+2*ei^2), (2*er*w-2*ei*p1-ei*g)/(2*er*w+2*ei*w+2*er*p1-2*ei*p1+er*g-ei*g), (2*er*w-2*ei*p2-ei*g)/(2*er*w+2*ei*w+2*er*p2-2*ei*p2+er*g-ei*g), (2*er*w-2*ei*p3-ei*g)/(2*er*w+2*ei*w+2*er*p3-2*ei*p3+er*g-ei*g)}, {-(2*ei*w+er*g)/(4*w^2+g^2+2*er^2+2*ei^2), (2*ei*w+2*er*p1+er*g)/(2*er*w+2*ei*w+2*er*p1-2*ei*p1+er*g-ei*g), (2*ei*w+2*er*p2+er*g)/(2*er*w+2*ei*w+2*er*p2-2*ei*p2+er*g-ei*g), (2*ei*w+2*er*p3+er*g)/(2*er*w+2*ei*w+2*er*p3-2*ei*p3+er*g-ei*g)}, {(4*w^2+g^2+er^2+ei^2)/(4*w^2+g^2+2*er^2+2*ei^2), -(4*p1*w^2+4*g*w^2+4*p1^3+8*g*p1^2+5*g^2*p1+2*er^2*p1+2*ei^2*p1+g^3 +er^2*g+ei^2*g) /((p1+g)*(2*er*w+2*ei*w+2*er*p1-2*ei*p1+er*g-ei*g)), -(4*p2*w^2+4*g*w^2+4*p2^3+8*g*p2^2+5*g^2*p2+2*er^2*p2+2*ei^2*p2+g^3 +er^2*g+ei^2*g) /((p2+g)*(2*er*w+2*ei*w+2*er*p2-2*ei*p2+er*g-ei*g)), -(4*p3*w^2+4*g*w^2+4*p3^3+8*g*p3^2+5*g^2*p3+2*er^2*p3+2*ei^2*p3+g^3 +er^2*g+ei^2*g) /((p3+g)*(2*er*w+2*ei*w+2*er*p3-2*ei*p3+er*g-ei*g))} }; In[2]:= si = MatrixPower[s, -1]; (* inversion of s*) In[3]:= ByteCount[si] (* size, if no storage were shared *) Out[3]= 7425572 In[4]:= Together[si] (* cancel common terms *) Out[4]= {{-(((-(ei^2*g) - er^2*g + 4*g^3 + 4*g^2*p1 + 4*g^2*p2 + 4*g*p1*p2 + 4*g^2*p3 + 4*g*p1*p3 + 4*g*p2*p3 + 4*p1*p2*p3)* (2*ei^2 + 2*er^2 + g^2 + 4*w^2))/(4*ei^2*p1*p2*p3 + 4*er^2*p1*p2*p3)) , -(((2*ei^2 + 2*er^2 + g^2 + 4*w^2)* (er*g^3 + 2*er*g^2*p1 + 2*er*g^2*p2 + 4*er*g*p1*p2 + 2*er*g^2*p3 + 4*er*g*p1*p3 + 4*er*g*p2*p3 + 8*er*p1*p2*p3 - 8*ei*g^2*w - 4*ei*g*p1*w - 4*ei*g*p2*w - 4*ei*g*p3*w + 4*er*g*w^2))/ (8*ei^2*p1*p2*p3*w + 8*er^2*p1*p2*p3*w)), -(((2*ei^2 + 2*er^2 + g^2 + 4*w^2)* (ei*g^3 + 2*ei*g^2*p1 + 2*ei*g^2*p2 + 4*ei*g*p1*p2 + 2*ei*g^2*p3 + 4*ei*g*p1*p3 + 4*ei*g*p2*p3 + 8*ei*p1*p2*p3 + 8*er*g^2*w + 4*er*g*p1*w + 4*er*g*p2*w + 4*er*g*p3*w + 4*ei*g*w^2))/ (8*ei^2*p1*p2*p3*w + 8*er^2*p1*p2*p3*w)), -(g*(2*ei^2 + 2*er^2 + g^2 + 4*w^2))/(4*p1*p2*p3)}, {-(((g + p1)*(-ei^2 - er^2 + 4*g^2 + 4*g*p2 + 4*g*p3 + 4*p2*p3)* (-(ei*g) + er*g - 2*ei*p1 + 2*er*p1 + 2*ei*w + 2*er*w))/ (4*ei^2*p1^3 + 4*er^2*p1^3 - 4*ei^2*p1^2*p2 - 4*er^2*p1^2*p2 - 4*ei^2*p1^2*p3 - 4*er^2*p1^2*p3 + 4*ei^2*p1*p2*p3 + 4*er^2*p1*p2*p3)) , ((g + p1)*(ei*g - er*g + 2*ei*p1 - 2*er*p1 - 2*ei*w - 2*er*w)* (er*g^2 + 2*er*g*p2 + 2*er*g*p3 + 4*er*p2*p3 - 8*ei*g*w - 4*ei*p2*w - 4*ei*p3*w + 4*er*w^2))/ (8*ei^2*p1^3*w + 8*er^2*p1^3*w - 8*ei^2*p1^2*p2*w - 8*er^2*p1^2*p2*w - 8*ei^2*p1^2*p3*w - 8*er^2*p1^2*p3*w + 8*ei^2*p1*p2*p3*w + 8*er^2*p1*p2*p3*w), ((g + p1)* (ei*g - er*g + 2*ei*p1 - 2*er*p1 - 2*ei*w - 2*er*w)* (ei*g^2 + 2*ei*g*p2 + 2*ei*g*p3 + 4*ei*p2*p3 + 8*er*g*w + 4*er*p2*w + 4*er*p3*w + 4*ei*w^2))/ (8*ei^2*p1^3*w + 8*er^2*p1^3*w - 8*ei^2*p1^2*p2*w - 8*er^2*p1^2*p2*w - 8*ei^2*p1^2*p3*w - 8*er^2*p1^2*p3*w + 8*ei^2*p1*p2*p3*w + 8*er^2*p1*p2*p3*w), -(((g + p1)* (-(ei*g) + er*g - 2*ei*p1 + 2*er*p1 + 2*ei*w + 2*er*w))/ (4*p1^3 - 4*p1^2*p2 - 4*p1^2*p3 + 4*p1*p2*p3))}, {-(((g + p2)*(ei^2 + er^2 - 4*g^2 - 4*g*p1 - 4*g*p3 - 4*p1*p3)* (-(ei*g) + er*g - 2*ei*p2 + 2*er*p2 + 2*ei*w + 2*er*w))/ (4*ei^2*p1*p2^2 + 4*er^2*p1*p2^2 - 4*ei^2*p2^3 - 4*er^2*p2^3 - 4*ei^2*p1*p2*p3 - 4*er^2*p1*p2*p3 + 4*ei^2*p2^2*p3 + 4*er^2*p2^2*p3)) , ((g + p2)*(ei*g - er*g + 2*ei*p2 - 2*er*p2 - 2*ei*w - 2*er*w)* (-(er*g^2) - 2*er*g*p1 - 2*er*g*p3 - 4*er*p1*p3 + 8*ei*g*w + 4*ei*p1*w + 4*ei*p3*w - 4*er*w^2))/ (8*ei^2*p1*p2^2*w + 8*er^2*p1*p2^2*w - 8*ei^2*p2^3*w - 8*er^2*p2^3*w - 8*ei^2*p1*p2*p3*w - 8*er^2*p1*p2*p3*w + 8*ei^2*p2^2*p3*w + 8*er^2*p2^2*p3*w), ((g + p2)* (ei*g - er*g + 2*ei*p2 - 2*er*p2 - 2*ei*w - 2*er*w)* (-(ei*g^2) - 2*ei*g*p1 - 2*ei*g*p3 - 4*ei*p1*p3 - 8*er*g*w - 4*er*p1*w - 4*er*p3*w - 4*ei*w^2))/ (8*ei^2*p1*p2^2*w + 8*er^2*p1*p2^2*w - 8*ei^2*p2^3*w - 8*er^2*p2^3*w - 8*ei^2*p1*p2*p3*w - 8*er^2*p1*p2*p3*w + 8*ei^2*p2^2*p3*w + 8*er^2*p2^2*p3*w), ((g + p2)* (-(ei*g) + er*g - 2*ei*p2 + 2*er*p2 + 2*ei*w + 2*er*w))/ (4*p1*p2^2 - 4*p2^3 - 4*p1*p2*p3 + 4*p2^2*p3)}, {-(((-ei^2 - er^2 + 4*g^2 + 4*g*p1 + 4*g*p2 + 4*p1*p2)*(g + p3)* (-(ei*g) + er*g - 2*ei*p3 + 2*er*p3 + 2*ei*w + 2*er*w))/ (4*ei^2*p1*p2*p3 + 4*er^2*p1*p2*p3 - 4*ei^2*p1*p3^2 - 4*er^2*p1*p3^2 - 4*ei^2*p2*p3^2 - 4*er^2*p2*p3^2 + 4*ei^2*p3^3 + 4*er^2*p3^3)), ((g + p3)*(ei*g - er*g + 2*ei*p3 - 2*er*p3 - 2*ei*w - 2*er*w)* (er*g^2 + 2*er*g*p1 + 2*er*g*p2 + 4*er*p1*p2 - 8*ei*g*w - 4*ei*p1*w - 4*ei*p2*w + 4*er*w^2))/ (8*ei^2*p1*p2*p3*w + 8*er^2*p1*p2*p3*w - 8*ei^2*p1*p3^2*w - 8*er^2*p1*p3^2*w - 8*ei^2*p2*p3^2*w - 8*er^2*p2*p3^2*w + 8*ei^2*p3^3*w + 8*er^2*p3^3*w), ((g + p3)*(ei*g - er*g + 2*ei*p3 - 2*er*p3 - 2*ei*w - 2*er*w)* (ei*g^2 + 2*ei*g*p1 + 2*ei*g*p2 + 4*ei*p1*p2 + 8*er*g*w + 4*er*p1*w + 4*er*p2*w + 4*ei*w^2))/ (8*ei^2*p1*p2*p3*w + 8*er^2*p1*p2*p3*w - 8*ei^2*p1*p3^2*w - 8*er^2*p1*p3^2*w - 8*ei^2*p2*p3^2*w - 8*er^2*p2*p3^2*w + 8*ei^2*p3^3*w + 8*er^2*p3^3*w), -(((g + p3)*(-(ei*g) + er*g - 2*ei*p3 + 2*er*p3 + 2*ei*w + 2*er*w))/ (4*p1*p2*p3 - 4*p1*p3^2 - 4*p2*p3^2 + 4*p3^3))}} Roman Maeder (*----------------------------------------------------------------------*) From: wheeler@super.ORG (Ferrell S. Wheeler) Subject: Combinatorica, etc... Date: 10 May 90 15:05:55 GMT Newsgroups: sci.math.symbolic I was at the Mathematica Conference in January and I heard about alot of new packages, both commercial and public, that were announced and would "soon be available." What is the status of these packages, in particular Steve Skiena's Combinatorica and Ilan Vardi's elliptic curve package? Any information on these or others would be appreciated. If a new package is placed in the ftp archives maintained by Steve Christensen, then an announcement in this news group would be appreciated. Thanks, Ferrell Wheeler wheeler@super.org (*----------------------------------------------------------------------*) From: monagan@inf.ethz.ch (Michael) Subject: Re: Problem14 Summary: symbolic matrix inverse Date: 11 May 90 16:27:27 GMT Newsgroups: sci.math.symbolic In article <22001@ethz-inf.UUCP>, maeder@inf.ethz.ch (Roman Maeder) writes: > > From: rp@XN.LL.MIT.EDU (Richard Pavelle) > > Subject: Problem14 > > Keywords: A difficult matrix inversion and simplification > > > > I encountered a problem this week which makes a good candidate > > for the 14th entry in the series I am submitting to the > > group. The problem arises in photon scattering and involves > > little more than inverting a particular 4x4 matrix. But owing > > to the nature of the matrix the components of the inverse are > > huge. It therefore creates an unusually difficult matrix > > inversion problem for my MACSYMA. > > (all following timings are with Mathematica 1.2 on a Sun 4/330) > > Well, the inversion is no problem, it takes about 14 seconds to > compute it, but trying to print the result is next to impossible. > Canceling common terms in the numerators and denominators > brings the output down to reasonable size, however (this takes about > 25 min.). Max memory used was about 4.5MB. > ... Not to be outdone by my new colleague, I ran it in Maple. Takes only 30 seconds and under 1 MB to compute, simplify (i.e. cancel common terms in the numerators and denominators which is done automatically in Maple) and print the inverse in Maple 4.3 on a DEC station. Mike monagan@inf.ethz.ch |\^/| ._|\| |/|_. Licensed by the University of Waterloo \ MAPLE / Version 4.3 --- Mar 1989 <____ ____ > For on-line help, type help(); | > s:=array( > [[(er^2+ei^2)/(4*w^2+g^2+2*er^2+2*ei^2), > -(er^2+ei^2)*(2*p1+g)/((p1+g)*(2*er*w+2*ei*w+2*er*p1-2*ei*p1+er*g-ei*g)), > -(er^2+ei^2)*(2*p2+g)/((p2+g)*(2*er*w+2*ei*w+2*er*p2-2*ei*p2+er*g-ei*g)), > -(er^2+ei^2)*(2*p3+g)/((p3+g)*(2*er*w+2*ei*w+2*er*p3-2*ei*p3+er*g-ei*g))], > [-(2*er*w-ei*g)/(4*w^2+g^2+2*er^2+2*ei^2), > (2*er*w-2*ei*p1-ei*g)/(2*er*w+2*ei*w+2*er*p1-2*ei*p1+er*g-ei*g), > (2*er*w-2*ei*p2-ei*g)/(2*er*w+2*ei*w+2*er*p2-2*ei*p2+er*g-ei*g), > (2*er*w-2*ei*p3-ei*g)/(2*er*w+2*ei*w+2*er*p3-2*ei*p3+er*g-ei*g)], > [-(2*ei*w+er*g)/(4*w^2+g^2+2*er^2+2*ei^2), > (2*ei*w+2*er*p1+er*g)/(2*er*w+2*ei*w+2*er*p1-2*ei*p1+er*g-ei*g), > (2*ei*w+2*er*p2+er*g)/(2*er*w+2*ei*w+2*er*p2-2*ei*p2+er*g-ei*g), > (2*ei*w+2*er*p3+er*g)/(2*er*w+2*ei*w+2*er*p3-2*ei*p3+er*g-ei*g)], > [(4*w^2+g^2+er^2+ei^2)/(4*w^2+g^2+2*er^2+2*ei^2), > -(4*p1*w^2+4*g*w^2+4*p1^3+8*g*p1^2+5*g^2*p1+2*er^2*p1+2*ei^2*p1+g^3 > +er^2*g+ei^2*g) > /((p1+g)*(2*er*w+2*ei*w+2*er*p1-2*ei*p1+er*g-ei*g)), > -(4*p2*w^2+4*g*w^2+4*p2^3+8*g*p2^2+5*g^2*p2+2*er^2*p2+2*ei^2*p2+g^3 > +er^2*g+ei^2*g) > /((p2+g)*(2*er*w+2*ei*w+2*er*p2-2*ei*p2+er*g-ei*g)), > -(4*p3*w^2+4*g*w^2+4*p3^3+8*g*p3^2+5*g^2*p3+2*er^2*p3+2*ei^2*p3+g^3 > +er^2*g+ei^2*g) > /((p3+g)*(2*er*w+2*ei*w+2*er*p3-2*ei*p3+er*g-ei*g))]]): > evalm(1/s); 2 2 [1/4 (- 4 p2 p3 p1 - 4 p1 p2 g - 4 g p1 - 4 p1 g p3 - 4 g p2 - 4 p2 g p3 2 2 3 2 2 2 2 2 + er g + ei g - 4 g - 4 g p3) (4 w + g + 2 er + 2 ei ) / 2 2 2 2 2 2 / ((er + ei ) p2 p3 p1), - 1/8 (4 w + g + 2 er + 2 ei ) ( / ... (p3 + g) (2 er w + 2 ei w + 2 er p3 - 2 ei p3 + er g - ei g) - 1/4 ------------------------------------------------------------] 2 (p1 p2 - p3 p1 + p3 - p2 p3) p3 > quit bytes used=7585924, alloc=925696, time=28.950 (*----------------------------------------------------------------------*) From: GFX@psuvm.psu.edu Subject: Solving equations in Mathematica Date: 13 May 90 18:18:57 GMT Newsgroups: sci.math.symbolic Hi! I just received my copy of Mathematica and was anxious to see how easy it would be to explore the behavior of equations as we change some parameters. Well, apparently Mathematica cannot solve the equations I am working with... Integrating the differential equation is easy and give: 2 -0.1 - x1 x2 E (10. A x2 - ---) -0.1 - x1 2 2 m (1 - E ) (-0.01 m + 10. A x1 - x1 ) E V = -------------------------------------------- + -------------------------- 0.1 + x1 0.1 + x2 where x1, x2 and m are control variables, and A is an exogenous variable. The problem is first to find optimal values of x1, x2, and m, and what is of real interest to me is to characterize the change in optimal values for certain values of A. (values of x1, x2, and m that maximize V|A) So, first I compute first derivatives of V wrt x1, x2, and m, and solve simul- taneously: Rx1 = D[V,x1] Rx2 = D[V,x2] Rm = D[V,m] Solve[Rx1 == 0, Rx2 == 0,Rm == 0,{x1,x2,m}] All I get is {{}}, that is an empty solution set. Funny thing is that I know how x1*, x2* and m* behave as a function of A (increasing concave, increasing more concave and U-concave), both from pencil paper and numerical simulations. Could someone tell me what I am doing wrong? Can this be solved on Maple or Macsyma? Thanks. Stephane (*----------------------------------------------------------------------*) From: tbray@watsol.waterloo.edu (Tim Bray) Subject: Comparative review of Symbolic Math Software Date: 14 May 90 01:09:21 GMT Newsgroups: sci.math.symbolic For those who are interested, the May 29th article of PC magazine has a comparative review of Derive, Macsyma, Maple, and Mathematica. Bearing in mind that it's the DOS versions under review, and that the intended audience is rather less technical than the readers of this group, it still may be worth reading. Tim Bray, Waterloo Maple Software (tbray@watsol.waterloo.edu) (*----------------------------------------------------------------------*) From: GFX@psuvm.psu.edu Subject: Re: Solving equations in Mathematica (eqn fmt) Date: 14 May 90 02:36:58 GMT Newsgroups: sci.math.symbolic [Someone brought to my attention the fact that the equation was impossible to read, because of formatting problem. Since here it looks good I can only suppose that it's been wrapped unto itself during transmission. So here's my question again, with the equation now on two lines.] > >Hi! I just received my copy of Mathematica and was anxious to see how easy >it would be to explore the behavior of equations as we change some parameters. >Well, apparently Mathematica cannot solve the equations I am working with... > >Integrating the differential equation is easy and give: > > -0.1 - x1 2 2 (1 - E ) (-0.01 m + 10. A x1 - x1 ) V = -------------------------------------------- 0.1 + x1 2 -0.1 - x1 x2 E (10. A x2 - ---) m E + -------------------------- 0.1 + x2 >where x1, x2 and m are control variables, and A is an exogenous variable. The >problem is first to find optimal values of x1, x2, and m, and what is of real >interest to me is to characterize the change in optimal values for certain >values of A. (values of x1, x2, and m that maximize V|A) > >So, first I compute first derivatives of V wrt x1, x2, and m, and solve simul- >taneously: > > Rx1 = D[V,x1] > Rx2 = D[V,x2] > Rm = D[V,m] > > Solve[Rx1 == 0, Rx2 == 0,Rm == 0,{x1,x2,m}] > >All I get is {{}}, that is an empty solution set. Funny thing is that I know >how x1*, x2* and m* behave as a function of A (increasing concave, increasing >more concave and U-concave), both from pencil paper and numerical simulations. >Could someone tell me what I am doing wrong? Can this be solved on Maple or >Macsyma? Thanks. Stephane (*----------------------------------------------------------------------*) From: coopere@rocky2.rockefeller.edu (Ellis D. Cooper) Subject: Riemann Surface of Algebraic Function in Mathematica Date: 14 May 90 21:40:09 GMT Newsgroups: sci.math.symbolic (Richard Bumby already knows I am interested in this.) I could use help in Mathematica programming (data structures, algorithms) to construct the Riemann Surface of an algebraic function represented by a polynomial equation P[w,z]==0. I believe this is connected to Newton's Polygon Method and Puisseux series. I have books by Bliss, Hille, Siegel and Bruno which almost surely give all the mathematics. Do I have to do the entire translation into programming, or has someone already gone the route ? (*----------------------------------------------------------------------*) From: GFX@psuvm.psu.edu Subject: Notebooks on Economics Date: 15 May 90 03:16:52 GMT Newsgroups: sci.math.symbolic First, thanks to all of those who replied to my post. Special thanks to Marko.Petkovsek@B.GP.CS.CMU.EDU who pointed out that equation systems must be enclosed in brackets. Properly expressed, mathematica cannot find a closed form solution, but it churns out numerical solutions quite fast, so it's no big deal (just sad :). Now, I would like to know if there are sources of FTPable notebooks on applications relevant to Economics; or notebooks concerned with applications of optimal control theory and so on. One thing I'd like to see, for example, is a "good" code to explore the behavior of functions for which there are no closed form solutions. My problem, today, is that it seems that FindRoot[] cannot accept a range of parameter values: it solves for one set of parameters. Thus, to plot x* f(A), one must build a loop, collect the values of x* in a list, and finally plot the list. Somehow, I feel like I'd need to find a good intro to symbolic programming. Any suggestion? Thanks. Stephane (*----------------------------------------------------------------------*) From: ap10+@andrew.cmu.edu (Anand Patwardhan) Subject: Why the complex root? Date: 15 May 90 12:02:13 GMT Newsgroups: sci.math.symbolic For some strange reason, mathematica insists on giving me one complex root for the foll. polynomial equation (f[x] == 0) when a plot shows that there clearly is a root at the real part of that value. (Besides, just *one* complex root??) Is this just a numerical glitch? See below: ---------------- Mathematica (DECstation 3100) 1.2 (August 22, 1989) [With pre-loaded data] by S. Wolfram, D. Grayson, R. Maeder, H. Cejtin, S. Omohundro, D. Ballman and J. Keiper with I. Rivin and D. Withoff Copyright 1988,1989 Wolfram Research Inc. -- X11 windows graphics initialized -- In[1]:= f1[x1] := 1 + (k (2 x1 -1)/(x1^2 (1 - x1))) (* k is arbitrary *) In[2]:= k = 100 Out[2]= 100 In[3]:= N[Solve[f1[x1] == 0, x1]] Out[3]= {{x1 -> 14.4035}, {x1 -> -13.9029}, -15 > {x1 -> 0.499376 - 3.07674 10 I}} In[4]:= f2[x2] := x2^2 (1 - x2) + k (2 x2 - 1) (* f1[x1] == 0 reduces to this, assuming that x1 is non-zero or unity. *) In[5]:= N[Solve[f2[x2] == 0, x2]] Out[5]= {{x2 -> 14.4035}, {x2 -> -13.9029}, -15 > {x2 -> 0.499376 - 3.07674 10 I}} In[6]:= -------------------- Any ideas? Thanks Anand ------------------------------------------------------------------------------ Anand Patwardhan |INTERNET : ap10@andrew.cmu.edu Dept. of Engg. and |BITNET : apat@drycas.BITNET Public Policy, C.M.U |(others)..{harvard,psuvax1}!andrew.cmu.edu!ap10 Pittsburgh PA 15213 |VOICE : (412)-268-5617 (office) ------------------------------------------------------------------------------ (*----------------------------------------------------------------------*) From: oliveria@caen.engin.umich.edu (ROQUE DONIZETE DE OLIVEIRA) Subject: plasma dispersion function in mathematica Date: 14 May 90 18:27:02 GMT Newsgroups: sci.math.symbolic I realize this is a long shot but does anyone have a mathematica macro that computes generalized plasma dispersion function, which is defined as below: c Zm(m,z) = 1 / sqrt(pi) * def. integral from -Infinity c to Infinity of Exp( -t * t) * (t ** m ) dt / (t - z). c for Im(z) > 0 and analytically continued for Im(z) <= 0. c c An equivalent formulation for the standard (Fried-Conte) c plasma dispersion function is c Zm(0,z) = sqrt(Pi) * I * W(z) c c where c W(z) = Exp(-z * z) * Erfc( -I * z) . c c here Erfc(z) = complementary error function = c 2 / Sqrt(Pi) * def. integral from z to Infinity of c Exp( -t * t) dt. c c The generalized functions Zm(m,z)) satisfy the following c recursion relations c c Zm(m+2,z) = z * Zm(m+1,z) c Zm(m+1,z) = factorial((m-1)/2) + z * Zm(m,z) , c c for m even where c c factorial(n-0.5) = (n-0.5)*(n-1.5)*(n-2.5)*...*(0.5), n >= 1, c factorial(-0.5) = 1. I have a 250-line fortran code the calculates it but I'm trying to use mathematica in my research and I'll need such a beast converted to mathematica style. Even the code for the Erf function in mathematica style would get me started. Thanks for any help you can give me. Roque Oliveira oliveria@caen.engin.umich.edu (*----------------------------------------------------------------------*) From: judge@gpu.utcs.utoronto.ca (Peter Judge) Subject: Digital Filter Design Packages for Mathematica Date: 16 May 90 19:13:36 GMT Newsgroups: sci.math.symbolic Hi, Does anyone know if there are any Mathematica Packages for designing digital filters? Thanks. Please reply by e-mail. Peter Judge (judge@credit.erin.utoronto.ca) -- =============================================== judge@gpu.utcs.utoronto.ca (Peter Judge) =============================================== (*----------------------------------------------------------------------*) From: irh@bby.oz (Ian R Heddle) Subject: Mathematica Integration Date: 17 May 90 00:37:34 GMT Newsgroups: sci.math.symbolic Can anyone give me any suggestions as to how I can get Mathematica to do complex integrations? The equation that I've been trying to integrate describes the surface area of an elipoid. I've attempted to use the Integrate fn for the definite and indefinite integrals of the following equation with no result. Any suggestions would be greatly appreciated. Equation: (b^2*c^2*Cos[phi]^4*Cos[theta]^2 + a^2*b^2*Cos[phi]^2*Sin[phi]^2 + a^2*c^2*Sin[phi]^4*Sin[theta]^2)^0.5 phi 0 -> pi theta 0 -> 2Pi -- ________________________________ Ian Heddle Burdett, Buckeridge and Young Melbourne, Australia Internet irh@melba.bby.oz.au (*----------------------------------------------------------------------*) From: sdw@hpsad.HP.COM (Steve Warwick) Subject: Mathematica and Simplify Date: 17 May 90 15:57:55 GMT Newsgroups: sci.math.symbolic Mathematica seems to have problems with the simplifications of perfect squares - I have had problems finding the "Correct" simplification of such expressions and have tracked it down to the following problem: In[8]:= f1 = a-b Out[8]= a - b In[9]:= f2 = b-a Out[9]= -a + b In[10]:= Simplify[Sqrt[Expand[f1^2]]] Out[10]= a - b In[11]:= Simplify[Sqrt[Expand[f2^2]]] Out[11]= a - b a,b,f1,f2 were undefined before trying this... It seems that such simplifications should return multiple results, and for more complex formula with multiple roots of squares, should return a list of the possible simplifications, culling out duplicate results. Comments?? -- Steven Warwick Hewlett-Packard sdw@hpsad (*----------------------------------------------------------------------*) From @vmd.cso.uiuc.edu,@VM.BYU.EDU:smithw@mathnx.byu.edu Tue May 22 16:06:15 1990 Received: from vmd.cso.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA21771; Tue, 22 May 90 16:06:13 -0500 Received: from VM.BYU.EDU by VMD.CSO.UIUC.EDU (IBM VM SMTP R1.2) with BSMTP id 8871; Tue, 22 May 90 16:06:23 CDT Received: from BYUVM by VM.BYU.EDU (Mailer R2.05) with BSMTP id 3837; Tue, 22 May 90 14:45:05 MDT Received: from mathnx.byu.edu.byu.edu by VM.BYU.EDU (IBM VM SMTP R1.2.1) with TCP; Tue, 22 May 90 14:45:04 MDT Received: by mathnx.byu.edu.byu.edu (NeXT-1.0 (From Sendmail 5.52)/NeXT-1.0) id AA04404; Mon, 22 May 89 14:42:12 GMT-0700 Date: Mon, 22 May 89 14:42:12 GMT-0700 From: smithw@mathnx.byu.edu (William V. Smith) Message-Id: <8905222142.AA04404@ mathnx.byu.edu.byu.edu > To: mathgroup@yoda.ncsa.uiuc.edu Subject: mathematica in the classroom Status: RO We are interested in talking to folks about the pros and cons of using mathematica (and CAS in general)in or as an adjunct to the classroom in teaching mathematics, particularly calculus but at any level up through graduate courses. If you are involved or know of people who are involved in such projects who would be willing to discuss what they have learned from this please let me know. Thanks. Bill Smith smithw@mathnx.byu.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Wed May 23 00:55:52 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA22870; Wed, 23 May 90 00:55:51 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA23357; Wed, 23 May 90 00:52:10 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA22129; Tue, 22 May 90 23:46:16 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA22125; Tue, 22 May 90 23:46:14 -0500 Message-Id: <9005230446.AA22125@yoda.ncsa.uiuc.edu> Date: Mon, 21 May 90 14:03:59 GMT-0700 From: smithw@mathnx.byu.edu (William V. Smith) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Mathematica bug on NeXT fix Status: RO There is a fix for the mathematica bug (together function) on the NeXT. I sent email to our area rep (in Denver) and he got back to me the same day saying that he was putting an OD in the mail with the fix on it. Nice work NeXT . . . From mathgroup-adm@yoda.ncsa.uiuc.edu Wed May 23 03:02:36 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA23030; Wed, 23 May 90 03:02:35 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA25771; Wed, 23 May 90 02:58:56 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA22135; Tue, 22 May 90 23:46:31 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA22131; Tue, 22 May 90 23:46:30 -0500 Message-Id: <9005230446.AA22131@yoda.ncsa.uiuc.edu> Date: Tue, 22 May 90 16:52:29 EDT From: mcdonald@quark.umd.edu (Bill MacDonald) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Square root of squares Status: RO The following Mathematica command will return f1 or f2 as appropriate. Solve[c==f1^2,c] Solve[c==f2^2,c] If your suggestion were followed, Mathematica could never do the simplest calculation involving square roots without getting hung up by delivering two or more roots every time Sqrt[] was requested. If you want multiple roots of an expression, treat it as you would an equation. From mathgroup-adm@yoda.ncsa.uiuc.edu Wed May 23 03:53:27 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA23134; Wed, 23 May 90 03:53:26 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA26458; Wed, 23 May 90 03:49:48 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA22155; Tue, 22 May 90 23:47:06 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA22151; Tue, 22 May 90 23:47:04 -0500 Message-Id: <9005230447.AA22151@yoda.ncsa.uiuc.edu> Date: Mon, 22 May 89 14:42:12 GMT-0700 From: smithw@mathnx.byu.edu (William V. Smith) To: mathgroup@yoda.ncsa.uiuc.edu Subject: mathematica in the classroom Status: RO We are interested in talking to folks about the pros and cons of using mathematica (and CAS in general)in or as an adjunct to the classroom in teaching mathematics, particularly calculus but at any level up through graduate courses. If you are involved or know of people who are involved in such projects who would be willing to discuss what they have learned from this please let me know. Thanks. Bill Smith smithw@mathnx.byu.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Wed May 23 04:03:16 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA23140; Wed, 23 May 90 04:03:15 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA26622; Wed, 23 May 90 03:59:25 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA22150; Tue, 22 May 90 23:46:57 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA22146; Tue, 22 May 90 23:46:55 -0500 Message-Id: <9005230446.AA22146@yoda.ncsa.uiuc.edu> From: macg@SLCS.SLB.COM (Bill Macgregor) Date: Tue, 22 May 90 16:03:22 CDT To: mathgroup@yoda.ncsa.uiuc.edu Subject: SUMMARY-software defect list poll Status: RO In a message to the mailing list yesterday, I asked the questions: (1) How many readers of the mailing list believe WRI should, in the interests of good faith with its customers, make public a list of "known Mma kernel defects"? (2) Would it be sufficient for WRI to make such a list available on an internet file server? I received 46 responses. All were positive regarding question (1), the desirability of a published Mma defect list. Most were positive regarding (2), although a substantial minority felt that publication via internet file server would not reach enough of the Mathematica user community. One respondent made the point that the wording of the questions hardly permitted a negative response. I can only hope that WRI agrees. The number of responses and the comments that accompanied them are more significant than the tally. 46 people felt strongly enough about the issue to take time to respond, and a number of the responses were emphatic. We are justified, I believe, in hypothesizing that this is an important issue for the Mma user community at large. Here is an unordered summary of the comments I found to be most interesting and/or most often repeated: * Collectively, users waste a great deal of time rediscovering known defects and reinventing workarounds. * It is in WRI's interests to publish a software defect list, rather than to allow a third party to do so. * WRI's policy of providing updates to registered users when critical defects are found is commendable. * Availability of a software defect list to the internet- accessible users is a good start, but leaves out many Mma users. What about publication of the list in the Mma Journal? Or a technical newsletter, by subscription, if necessary, to cover costs? * WRI should verify errors before publishing them (keep the noise level down). * A software defect list could contain a statement of the problem, a description of workarounds, and a predicted disposition (e.g., fixed in next release, update available by request, update mailed to registered users). * Workarounds and package updates could be made available via anonymous ftp (possibly from ncsa?). Using the netlib software would allow access to the repository via email from any reachable network. * The registration form should include a "preferred contact method" for update information, e.g., an email address or paper mail, or maybe fax. * Could WRI keep documentation updates online, accessible via ftp? Maybe the entire Reference Guide? Could users get a file via ftp to update the local Information database? * Just providing a software defect list on paper, available on request to WRI, would be a big help. Sending incremental change notices to the mathgroup mailing list would be a good idea, too. Thanks to all of you who took the time to respond. - Bill MacGregor From mathgroup-adm@yoda.ncsa.uiuc.edu Wed May 23 02:12:25 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA22976; Wed, 23 May 90 02:12:24 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA24983; Wed, 23 May 90 02:08:45 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA22140; Tue, 22 May 90 23:46:39 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA22136; Tue, 22 May 90 23:46:37 -0500 Message-Id: <9005230446.AA22136@yoda.ncsa.uiuc.edu> Date: Tue, 22 May 90 15:12:55 -0400 From: jack@sun.udel.edu To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Limit[] trouble Status: RO When running the problem, Limit[ Cos[1/x^2]^(x^4), x->Infinity] on a Sun, using Mathmatica 1.2, I also obtained a Sementation Fault. However, using Mathematica 1.1, I obtain... In[1]:= Limit[ Cos[1/x^2]^(x^4), x->Infinity] Limit::nlm: Could not find definite limit. 4 -2 x Out[1]= Limit[Cos[x ] , x -> Infinity] From mathgroup-adm@yoda.ncsa.uiuc.edu Wed May 23 02:44:59 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA23014; Wed, 23 May 90 02:44:58 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA25542; Wed, 23 May 90 02:41:20 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA22145; Tue, 22 May 90 23:46:46 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA22141; Tue, 22 May 90 23:46:45 -0500 Message-Id: <9005230446.AA22141@yoda.ncsa.uiuc.edu> Date: Tue, 22 May 90 15:12:55 -0400 From: jack@sun.udel.edu To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Limit[] trouble Status: RO When running the problem, Limit[ Cos[1/x^2]^(x^4), x->Infinity] on a Sun, using Mathmatica 1.2, I also obtained a Sementation Fault. However, using Mathematica 1.1, I obtain... In[1]:= Limit[ Cos[1/x^2]^(x^4), x->Infinity] Limit::nlm: Could not find definite limit. 4 -2 x Out[1]= Limit[Cos[x ] , x -> Infinity] From Jim_Wendel@ub.cc.umich.edu Wed May 23 17:07:27 1990 Received: from umich.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA24098; Wed, 23 May 90 17:07:25 -0500 Received: from ubmts.cc.umich.edu by umich.edu (5.61/1123-1.0) id AA28201; Wed, 23 May 90 18:07:23 -0400 Date: Wed, 23 May 90 18:07:10 EDT From: Jim_Wendel@ub.cc.umich.edu To: mathgroup@yoda.ncsa.uiuc.edu Message-Id: <5371595@ub.cc.umich.edu> Status: RO Concerning Limit[Cos[1/x^2]^(x^4),x->Infinity], I get the correct answer 1/Sqrt[E] on a Mac II. From tleen@cse.ogi.edu Thu May 24 16:02:06 1990 Received: from cse.ogi.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA25663; Thu, 24 May 90 16:01:58 -0500 Received: by cse.ogi.edu (5.61+eap+OGI_1.1.named/IDA-1.2.8+OGI_1.11) id AA14119; Thu, 24 May 90 14:01:44 -0700 Date: Thu, 24 May 90 14:01:44 -0700 From: Todd Leen Message-Id: <9005242101.AA14119@cse.ogi.edu> To: mathgroup-request@yoda.ncsa.uiuc.edu Subject: Mailing list Cc: tleen@cse.ogi.edu Status: RO I am using Mathematica to do perturbation expansions for dynamical systems analysis of neural network learning. Please add me to your mailing list. Also, if you know of anyone who has written packages for i. Liapunov Schmidt reduction ii. Center manifold expansions iii. Reduction to normal form I would appreciate any contacts. Thanks tleen@cse.ogi.edu From marzetta@iam.unibe.ch Fri May 25 03:47:22 1990 Received: from [130.59.1.2] by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA26654; Fri, 25 May 90 03:47:14 -0500 Received: by chx400.switch.ch (5.61/Ultrix2.4-C) id AA24323; Fri, 25 May 90 10:47:52 +0200 Date: 25 May 90 10:14 +0200 From: Markus Marzetta To: Message-Id: <205:marzetta@iam.unibe.ch> Subject: ii) Limit[] trouble Status: RO Can anyone explain this singular behaviour: > Mathematica (sun4) 1.2 (August 22, 1989) [With pre-loaded data] > by S. Wolfram, D. Grayson, R. Maeder, H. Cejtin, > S. Omohundro, D. Ballman and J. Keiper > with I. Rivin and D. Withoff > Copyright 1988,1989 Wolfram Research Inc. > -- X11 windows graphics initialized -- > > In[1]:= Limit[(1+1/n)^n,n->Infinity] > > Out[1]= E > > In[2]:= Limit[(1+1/(n+1))^(n+1),n->Infinity] > > Out[2]= E > > In[3]:= Limit[(1+1/n)^(n+1),n->Infinity] > > 1/(1 + 1/n) > Out[3]= E > > In[4]:= Limit[%,n->Infinity] > > Out[4]= E I suppose in general the variable bound by "Limit" should not appear in the result; am I right? Markus Marzetta From mathgroup-adm@yoda.ncsa.uiuc.edu Sat May 26 05:13:10 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA28530; Sat, 26 May 90 05:13:09 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA15392; Sat, 26 May 90 05:09:32 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA28371; Sat, 26 May 90 02:20:00 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA28367; Sat, 26 May 90 02:19:58 -0500 Message-Id: <9005260719.AA28367@yoda.ncsa.uiuc.edu> Date: 25 May 90 10:14 +0200 From: Markus Marzetta To: Subject: ii) Limit[] trouble Status: RO Can anyone explain this singular behaviour: > Mathematica (sun4) 1.2 (August 22, 1989) [With pre-loaded data] > by S. Wolfram, D. Grayson, R. Maeder, H. Cejtin, > S. Omohundro, D. Ballman and J. Keiper > with I. Rivin and D. Withoff > Copyright 1988,1989 Wolfram Research Inc. > -- X11 windows graphics initialized -- > > In[1]:= Limit[(1+1/n)^n,n->Infinity] > > Out[1]= E > > In[2]:= Limit[(1+1/(n+1))^(n+1),n->Infinity] > > Out[2]= E > > In[3]:= Limit[(1+1/n)^(n+1),n->Infinity] > > 1/(1 + 1/n) > Out[3]= E > > In[4]:= Limit[%,n->Infinity] > > Out[4]= E I suppose in general the variable bound by "Limit" should not appear in the result; am I right? Markus Marzetta From mathgroup-adm@yoda.ncsa.uiuc.edu Sat May 26 04:17:51 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA28472; Sat, 26 May 90 04:17:50 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA14542; Sat, 26 May 90 04:14:13 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA28366; Sat, 26 May 90 02:19:52 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA28362; Sat, 26 May 90 02:19:50 -0500 Message-Id: <9005260719.AA28362@yoda.ncsa.uiuc.edu> Date: Thu, 24 May 90 14:01:44 -0700 From: Todd Leen To: mathgroup-request@yoda.ncsa.uiuc.edu Subject: Mailing list Status: RO I am using Mathematica to do perturbation expansions for dynamical systems analysis of neural network learning. Please add me to your mailing list. Also, if you know of anyone who has written packages for i. Liapunov Schmidt reduction ii. Center manifold expansions iii. Reduction to normal form I would appreciate any contacts. Thanks tleen@cse.ogi.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Sat May 26 03:18:05 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA28400; Sat, 26 May 90 03:18:02 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA13578; Sat, 26 May 90 03:14:21 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA28361; Sat, 26 May 90 02:19:43 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA28357; Sat, 26 May 90 02:19:42 -0500 Message-Id: <9005260719.AA28357@yoda.ncsa.uiuc.edu> Date: Wed, 23 May 90 18:07:10 EDT From: Jim_Wendel@ub.cc.umich.edu To: mathgroup@yoda.ncsa.uiuc.edu Status: RO Concerning Limit[Cos[1/x^2]^(x^4),x->Infinity], I get the correct answer 1/Sqrt[E] on a Mac II. From @vmd.cso.uiuc.edu:SAF8613@TAMSTAR.BITNET Sun May 27 22:56:16 1990 Received: from vmd.cso.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA29801; Sun, 27 May 90 22:56:13 -0500 Message-Id: <9005280356.AA29801@yoda.ncsa.uiuc.edu> Received: from TAMSTAR.BITNET by VMD.CSO.UIUC.EDU (IBM VM SMTP R1.2) with BSMTP id 1787; Sun, 27 May 90 22:56:26 CDT Date: Sun, 27 May 90 21:43 CDT From: Subject: Perturbation theory and symbolic computation To: mathgroup@yoda.ncsa.uiuc.edu X-Original-To: mathgroup@yoda.ncsa.uiuc.edu, tleen@cse.ogi.edu, SAF8613 Status: RO >I am using Mathematica to do perturbation expansions for dynamical >systems analysis of neural network learning. Please add me to your >mailing list. Also, if you know of anyone who has written packages for > >i. Liapunov Schmidt reduction >ii. Center manifold expansions >iii. Reduction to normal form > >I would appreciate any contacts. > >Thanks >tleen@cse.ogi.edu (Todd Leen) Precisely the three topics listed (and others) are discussed in the book by Richard H. Rand and Dieter Armbruster, "Perturbation Methods, Bifurcation Theory and Computer Algebra" (Springer- Verlag, Applied Mathematical Sciences vol. 65, 1987). All their code is in MACSYMA, but presumably it could be translated into Mathematica with reasonable effort. Steve Fulling fulling@sarastro.tamu.edu saf8613@tamstar.bitnet From @vmd.cso.uiuc.edu:SAF8613@TAMSTAR.BITNET Sun May 27 22:56:20 1990 Received: from vmd.cso.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA29806; Sun, 27 May 90 22:56:18 -0500 Message-Id: <9005280356.AA29806@yoda.ncsa.uiuc.edu> Received: from TAMSTAR.BITNET by VMD.CSO.UIUC.EDU (IBM VM SMTP R1.2) with BSMTP id 1792; Sun, 27 May 90 22:56:27 CDT Date: Sun, 27 May 90 21:45 CDT From: Subject: Sqrt[x^2], and Mathematica in the classroom To: mathgroup@yoda.ncsa.uiuc.edu X-Original-To: mathgroup@yoda.ncsa.uiuc.edu, smithw@mathnx.byu.edu, SAF8613 Status: RO >>Mathematica seems to have problems with the >>simplifications of perfect squares - I have had problems finding the >>"Correct" simplification of such expressions and have tracked it >>down to the following problem: >> >>In[8]:= f1 = a-b >> >>Out[8]= a - b >> >>In[9]:= f2 = b-a >> >>Out[9]= -a + b >> >>In[10]:= Simplify[Sqrt[Expand[f1^2]]] >> >>Out[10]= a - b >> >>In[11]:= Simplify[Sqrt[Expand[f2^2]]] >> >>Out[11]= a - b >> >> >>a,b,f1,f2 were undefined before trying this... >> >> >>It seems that such simplifications should return multiple results, and >>for more complex formula with multiple roots of squares, should return a >>list of the possible simplifications, culling out duplicate results. >>Comments?? >> >> Steven Warwick > >The following Mathematica command will return f1 or f2 as appropriate. >Solve[c==f1^2,c] >Solve[c==f2^2,c] >If your suggestion were followed, Mathematica could never do the simplest >calculation involving square roots without getting hung up by delivering >two or more roots every time Sqrt[] was requested. If you want multiple roots >of an expression, treat it as you would an equation. > > (Bill MacDonald) But the square root (of a positive number) is by definition a positive number. If Mathematica can't test which of the two candidates is the positive one, it should leave the function unevaluated, which is its usual default behavior when it doesn't know enough about the argument of a function to evaluate the function. It should not make a random guess of the sign, as that could lead to serious, unnoticed errors in complicated calculations. At the very least, this "feature" should be explained in the Mathematica Book so that users can try to work around it. The documentation for the function Positive[] states that "A definition like Positive[x] = True effectively specifies that x is a positive number." However, I find that (1) One must Unprotect[Positive] before stating such a definition. (2) Setting Positive[a-b] = True leaves Positive[b-a] undetermined. (3) Setting Positive[b-a] = False does not help the Sqrt[] function to find the right sign. ---------------------------------------------------------- In[1]:= f1=a-b Out[1]= a - b In[2]:= f2=b-a Out[2]= -a + b In[3]:= s1=f1^2 2 Out[3]= (a - b) In[4]:= s2=f2^2 2 Out[4]= (-a + b) In[5]:= r1=Sqrt[s1] Out[5]= a - b In[6]:= r2=Sqrt[s2] Out[6]= -a + b In[11]:= Unprotect[Positive] Out[11]= {Positive} In[12]:= Positive[a-b]=True Out[12]= True In[13]:= Positive[b-a] Out[13]= Positive[-a + b] In[15]:= Positive[b-a]=False Out[15]= False In[17]:= Sqrt[s2] Out[17]= -a + b In[18]:= Positive[%] Out[18]= False In[19]:= Quit ------------------------------------------------------------- Generally speaking, although rich in functions and the treatment thereof, Mathematica seems to be weak in "predicates" and relations -- that is, functions whose value is True or False rather than a number, a list, or whatever. When a predicate must be evaluated in order to evaluate a function, the program tends to make a random default assumption. I see no reason in principle why logical functions could not be treated as fully and consistently as algebraic functions have been. Another example: Mathematica does not include functions for taking the real and imaginary parts of an expression. (Re[] and Im[] work only if the argument is a particular complex number.) Presumably the reason is that to implement such a function requires a way of specifying which of the variables in the expression represent real numbers -- i.e., a predicate RealQ[]. At least Mathematica does not assume that all expressions that don't involve an explicit "I" are real! In answer to the question of William Smith about Mathematica in the classroom: The Sqrt[x^2] = x fallacy is only one of many instances where Mathematica makes the very errors that we are trying to teach our students to avoid. (Does this make it valuable as an object lesson?) The lack of support for logical relations (especially inequalities) makes it very difficult to use Mathematica in first-semester calculus courses, though it may be very useful in later courses. I hope (and expect) that later versions of the program will live up better to its billing as "A system for doing mathematics by computer". Granted that "mathematics" does not mean the same thing to the majority of WRI's customers that it does to an academic mathematician (I don't expect the program to prove theorems in functional analysis), we still should insist that it outgrow its freshman naivete before depending on it as a TA. S. A. Fulling Professor of Mathematics Texas A&M University fulling@sarastro.tamu.edu saf8613@tamstar.bitnet From MAILER-DAEMON@ndcvx.cc.nd.edu Tue May 29 00:24:10 1990 Received: from uunet.UU.NET by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA02044; Tue, 29 May 90 00:24:08 -0500 Received: from ndcva.cc.nd.edu by uunet.uu.net (5.61/1.14) with SMTP id AA01734; Tue, 29 May 90 01:23:59 -0400 Received: from [128.174.222.70] by ndcvx.cc.nd.edu (5.61/1.34) id AA09390; Tue, 29 May 90 00:24:57 -0500 Date: Tue, 29 May 90 00:24:57 -0500 From: MAILER-DAEMON@ndcvx.cc.nd.edu (Mail Delivery Subsystem) Subject: Returned mail: Host unknown Message-Id: <9005290524.AA09390@ndcvx.cc.nd.edu> To: Status: RO ----- Transcript of session follows ----- 421 ndcvb.cc.nd.edu.tcpld... Deferred: No such file or directory 550 ... Host unknown: No such file or directory ----- Unsent message follows ----- Received: from [128.174.222.70] by ndcvx.cc.nd.edu (5.61/1.34) id AA09365; Tue, 29 May 90 00:24:57 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA01003; Mon, 28 May 90 22:43:36 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA00999; Mon, 28 May 90 22:43:34 -0500 Date: Mon, 28 May 90 22:43:34 -0500 Message-Id: <9005290343.AA00999@yoda.ncsa.uiuc.edu> From: SAF8613@tamstar.bitnet Subject: Perturbation theory and symbolic computation To: mathgroup@yoda.ncsa.uiuc.edu Status: RO >I am using Mathematica to do perturbation expansions for dynamical >systems analysis of neural network learning. Please add me to your >mailing list. Also, if you know of anyone who has written packages for > >i. Liapunov Schmidt reduction >ii. Center manifold expansions >iii. Reduction to normal form > >I would appreciate any contacts. > >Thanks >tleen@cse.ogi.edu (Todd Leen) Precisely the three topics listed (and others) are discussed in the book by Richard H. Rand and Dieter Armbruster, "Perturbation Methods, Bifurcation Theory and Computer Algebra" (Springer- Verlag, Applied Mathematical Sciences vol. 65, 1987). All their code is in MACSYMA, but presumably it could be translated into Mathematica with reasonable effort. Steve Fulling fulling@sarastro.tamu.edu saf8613@tamstar.bitnet From MAILER-DAEMON@ndcvx.cc.nd.edu Tue May 29 01:00:08 1990 Received: from uunet.UU.NET by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA02102; Tue, 29 May 90 01:00:06 -0500 Received: from ndcva.cc.nd.edu by uunet.uu.net (5.61/1.14) with SMTP id AA09096; Tue, 29 May 90 01:59:32 -0400 Received: from [128.174.222.70] by ndcvx.cc.nd.edu (5.61/1.34) id AA09630; Tue, 29 May 90 01:00:30 -0500 Date: Tue, 29 May 90 01:00:30 -0500 From: MAILER-DAEMON@ndcvx.cc.nd.edu (Mail Delivery Subsystem) Subject: Returned mail: Host unknown Message-Id: <9005290600.AA09630@ndcvx.cc.nd.edu> To: Status: RO ----- Transcript of session follows ----- 421 ndcvb.cc.nd.edu.tcpld... Deferred: No such file or directory 550 ... Host unknown: No such file or directory ----- Unsent message follows ----- Received: from [128.174.222.70] by ndcvx.cc.nd.edu (5.61/1.34) id AA09627; Tue, 29 May 90 01:00:30 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA01009; Mon, 28 May 90 22:44:12 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA01005; Mon, 28 May 90 22:44:10 -0500 Message-Id: <9005290344.AA01005@yoda.ncsa.uiuc.edu> Date: Sun, 27 May 90 21:45 CDT From: SAF8613@tamstar.bitnet Subject: Sqrt[x^2], and Mathematica in the classroom To: mathgroup@yoda.ncsa.uiuc.edu Status: RO >>Mathematica seems to have problems with the >>simplifications of perfect squares - I have had problems finding the >>"Correct" simplification of such expressions and have tracked it >>down to the following problem: >> >>In[8]:= f1 = a-b >> >>Out[8]= a - b >> >>In[9]:= f2 = b-a >> >>Out[9]= -a + b >> >>In[10]:= Simplify[Sqrt[Expand[f1^2]]] >> >>Out[10]= a - b >> >>In[11]:= Simplify[Sqrt[Expand[f2^2]]] >> >>Out[11]= a - b >> >> >>a,b,f1,f2 were undefined before trying this... >> >> >>It seems that such simplifications should return multiple results, and >>for more complex formula with multiple roots of squares, should return a >>list of the possible simplifications, culling out duplicate results. >>Comments?? >> >> Steven Warwick > >The following Mathematica command will return f1 or f2 as appropriate. >Solve[c==f1^2,c] >Solve[c==f2^2,c] >If your suggestion were followed, Mathematica could never do the simplest >calculation involving square roots without getting hung up by delivering >two or more roots every time Sqrt[] was requested. If you want multiple roots >of an expression, treat it as you would an equation. > > (Bill MacDonald) But the square root (of a positive number) is by definition a positive number. If Mathematica can't test which of the two candidates is the positive one, it should leave the function unevaluated, which is its usual default behavior when it doesn't know enough about the argument of a function to evaluate the function. It should not make a random guess of the sign, as that could lead to serious, unnoticed errors in complicated calculations. At the very least, this "feature" should be explained in the Mathematica Book so that users can try to work around it. The documentation for the function Positive[] states that "A definition like Positive[x] = True effectively specifies that x is a positive number." However, I find that (1) One must Unprotect[Positive] before stating such a definition. (2) Setting Positive[a-b] = True leaves Positive[b-a] undetermined. (3) Setting Positive[b-a] = False does not help the Sqrt[] function to find the right sign. ---------------------------------------------------------- In[1]:= f1=a-b Out[1]= a - b In[2]:= f2=b-a Out[2]= -a + b In[3]:= s1=f1^2 2 Out[3]= (a - b) In[4]:= s2=f2^2 2 Out[4]= (-a + b) In[5]:= r1=Sqrt[s1] Out[5]= a - b In[6]:= r2=Sqrt[s2] Out[6]= -a + b In[11]:= Unprotect[Positive] Out[11]= {Positive} In[12]:= Positive[a-b]=True Out[12]= True In[13]:= Positive[b-a] Out[13]= Positive[-a + b] In[15]:= Positive[b-a]=False Out[15]= False In[17]:= Sqrt[s2] Out[17]= -a + b In[18]:= Positive[%] Out[18]= False In[19]:= Quit ------------------------------------------------------------- Generally speaking, although rich in functions and the treatment thereof, Mathematica seems to be weak in "predicates" and relations -- that is, functions whose value is True or False rather than a number, a list, or whatever. When a predicate must be evaluated in order to evaluate a function, the program tends to make a random default assumption. I see no reason in principle why logical functions could not be treated as fully and consistently as algebraic functions have been. Another example: Mathematica does not include functions for taking the real and imaginary parts of an expression. (Re[] and Im[] work only if the argument is a particular complex number.) Presumably the reason is that to implement such a function requires a way of specifying which of the variables in the expression represent real numbers -- i.e., a predicate RealQ[]. At least Mathematica does not assume that all expressions that don't involve an explicit "I" are real! In answer to the question of William Smith about Mathematica in the classroom: The Sqrt[x^2] = x fallacy is only one of many instances where Mathematica makes the very errors that we are trying to teach our students to avoid. (Does this make it valuable as an object lesson?) The lack of support for logical relations (especially inequalities) makes it very difficult to use Mathematica in first-semester calculus courses, though it may be very useful in later courses. I hope (and expect) that later versions of the program will live up better to its billing as "A system for doing mathematics by computer". Granted that "mathematics" does not mean the same thing to the majority of WRI's customers that it does to an academic mathematician (I don't expect the program to prove theorems in functional analysis), we still should insist that it outgrow its freshman naivete before depending on it as a TA. S. A. Fulling Professor of Mathematics Texas A&M University fulling@sarastro.tamu.edu saf8613@tamstar.bitnet From mathgroup-adm@yoda.ncsa.uiuc.edu Tue May 29 13:05:18 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA02665; Tue, 29 May 90 13:05:17 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA02994; Tue, 29 May 90 13:01:43 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA02610; Tue, 29 May 90 12:19:12 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA02606; Tue, 29 May 90 12:19:10 -0500 Message-Id: <9005291719.AA02606@yoda.ncsa.uiuc.edu> Date: Tue, 29 May 90 09:41:47 EDT From: mcdonald@quark.umd.edu (Bill MacDonald) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Mathematica's Handling of Overflow and Underflow Status: RO Mathematica's handling of Overflow and Underflow do not seem to be consistent and evidence for this is found in the following anomalies. In[1]:= Overflow[]==Underflow[] Out[1]= True In[2]:= Overflow[]===Underflow[] Out[2]= True In[3]:= Overflow[] > 0 Out[3]= True In[4]:= Overflow[] < 1/(10^100) Out[4]= True In[5]:= Chop[Overflow[]] Out[5]= 0 Mathematica is at least consistent in that the last three statements are also True for Underflow[]. Note that In[6]:= Head[Overflow[]] Out[6]= Real is also true of Underflow[]. From mathgroup-adm@yoda.ncsa.uiuc.edu Tue May 29 14:56:46 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA02849; Tue, 29 May 90 14:56:29 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA05215; Tue, 29 May 90 14:52:55 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA02620; Tue, 29 May 90 12:19:27 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA02616; Tue, 29 May 90 12:19:26 -0500 Message-Id: <9005291719.AA02616@yoda.ncsa.uiuc.edu> Date: Tue, 29 May 90 10:58:44 +0200 From: lie@itk.unit.no To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: setting element of list Status: RO The following example will explain my problem: -------------- Mathematica (sun4) 1.2 (August 3, 1989) [With pre-loaded data] by S. Wolfram, D. Grayson, R. Maeder, H. Cejtin, S. Omohundro, D. Ballman and J. Keiper with I. Rivin and D. Withoff Copyright 1988,1989 Wolfram Research Inc. -- X11 windows graphics initialized -- In[1]:= h[s_]={{(1-s)/(1+s+s^2)}} 1 - s Out[1]= {{----------}} 2 1 + s + s In[2]:= h[s][[1,1]] 1 - s Out[2]= ---------- 2 1 + s + s In[3]:= h[s_][[1,1]]=3 Part::nonsymb: h[s_] in assignment of part is not a symbol. Out[3]= 3 In[4]:= h[s][[1,1]]=3 Part::nonsymb: h[s] in assignment of part is not a symbol. Out[4]= 3 In[5]:= h[[1,1]]=3 Part::noval: Symbol h in part assignment does not have an immediate value. Out[5]= 3 In[6]:= ?????? ---------------------- What is the correct way of setting element {1,1} of h[s] to 3? Why doesn't "my" methods work?? -------- Two other "problems". 1) There is a bug in our version of ListContourPlot (Sun version): the command requires the table to be square (i.e., the same numberof rows and columns). The Macintosh versions allows for rectangular tables. 2) In general, I'm not impressed by the quality of the numerical algorithms that are used. The Roots command, for instance, fails to find the correct roots of a certain polynomial of degree 10, whereas Matlab appears to solve the problem easily. ---------- -Bernt Lie, lie@itk.unit.no From mathgroup-adm@yoda.ncsa.uiuc.edu Tue May 29 15:04:22 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA02860; Tue, 29 May 90 15:04:21 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA05382; Tue, 29 May 90 15:00:49 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA02631; Tue, 29 May 90 12:20:25 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA02627; Tue, 29 May 90 12:20:23 -0500 Message-Id: <9005291720.AA02627@yoda.ncsa.uiuc.edu> Date: Tue, 29 May 90 12:03:26 CDT From: withoff@wri.UUCP (David Withoff) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Sqrt[x^2], and Mathematica in the classroom Status: RO While the comments about Sqrt[x^2] ==> x, real and imaginary parts of expressions, inequalities, predicates, and so forth, are true of Mathematica in its "raw" (unprogrammed) state, it is often straightforward to program Mathematica to have almost any desired behaviour. For example, there are indeed functions for obtaining the real and imaginary parts of expressions: In[1]:= << ReIm.m In[2]:= Re[a] ^= a; Im[a] ^= 0; Re[b] ^= x; Im[b] ^= y; In[3]:= Re[(a + b)^2 + Sin[b]] -y y 2 2 (E + E ) Sin[x] Out[3]= (a + x) - y + ----------------- 2 In[4]:= Im[b Exp[a b]] a x a x Out[4]= E y Cos[a y] + E x Sin[a y] The package ReIm.m is a short collection of simple rules, and can be extended as necessary. It also represents a good example of a useful approach for dealing with a number of related problems, such as equations, predicates, and inequalities. Without programmability, Mathematica (although quite powerful as a calculator) is rather limited -- but that's like saying that a car is limited when the engine isn't running. If the user chooses not to start the engine, they might be better off with a different product. As for Mathematica the classroom, I know it is widely used for this purpose, including first semester calculus, and I too am interested in hearing about the experiences of people who have incorporated it into their teaching. Dave Withoff Wolfram Research withoff@wri.com From mathgroup-adm@yoda.ncsa.uiuc.edu Tue May 29 14:14:07 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA02762; Tue, 29 May 90 14:14:06 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA04414; Tue, 29 May 90 14:10:32 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA02615; Tue, 29 May 90 12:19:19 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA02611; Tue, 29 May 90 12:19:18 -0500 Message-Id: <9005291719.AA02611@yoda.ncsa.uiuc.edu> Date: Tue, 29 May 90 09:52:33 +0300 From: pjanhune@finsun.CSC.FI Apparently-To: mathgroup@yoda.ncsa.uiuc.edu Status: RO To obtain a simplified Re or Im of a symbolic expression, try this: (suppose f is a symbolic expression) < f, Im[f_?(FreeQ[#,I]&)] :> 0} This assumes all subexpressions of f not containing an explicit I to be real. It works, of course, correctly only if all symbols appearing in f are assumed to be real and, further, if there are no square roots of negative arguments etc. among the subexpressions of f. Pekka Janhunen Finnish Meteorological Institute, Geophysics Dept. pjanhune@finsun.csc.fi From mathgroup-adm@yoda.ncsa.uiuc.edu Tue May 29 19:02:54 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA03301; Tue, 29 May 90 19:02:54 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA10798; Tue, 29 May 90 18:59:23 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA03173; Tue, 29 May 90 17:57:28 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA03169; Tue, 29 May 90 17:57:27 -0500 Message-Id: <9005292257.AA03169@yoda.ncsa.uiuc.edu> To: mathgroup@yoda.ncsa.uiuc.edu Subject: Overflow and Underflow Date: Tue, 29 May 90 11:27:50 PDT From: jacobson@cello.hpl.hp.com Status: RO It was only upon reading Bill McDonald's message that I discovered the existance of Overflow and Underflow. Where are these documented? If I try the "?" or "??" specal forms, I only find that they are protected. They are not mentioned in the Mathematica book or the Version 1.2 Reference Guide Updates. -- David Jacobson From @uunet.UU.NET:keiper@wri.UUCP Tue May 29 19:38:10 1990 Received: from uunet.UU.NET by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA03345; Tue, 29 May 90 19:38:08 -0500 Received: from wri.UUCP by uunet.uu.net (5.61/1.14) with UUCP id AA26439; Tue, 29 May 90 20:37:24 -0400 From: keiper@wri.UUCP Received: by WRI.com (3.2/SMI-3.0DEV3) id AA06736; Tue, 29 May 90 19:13:23 CDT Message-Id: <9005300013.AA06736@WRI.com> Date: Tue, 29 May 90 19:13:21 CDT To: jacobson@cello.hpl.hp.com Subject: Re: Overflow and Underflow Cc: mathgroup@yoda.ncsa.uiuc.edu Status: RO In[1]:= ?Overflow Overflow[] is the result of a numerical calculation whose result is too large to represent. In[1]:= ?Underflow Underflow[] is the result of a numerical calculation whose result is too small to represent. These "functions" were not documented in the manual because it is intended that in the future Mathematica will be able to deal with truly arbitrary sized numbers. The fact that they were not documented on-line is a bug. As can be seen above they are docmented in the internal development version and will also be documented in the next release; Mathematica is not yet able to deal with numbers on the order of 10.^1000000000. Jerry Keiper Wolfram Research, Inc. keiper@wri.com From @VM.BYU.EDU:smithw@mathnx.byu.edu Tue May 29 18:16:41 1990 Received: from vm.byu.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA03217; Tue, 29 May 90 18:16:39 -0500 Received: from mathnx.byu.edu.byu.edu by VM.BYU.EDU (IBM VM SMTP R1.2.1) with TCP; Tue, 29 May 90 17:16:38 MDT Received: by mathnx.byu.edu.byu.edu (NeXT-1.0 (From Sendmail 5.52)/NeXT-1.0) id AA01909; Tue, 29 May 90 17:17:11 MDT Date: Tue, 29 May 90 17:17:11 MDT From: smithw@mathnx.byu.edu (William V. Smith) Message-Id: <9005292317.AA01909@ mathnx.byu.edu.byu.edu > To: mathgroup@yoda.ncsa.uiuc.edu Subject: Limits in NeXT Mathematica Cc: Mitch_Green@next.com Status: RO I have the recent fix for Mathematica on the NeXT, but it still seems to have the problem with limits. With Limit[Cos[1/x^2]^(x^4),x->Infinity] I get "bus error" from a remote login session and it just seems to go on forever if you run it from the console. From mathgroup-adm@yoda.ncsa.uiuc.edu Tue May 29 20:03:02 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA03387; Tue, 29 May 90 20:03:01 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA12223; Tue, 29 May 90 19:59:29 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA03168; Tue, 29 May 90 17:57:21 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA03164; Tue, 29 May 90 17:57:19 -0500 Message-Id: <9005292257.AA03164@yoda.ncsa.uiuc.edu> Date: Tue, 29 May 90 12:03:26 CDT From: withoff@wri.UUCP (David Withoff) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Sqrt[x^2], and Mathematica in the classroom Status: RO While the comments about Sqrt[x^2] ==> x, real and imaginary parts of expressions, inequalities, predicates, and so forth, are true of Mathematica in its "raw" (unprogrammed) state, it is often straightforward to program Mathematica to have almost any desired behaviour. For example, there are indeed functions for obtaining the real and imaginary parts of expressions: In[1]:= << ReIm.m In[2]:= Re[a] ^= a; Im[a] ^= 0; Re[b] ^= x; Im[b] ^= y; In[3]:= Re[(a + b)^2 + Sin[b]] -y y 2 2 (E + E ) Sin[x] Out[3]= (a + x) - y + ----------------- 2 In[4]:= Im[b Exp[a b]] a x a x Out[4]= E y Cos[a y] + E x Sin[a y] The package ReIm.m is a short collection of simple rules, and can be extended as necessary. It also represents a good example of a useful approach for dealing with a number of related problems, such as equations, predicates, and inequalities. Without programmability, Mathematica (although quite powerful as a calculator) is rather limited -- but that's like saying that a car is limited when the engine isn't running. If the user chooses not to start the engine, they might be better off with a different product. As for Mathematica the classroom, I know it is widely used for this purpose, including first semester calculus, and I too am interested in hearing about the experiences of people who have incorporated it into their teaching. Dave Withoff Wolfram Research withoff@wri.com >From @uunet.UU.NET:keiper@wri.UUCP Tue May 29 15:23:02 1990 Received: from uunet.UU.NET by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA02880; Tue, 29 May 90 15:22:59 -0500 Received: from wri.UUCP by uunet.uu.net (5.61/1.14) with UUCP id AA04280; Tue, 29 May 90 16:22:59 -0400 From: keiper@wri.UUCP Received: by WRI.com (3.2/SMI-3.0DEV3) id AA02495; Tue, 29 May 90 15:17:22 CDT Message-Id: <9005292017.AA02495@WRI.com> Date: Tue, 29 May 90 15:17:20 CDT To: lie@itk.unit.no Subject: Re: setting element of list Cc: mathgroup@yoda.ncsa.uiuc.edu Status: RO > What is the correct way of setting element {1,1} of h[s] to 3? You can't. h[s] has a Head of "h" and a single argument "s". Since s is a Symbol it does not have a first Part. Now you say "But h[s][[1, 1]] is ...". But, in the statement h[s][[1, 1]] = 3, h[s] is not evaluated since Set[] is HoldFirst. If it weren't HoldFirst then things like a = b; a = 3 would result in setting the value of b to 3. Clearly you don't want this sort of thing to occur. If I may guess at what is intended, the following does work: In[11]:= h[s_]={{(1-s)/(1+s+s^2)}} 1 - s Out[11]= {{----------}} 2 1 + s + s In[12]:= a = h[s] 1 - s Out[12]= {{----------}} 2 1 + s + s In[13]:= a[[1,1]] = 3 Out[13]= 3 >From @uunet.UU.NET:keiper@wri.UUCP Tue May 29 15:23:02 1990 Received: from uunet.UU.NET by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA02880; Tue, 29 May 90 15:22:59 -0500 Received: from wri.UUCP by uunet.uu.net (5.61/1.14) with UUCP id AA04280; Tue, 29 May 90 16:22:59 -0400 From: keiper@wri.UUCP Received: by WRI.com (3.2/SMI-3.0DEV3) id AA02495; Tue, 29 May 90 15:17:22 CDT Message-Id: <9005292017.AA02495@WRI.com> Date: Tue, 29 May 90 15:17:20 CDT To: lie@itk.unit.no Subject: Re: setting element of list Cc: mathgroup@yoda.ncsa.uiuc.edu Status: RO > What is the correct way of setting element {1,1} of h[s] to 3? You can't. h[s] has a Head of "h" and a single argument "s". Since s is a Symbol it does not have a first Part. Now you say "But h[s][[1, 1]] is ...". But, in the statement h[s][[1, 1]] = 3, h[s] is not evaluated since Set[] is HoldFirst. If it weren't HoldFirst then things like a = b; a = 3 would result in setting the value of b to 3. Clearly you don't want this sort of thing to occur. If I may guess at what is intended, the following does work: In[11]:= h[s_]={{(1-s)/(1+s+s^2)}} 1 - s Out[11]= {{----------}} 2 1 + s + s In[12]:= a = h[s] 1 - s Out[12]= {{----------}} 2 1 + s + s In[13]:= a[[1,1]] = 3 Out[13]= 3 From xinwei@jessica.stanford.edu Tue May 29 17:16:16 1990 Received: from Jessica.Stanford.EDU by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA03136; Tue, 29 May 90 17:16:14 -0500 Received: from LOCALHOST by jessica.stanford.edu (5.59/25-eef) id AA25415; Tue, 29 May 90 15:16:07 PDT Message-Id: <9005292216.AA25415@jessica.stanford.edu> To: smithw@mathnx.byu.edu (William V. Smith) Cc: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: mathematica in the classroom In-Reply-To: Your message of Mon, 22 May 89 14:42:12 -0700. <9005230447.AA22151@yoda.ncsa.uiuc.edu> Date: Tue, 29 May 90 15:16:05 -0700 From: xinwei@jessica.stanford.edu Status: RO I'm working on a set of illustrations & exploratory workspaces in the form of Mathematica notebooks for topics in calculus, ordinary differential equations, complex analysis, and especially differential geometry. Suggestions for topics are most welcome. I'd like to try some of these on guinea pig students next year. Sha Xin Wei Math Dept. & Academic Information Resources Stanford From mathgroup-adm@yoda.ncsa.uiuc.edu Tue May 29 21:15:55 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA03630; Tue, 29 May 90 21:15:54 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA13421; Tue, 29 May 90 21:12:23 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA03478; Tue, 29 May 90 20:27:36 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA03474; Tue, 29 May 90 20:27:34 -0500 Message-Id: <9005300127.AA03474@yoda.ncsa.uiuc.edu> To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: mathematica in the classroom Date: Tue, 29 May 90 15:16:05 -0700 From: xinwei@jessica.stanford.edu Status: RO I'm working on a set of illustrations & exploratory workspaces in the form of Mathematica notebooks for topics in calculus, ordinary differential equations, complex analysis, and especially differential geometry. Suggestions for topics are most welcome. I'd like to try some of these on guinea pig students next year. Sha Xin Wei Math Dept. & Academic Information Resources Stanford From mathgroup-adm@yoda.ncsa.uiuc.edu Tue May 29 22:28:40 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA03785; Tue, 29 May 90 22:28:39 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA15492; Tue, 29 May 90 22:25:09 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA03471; Tue, 29 May 90 20:26:34 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA03467; Tue, 29 May 90 20:26:32 -0500 Message-Id: <9005300126.AA03467@yoda.ncsa.uiuc.edu> Date: Tue, 29 May 90 17:17:11 MDT From: smithw@mathnx.byu.edu (William V. Smith) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Limits in NeXT Mathematica Status: RO I have the recent fix for Mathematica on the NeXT, but it still seems to have the problem with limits. With Limit[Cos[1/x^2]^(x^4),x->Infinity] I get "bus error" from a remote login session and it just seems to go on forever if you run it from the console. >From xinwei@jessica.stanford.edu Tue May 29 17:16:16 1990 Received: from Jessica.Stanford.EDU by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA03136; Tue, 29 May 90 17:16:14 -0500 Received: from LOCALHOST by jessica.stanford.edu (5.59/25-eef) id AA25415; Tue, 29 May 90 15:16:07 PDT Message-Id: <9005292216.AA25415@jessica.stanford.edu> To: smithw@mathnx.byu.edu (William V. Smith) Cc: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: mathematica in the classroom In-Reply-To: Your message of Mon, 22 May 89 14:42:12 -0700. <9005230447.AA22151@yoda.ncsa.uiuc.edu> Date: Tue, 29 May 90 15:16:05 -0700 From: xinwei@jessica.stanford.edu Status: RO I'm working on a set of illustrations & exploratory workspaces in the form of Mathematica notebooks for topics in calculus, ordinary differential equations, complex analysis, and especially differential geometry. Suggestions for topics are most welcome. I'd like to try some of these on guinea pig students next year. Sha Xin Wei Math Dept. & Academic Information Resources Stanford From mathgroup-adm@yoda.ncsa.uiuc.edu Tue May 29 21:53:40 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA03690; Tue, 29 May 90 21:53:39 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA14600; Tue, 29 May 90 21:50:08 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA03464; Tue, 29 May 90 20:25:14 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA03460; Tue, 29 May 90 20:25:12 -0500 Message-Id: <9005300125.AA03460@yoda.ncsa.uiuc.edu> From: keiper@wri.UUCP Date: Tue, 29 May 90 19:13:21 CDT Subject: Re: Overflow and Underflow To: mathgroup@yoda.ncsa.uiuc.edu Status: RO In[1]:= ?Overflow Overflow[] is the result of a numerical calculation whose result is too large to represent. In[1]:= ?Underflow Underflow[] is the result of a numerical calculation whose result is too small to represent. These "functions" were not documented in the manual because it is intended that in the future Mathematica will be able to deal with truly arbitrary sized numbers. The fact that they were not documented on-line is a bug. As can be seen above they are docmented in the internal development version and will also be documented in the next release; Mathematica is not yet able to deal with numbers on the order of 10.^1000000000. Jerry Keiper Wolfram Research, Inc. keiper@wri.com From mathgroup-adm@yoda.ncsa.uiuc.edu Wed May 30 14:57:13 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA05033; Wed, 30 May 90 14:57:13 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA16181; Wed, 30 May 90 14:53:42 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA04944; Wed, 30 May 90 13:49:48 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA04940; Wed, 30 May 90 13:49:47 -0500 Message-Id: <9005301849.AA04940@yoda.ncsa.uiuc.edu> Date: Wed, 30 May 90 13:30:14 EDT From: Jim_Wendel@ub.cc.umich.edu To: mathgroup@yoda.ncsa.uiuc.edu Status: RO I ran into a TeX problem (on a Mac IIci using Textures.) I typed in the As far as I can tell I gave the input exactly as in In[3]. stuff on pg 158, executed TeXForm[%] and got almost the output specified, but when I typeset it in either AMS-TeX format or Plain TeX the denomi- nator factors 9801 and 396^(4n) blended to produce 9801396^(4n). The difference between my output and the textbook's lay in the order of the two factors (4n)! and 1103+26390n. From mathgroup-adm@yoda.ncsa.uiuc.edu Wed May 30 16:03:53 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA05107; Wed, 30 May 90 16:03:52 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA17666; Wed, 30 May 90 16:00:18 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA04952; Wed, 30 May 90 13:50:24 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA04948; Wed, 30 May 90 13:50:23 -0500 Message-Id: <9005301850.AA04948@yoda.ncsa.uiuc.edu> Date: Wed, 30 May 90 10:52:10 PDT From: kenward@mdivax1.UUCP (Gary Kenward) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Symbolic derivatives and function definition Status: RO I have a symbolic function of two variables, f[x,y], which is differentiable (f'[x,y] exists, and can be generated by Mathematica). What I would like to be able to do is assigne the symbolic result of D[f[x,y], x] to a new function, df [x,y], and be able to use df directly. So far the best solution I have been able to come up with is (I think this works): df[x_, y_] := D[f[u, v], u] /. u -> x /. v -> y I suspect that this is all wrong. In particular, it seems to me that each evaluation of df results in D[f . . .] being re-evaluated. Obviously, I am not a Mathematica expert. I am just learning, and I need a solution as soon as possible. Can anyone provide a solution? Gary W. Kenward Mobile Data International Richmond B.C. From mathgroup-adm@yoda.ncsa.uiuc.edu Wed May 30 17:03:35 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA05191; Wed, 30 May 90 17:03:34 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA18720; Wed, 30 May 90 16:59:59 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA04975; Wed, 30 May 90 13:59:00 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA04971; Wed, 30 May 90 13:58:58 -0500 Message-Id: <9005301858.AA04971@yoda.ncsa.uiuc.edu> Date: Wed, 30 May 90 14:12:07 +0300 From: pjanhune@finsun.CSC.FI To: mathgroup@ncsa.uiuc.edu Status: RO [The files below are found in /Symbolic/Mathematica/Packages/JANHUNEN directory on the anonymous ftp server. --- smc] Hello! I sent four Mathematica files to the /Symbolics/New directory on the FTP server. The files are DeltaTheta.m, DSubst.m, FortranDef.m and FortranDefDemo.m. They implement the Dirac Delta and Heaviside Theta functions, as well as variable and function substitutions in (e.g.) differential equations. The file FortranDef.m contains a fully automated method to generate, compile and call a Fortran program from an arbitrary Mathematica expression containing elementary functions. This can tremendously speed up e.g. the plotting of complicated expressions. The file FortranDefDemo.m contains examples on this. The files have been written on a MacII using a remote kernel running in a UNIX machine. The files should be readable without problem on a MacII Mathematica, but if you have trouble, please inform me, and I try to make an unformatted version of them. Pekka Janhunen Finnish Meteorological Institute Geophysics Dept. pjanhune@finsun.csc.fi From mathgroup-adm@yoda.ncsa.uiuc.edu Wed May 30 17:05:54 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA05197; Wed, 30 May 90 17:05:53 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA18784; Wed, 30 May 90 17:02:24 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA04934; Wed, 30 May 90 13:48:41 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA04930; Wed, 30 May 90 13:48:39 -0500 Message-Id: <9005301848.AA04930@yoda.ncsa.uiuc.edu> Subject: Sqrt... To: mathgroup@yoda.ncsa.uiuc.edu (mathgroup for mathematica) Date: Wed, 30 May 90 10:29:23 PDT From: Steven Warwick Status: RO An interesting challange for someone on the group might be to find a way to expand expressions which contain multiple roots of squares in such a way as to produce a list of the unique solutions i.e.: NewExpand[ ( Sqrt[a^2] + 1 ) / ( Sqrt[b^2] +1 ) ] gives: { (a+1)/(b+1) , (-a+1)/(b+1) , (a+1)/(-b+1) , (-a+1)/(-b+1) } preferrably, NewExpand would deal with any function which has multiple values as returned as a list. this behaviour is different than normal mathematica since lists in expressions are dealt with linearly: { a,b} + {c,d} results in {a+b,c+d} NewExpand effectivly produces the behaviour: { a,b} + {c,d} results in {a+c,a+d,b+c,b+d} this behaviour seems correct for the Sqrt case, but is probably not correct in general. One solution is to define something called a "combinatorial list" as opposed to the Mathematica "distributed list" and functions which return multiple values actually return the combinatorial list, allowing both behaviours in the same expression. On another topic, it seems like the traffic in this mailgroup is big enough to warrent switching over the the notes system. I know there were complaints from those in sci.math.symbolic about so much Mathematica traffic, so perhaps it be best to create a new group. How about it? -- Steven Warwick Hewlett-Packard sdw@hpsad From mathgroup-adm@yoda.ncsa.uiuc.edu Wed May 30 17:57:56 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA05302; Wed, 30 May 90 17:57:55 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA19666; Wed, 30 May 90 17:54:26 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA04920; Wed, 30 May 90 13:47:41 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA04916; Wed, 30 May 90 13:47:39 -0500 Message-Id: <9005301847.AA04916@yoda.ncsa.uiuc.edu> Date: Wed, 30 May 90 10:13:02 CDT From: drdan@src.honeywell.com (Dan Johnson) To: mathgroup@WRI.UUCP Subject: Which[] behaviour Status: RO There is a 'foolish inconsistency' between the behaviours of If[] and Which[] which can be worked around, but is annoying. I should note that this behaviour is documented. If we define the functionally identical functions f[z_] := Which[z<3,3, z>=3,4] and g[z_] := If[z<3,3, If[z>=3,4]] and then evaluate... Mathematica (sun3.68881) 1.2 (November 6, 1989) [With pre-loaded data] by S. Wolfram, D. Grayson, R. Maeder, H. Cejtin, S. Omohundro, D. Ballman and J. Keiper with I. Rivin and D. Withoff Copyright 1988,1989 Wolfram Research Inc. -- Tektronix graphics initialized -- In[1]:= f[z_] := Which[z<3,3, z>=3,4] In[2]:= g[z_] := If[z<3,3, If[z>=3,4]] In[3]:= f[zz] In[4]:= g[zz] Out[4]= If[zz < 3, 3, If[zz >= 3, 4]] What is happening is that If[] leaves ambiguous expressions unevaluated, while Which[] returns Null. This is a problem when using Which[] to define functions to be used elsewhere, i.e. In[5]:= NIntegrate[f[zz],{zz,0,5}] NIntegrate::notnum: Integrand Null is not numerical at {4.90072}. Out[5]= NIntegrate[f[zz], {zz, 0, 5}] In[6]:= NIntegrate[g[zz],{zz,0,4}] Out[6]= 13.0008 where the integration fails because Which[] evaluates the general expression. I would prefer to use Which[] rather than nested If[]'s because I often use up to 10 different conditions. Is there a way to turn off the behaviour in Which[] and get the same effect as in If[]? Daniel Johnson MN65-2500 (612) 782-7427 Honeywell Systems & Research Center drdan@SRC.Honeywell.COM (internet) 3660 Technology Drive Mpls, MN 55418 From mathgroup-adm@yoda.ncsa.uiuc.edu Thu May 31 15:57:06 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA06638; Thu, 31 May 90 15:57:05 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA06300; Thu, 31 May 90 15:53:52 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA06611; Thu, 31 May 90 15:21:17 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA06607; Thu, 31 May 90 15:21:15 -0500 Message-Id: <9005312021.AA06607@yoda.ncsa.uiuc.edu> From: macg@SLCS.SLB.COM (Bill Macgregor) Date: Wed, 23 May 90 15:18:05 CDT To: stevec@yoda.ncsa.uiuc.edu Subject: position open Status: RO [Here is a job posting of interest to Mathematica users - smc] Position: Research Scientist Immediate opening for someone to take on responsibility for the code generation component of the system described below (implemented in Mathematica); currently we are especially interested in code generation for parallel architectures such as the Connection Machine (we have one). Our preferred target languages are at the level of CM-Fortran rather than assembly or machine language, but special-purpose optimizations may require lower-level code generation. Longer term directions could include adding more knowledge about some of: different mathematical modeling domains, new algorithms, numerical analysis, performance prediction. Prefer candidate with PhD and background in numerical algorithms applied to engineering problems. Send resume or contact for more details: Elaine Kant Schlumberger Laboratory for Computer Science P.O. Box 200015, Austin, Texas 78720-0015 USA 512-331-3737 kant@slcs.slb.com Program: Design Environments Group Project: Synthesis of Finite Difference Programs The Sinapse system synthesizes mathematical modeling programs from descriptions of equations and algorithm choices. The goal is to help engineers minimize the time to design, implement, and evaluate mathematical models. Our initial focus is transforming models based on partial differential equations into efficient numerical codes in Fortran and C for multiple target architectures (including the Connection Machine). The system is implemented in Mathematica. An engineer can first work on symbolic formulations of problems in Mathematica and then have Sinapse generate a program embodying a numerical solution. To date, Sinapse has synthesized a modest number of programs, most of which are wave propagation programs that use finite difference techniques. The system can also synthesize a program that solves a deconblondie.volution problem with linear Bayesian inversion via Fourier transforms. Program specifications in the range of 10 to 50 lines generate target code of 50 to 1600 lines in time ranging from 10 seconds to several minutes. In a sample session, Sinapse helps the user express governing stress-strain equations in Mathematica, then analyzes and discretizes the equations to produce an explicit time-stepping solution code in Fortran. This includes transformation of partial differential equations into finite difference statements, and the selection of finite difference operators with staggering of the grids. Sinapse has domain-specific knowledge about absorbing, reflecting, and free-surface boundary conditions for wave propagation. The synthesis methods handle arbitrary dimensionality. Graphical results based on runs of the synthesized code have been displayed on a Silicon Graphics workstation to validate the accuracy of the generated code and to demonstrate the type of visualization available to modelers. Corporate Snapshot: The Schlumberger Laboratory for Computer Science (SLCS) is located in Austin, Texas. SLCS is the corporate-wide computer science research center for Schlumberger, an international corporation established over six decades ago. Schlumberger now has over 50,000 employees and a yearly revenue of six billion dollars. Schlumberger's Oil Field Services businesses sell products and services in the areas of oil and gas exploration and development. The Measurement & Systems businesses include CAD/CAM, automated testing equipment, gas and water metering, and electronic transactions. The primary goals of SLCS are to enhance quality, creativity, and productivity in software development. Total staff is now about 40. This includes people in services related to software practice, and in research on software reuse, design environments, knowledge systems, and modeling and simulation. From mathgroup-adm@yoda.ncsa.uiuc.edu Thu May 31 20:06:31 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA06860; Thu, 31 May 90 20:06:30 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA21907; Thu, 31 May 90 20:03:32 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA06803; Thu, 31 May 90 19:00:36 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA06799; Thu, 31 May 90 19:00:35 -0500 Message-Id: <9006010000.AA06799@yoda.ncsa.uiuc.edu> From: keiper@wri.UUCP Date: Thu, 31 May 90 14:28:27 CDT Subject: Re: Which[] behaviour To: mathgroup@yoda.ncsa.uiuc.edu Status: RO There are actually two bugs in the problem NIntegrate[Which[...], ...], both of which have been fixed in the current development version. These fixes will appear in the next release. The first bug has to do with NIntegrate: although it is claimed to be HoldAll, it isn't really so the Which[] gets evaluated to Null. The work around for this problem is to make the integrand not simply Which[...], but rather Which[...] /; NumberQ[x] where x is the variable of integration. This prevents the integrand from being evaluated until x is actually a number. The other bug is a design bug wrt Which[]. In the future Which[] will return unevaluated if none of the conditions are true. The current behavior will still be possible by explicitly giving a true condition at the end: Which[..., True, Null]. From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Jun 1 12:06:09 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA07937; Fri, 1 Jun 90 12:06:09 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA07913; Fri, 1 Jun 90 12:03:10 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA07859; Fri, 1 Jun 90 10:54:29 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA07855; Fri, 1 Jun 90 10:54:28 -0500 Message-Id: <9006011554.AA07855@yoda.ncsa.uiuc.edu> From: macg@SLCS.SLB.COM (Bill Macgregor) Date: Fri, 1 Jun 90 09:32:57 CDT To: mathgroup@yoda.ncsa.uiuc.edu Subject: pristine example--and a lesson Status: RO (For me; you may already know it. All of my lessons are learned the hard way, of course. On the 1-10 importance scale, this one rates a 9, I'd say.) -------------------- Consider this script (it's very simple): In[1]:= f[x_] := g[x] /; flag; In[2]:= e = f[x] + g[x] Out[2]= f[x] + g[x] In[3]:= e Out[3]= f[x] + g[x] In[4]:= flag = True Out[4]= True In[5]:= e Out[5]= f[x] + g[x] In[6]:= Update[] In[7]:= e Out[7]= 2 g[x] - Bill ----- End Included Message ----- From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Jun 1 12:58:54 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA08019; Fri, 1 Jun 90 12:58:52 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA08852; Fri, 1 Jun 90 12:55:56 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA07854; Fri, 1 Jun 90 10:54:21 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA07850; Fri, 1 Jun 90 10:54:20 -0500 Message-Id: <9006011554.AA07850@yoda.ncsa.uiuc.edu> From: keiper@wri.UUCP Date: Fri, 1 Jun 90 09:15:44 CDT To: kenward@mdivax1.UUCP Subject: Re: Symbolic derivatives and function definition Status: RO There may be a better way to do it, but here is one way: first, evaluate the symbolic derivative once: foo = D[f[u, v], u] this will be an expression involving u and v. Now define the function you really want: df[x_, y_] := foo /. {u -> x, v -> y} Note that the definition of foo uses "=" (evaluate this now), while the definition of df[] uses ":=" (delay the evaluation until df[x,y] is actually asked for.) Note that in many cases you could actually just do: df[x_, y_] = D[f[x, y], x] but this method is not quit as flexible. Jerry Keiper Wolfram Research, Inc. keiper@wri.com From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Jun 1 14:01:14 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA08158; Fri, 1 Jun 90 14:01:13 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA10119; Fri, 1 Jun 90 13:58:16 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA07849; Fri, 1 Jun 90 10:54:07 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA07845; Fri, 1 Jun 90 10:54:05 -0500 Message-Id: <9006011554.AA07845@yoda.ncsa.uiuc.edu> Date: Thu, 31 May 90 20:57 CDT From: SAF8613@tamstar.bitnet Subject: Sqrt[x^2] and predicates To: mathgroup@yoda.ncsa.uiuc.edu Status: RO I'm grateful to David Withoff of WRI for pointing out the ReIm.m package, and also the "^=" operator, which solves protection problems of the type I mentioned in my earlier message. Also, I see that Sec. 8.3 of Roman Maeder's book is relevant to the sort of problem we're discussing. I appreciate the importance of programming and packages, but I think that the main points of my message are still valid: 1. Evaluating Sqrt[x^2] as x when x is, or might be, negative is just flat wrong. [As is assuming that a function is continuous because there is no information to the contrary (and confusing "continuous" with "bounded" in documenting that behavior); as is evaluating Integrate[1/x^2, {x,-1,1}] as -2 instead of +Infinity.] 2. In Mathematica and its documentation, the treatment of predicates and relations seems needlessly inconsistent with (and much inferior to) that of non-Boolean-valued expressions and functions. It is hard to see how to define new ones, and those that exist are few, weak, and have poorly documented syntax. (Look up "Inequality" and "Greater" in the index.) To earn the title "System for Doing Mathematics by Computer", Mathematica should routinely be able to represent, and reason with, mathematical assertions such as "x is positive", "x is real", "x is greater than y". One would think that Mathematica's superb pattern-matching capability could do wonders with inequalities. Example: To tell the package ReIm.m that "x is imaginary", we seem to have to specify the real and imaginary parts of x (using the FUNCTIONS Re and Im) instead of using a mathematically natural syntax like "Imag[x]" or "ImagQ[x] ^= True". Example: The correct simplification rule for the square root is Sqrt[x_^2] := x /; Positive[x] Sqrt[x_^2] := -x /; Negative[x] [This is what Maeder (op.cit.) does to strengthen the absolute value function. Incidentally, Abs[] already has the correct default behavior: it doesn't try to guess the sign when it doesn't know it.] The problem is that considerably more programming needs to be done before these rules will accomplish much, because Positive[] and Negative[] are ignorant of their own basic properties: In[1]:= Positive[x] ^= True Out[1]= True In[2]:= Positive[y] ^= False Out[2]= False In[3]:= Negative[x] Out[3]= Negative[x] In[4]:= Positive[x-y] Out[4]= Positive[x - y] In[5]:= Expand[%] Out[5]= Positive[x - y] In[6]:= Quit Steve Fulling From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Jun 1 14:01:45 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA08164; Fri, 1 Jun 90 14:01:44 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA10126; Fri, 1 Jun 90 13:58:47 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA07843; Fri, 1 Jun 90 10:53:31 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA07839; Fri, 1 Jun 90 10:53:29 -0500 Message-Id: <9006011553.AA07839@yoda.ncsa.uiuc.edu> Date: Thu, 31 May 90 20:55 CDT From: SAF8613@tamstar.bitnet Subject: Consolidating the messages To: mathgroup@yoda.ncsa.uiuc.edu Status: RO >On another topic, it seems like the traffic in this mailgroup is big >enough to warrent switching over the the notes system. I know there >were complaints from those in sci.math.symbolic about so much >Mathematica traffic, so perhaps it be best to create a new group. How >about it? > > >Steven Warwick Dealing with 5 or 10 messages a day (each with its own header, etc.) has become a nuisance. I would prefer the system exemplified by TeXhax Digest, where the moderator collects the messages and sends them out as one large file every 3 days (say), or when the accumulation has reached (say) 20 kilobytes, whichever happens first. This would slow down responses, but copies of replies to specific queries should be sent directly to the original enquirer in any event. There may be people with email who don't have access to sci.math.*, so that option would cut them out. Steve Fulling From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Jun 1 16:35:37 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA08407; Fri, 1 Jun 90 16:35:36 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA13729; Fri, 1 Jun 90 16:32:37 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA08277; Fri, 1 Jun 90 14:48:00 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA08273; Fri, 1 Jun 90 14:47:58 -0500 Message-Id: <9006011947.AA08273@yoda.ncsa.uiuc.edu> Date: Fri, 1 Jun 90 15:39:55 EDT From: wang@pennmess.physics.upenn.edu ( Huangxin Wang) To: mathgroup-adm@yoda.ncsa.uiuc.edu Subject: Re: Symbolic derivatives and function definition Status: RO My way of doing it: df[x_, y_] := Release[D[f[x,y], x]] It work well for me. I believe if you simply do: df[x_, y_] = D[f[x, y], x] math will complain. Huangxin Wang of University of Pennsylvania From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Jun 1 17:14:03 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA08478; Fri, 1 Jun 90 17:14:02 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA14464; Fri, 1 Jun 90 17:11:06 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA08282; Fri, 1 Jun 90 14:48:08 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA08278; Fri, 1 Jun 90 14:48:06 -0500 Message-Id: <9006011948.AA08278@yoda.ncsa.uiuc.edu> Date: Fri, 1 Jun 90 15:49:35 EDT From: wang@pennmess.physics.upenn.edu ( Huangxin Wang) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Help with roots Status: RO Maybe the answer is so obvious, but can anyone point out to me that how to assign one of the root to a certain variable, say, FindRoot[ {x+y==0, x^3-y^2+1==0}, {x,1}, {y,1}] I want to assign the solution of x to variable z. Similarily, Solve[ x^3+x+3 == 0, x} how to assign root number 3 to z? From mathgroup-adm@yoda.ncsa.uiuc.edu Mon Jun 4 10:17:55 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA00664; Mon, 4 Jun 90 10:17:54 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA20045; Mon, 4 Jun 90 10:14:53 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA08282; Fri, 1 Jun 90 14:48:08 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA08278; Fri, 1 Jun 90 14:48:06 -0500 Message-Id: <9006011948.AA08278@yoda.ncsa.uiuc.edu> Date: Fri, 1 Jun 90 15:49:35 EDT From: wang@pennmess.physics.upenn.edu ( Huangxin Wang) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Help with roots Status: RO Maybe the answer is so obvious, but can anyone point out to me that how to assign one of the root to a certain variable, say, FindRoot[ {x+y==0, x^3-y^2+1==0}, {x,1}, {y,1}] I want to assign the solution of x to variable z. Similarily, Solve[ x^3+x+3 == 0, x} how to assign root number 3 to z? From mathgroup-adm@yoda.ncsa.uiuc.edu Mon Jun 4 12:15:58 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA01034; Mon, 4 Jun 90 12:15:57 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA23254; Mon, 4 Jun 90 12:13:01 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA00849; Mon, 4 Jun 90 11:15:12 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA00845; Mon, 4 Jun 90 11:15:10 -0500 Message-Id: <9006041615.AA00845@yoda.ncsa.uiuc.edu> From: Alfy_N_Riddle@cup.portal.com To: mathgroup@yoda.ncsa.uiuc.edu Subject: Apply&Map Date: Sat, 2-Jun-90 02:12:43 PDT Status: RO Mathematica Users: Rather often I have had the need to apply a function, which had several arguments, to each row of a list. I will not mention the kludges I used to use to do this, but a friend helped me find what a solution which now looks all TOO obvious. It may be useful to others. In[1]:= fn @@ #& /@ {{1,2},{3,4}} Out[1] = {fn[1,2], fn[3,4]} This code maps a pure function over a matrix, and then applies the desired function, fn, to each row. If your function uses options you can use: In[2]:= fn[ ##, opt1->2 ] @@ #& /@ {{1,2},{3,4}} Out[2]= {fn[1,2,opt1->2], fn[3,4,opt1->2]} Best wishes, Alfy Riddle (alfy@cup.portal.com) From mathgroup-adm@yoda.ncsa.uiuc.edu Mon Jun 4 13:14:08 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA01120; Mon, 4 Jun 90 13:14:07 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA24371; Mon, 4 Jun 90 13:11:13 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA00859; Mon, 4 Jun 90 11:15:26 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA00855; Mon, 4 Jun 90 11:15:25 -0500 Message-Id: <9006041615.AA00855@yoda.ncsa.uiuc.edu> Date: Fri, 1 Jun 90 19:30:29 PDT From: marchett@cod.nosc.mil (David J. Marchette) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Integrating Gaussians Status: RO Here's a simple integration question: I would like to integrate Exp[-x^2/(2 sigma^2)] from -Infinity to Infinity. If I do the obvious: Integrate[Exp[-x^2/(2 sigma^2)],{x,-Infinity,Infinity}] I get an expression involving the error function Erf and Infinity. This is obviously because Mathematica doesn't know what sigma is. How do I tell Mathematica that sigma > 0 (and finite)? Of course, I could just tell Mathematica how to do the integral, but I want to do some integrations where things like the above occur in many variations. (By the way, I'm using 1.2 on a 386 and a Mac II). Any suggestions? Thanks in advance, David Marchette Naval Ocean Systems Center San Diego, Ca From mathgroup-adm@yoda.ncsa.uiuc.edu Mon Jun 4 14:24:27 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA01283; Mon, 4 Jun 90 14:24:26 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA25913; Mon, 4 Jun 90 14:21:31 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA00854; Mon, 4 Jun 90 11:15:20 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA00850; Mon, 4 Jun 90 11:15:18 -0500 Message-Id: <9006041615.AA00850@yoda.ncsa.uiuc.edu> Date: Fri, 1 Jun 90 12:59:28 PDT From: ghe@nucthy.PHYSICS.ORST.EDU (Guangliang He) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Consolidating the messages Status: RO [In your message entitled "Consolidating the messages", on May 31, you write:] > > Dealing with 5 or 10 messages a day (each with its own >header, etc.) has become a nuisance. I would prefer the system >exemplified by TeXhax Digest, where the moderator collects the >messages and sends them out as one large file every 3 days (say), >or when the accumulation has reached (say) 20 kilobytes, >whichever happens first. > > This would slow down responses, but copies of replies to >specific queries should be sent directly to the original enquirer >in any event. > > There may be people with email who don't have access to >sci.math.*, so that option would cut them out. > > Steve Fulling > Personally, I don't like to read those Digest type things. It forces me to (at least) scan over all the messages before I could reach the message I want to read. I'm much happier to deal with individual messages. Of course, creating a new news group is a much better idea. But as always, it's only my own opinion. -- Guangliang He ghe@PHYSICS.ORST.EDU hegl@ORSTVM.BITNET From jacobson@cello.hpl.hp.com Mon Jun 4 14:45:35 1990 Received: from hplms2.hpl.hp.com by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA01345; Mon, 4 Jun 90 14:45:34 -0500 Received: from cello.hpl.hp.com by hplms2.hpl.hp.com with SMTP (15.11.1.3/15.5+IOS 3.20) id AA27732; Mon, 4 Jun 90 12:46:05 pdt Received: from localhost by cello.HPL.HP.COM; Mon, 4 Jun 90 12:45:31 pdt To: stevec@yoda.ncsa.uiuc.edu Subject: newsgroup vs. digest vs. status quo Date: Mon, 04 Jun 90 12:45:28 PDT Message-Id: <2068.644528728@cello> From: jacobson@cello.hpl.hp.com Status: RO I'm against making the mathgroup into a newsgroup. I never get around to looking at news. Things falling into my mailbox get seen. If people are bothered with the number of things, then a digest is the answer (in my opinion). But send out the digest every day or every other day at the most. Three days would slow down interaction too much. -- David From mathgroup-adm@yoda.ncsa.uiuc.edu Mon Jun 4 14:11:46 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA01247; Mon, 4 Jun 90 14:11:45 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA25644; Mon, 4 Jun 90 14:08:46 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA00865; Mon, 4 Jun 90 11:15:45 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA00861; Mon, 4 Jun 90 11:15:44 -0500 Message-Id: <9006041615.AA00861@yoda.ncsa.uiuc.edu> From: keiper@wri.UUCP Date: Mon, 4 Jun 90 10:22:33 CDT To: mathgroup@ncsa.uiuc.edu Subject: Re: Help with roots Status: RO Results of FindRoot[] and Solve[] are given as rules because in multi-variable cases we need to be able to easily associate the root with the various variables. This is done with ReplaceAll[] (i.e. "/.") In[1]:= FindRoot[ {x+y==0, x^3-y^2+1==0}, {x,-1}, {y,1}] Out[1]= {x -> -0.754878, y -> 0.754878} In[2]:= z = x /. % Out[2]= -0.754878 In[3]:= Solve[ x^3+x+3 == 0, x]; In[4]:= z = x /. %[[3]] -1 3 Sqrt[247] 1/3 -(----------------------- + (-(-) + ---------) ) 3 Sqrt[247] 1/3 2 6 Sqrt[3] 3 (-(-) + ---------) 2 6 Sqrt[3] Out[4]= -------------------------------------------------- - 2 1 3 Sqrt[247] 1/3 Sqrt[-3] (----------------------- + (-(-) + ---------) ) 3 Sqrt[247] 1/3 2 6 Sqrt[3] 3 (-(-) + ---------) 2 6 Sqrt[3] > ---------------------------------------------------------- 2 Jerry B. Keiper Wolfram Research, Inc. keiper@wri.com From mathgroup-adm@yoda.ncsa.uiuc.edu Mon Jun 4 15:28:08 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP (5.61+/IDA-1.2.8) id AA01420; Mon, 4 Jun 90 15:28:07 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA26781; Mon, 4 Jun 90 15:09:25 CDT Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA01157; Mon, 4 Jun 90 13:18:28 -0500 Received: by yoda.ncsa.uiuc.edu (5.61+/IDA-1.2.8) id AA01153; Mon, 4 Jun 90 13:18:26 -0500 Message-Id: <9006041818.AA01153@yoda.ncsa.uiuc.edu> Date: Mon, 4 Jun 90 13:14:54 CDT From: Elaine Kant To: mathgroup@yoda.ncsa.uiuc.edu Subject: Apply&Map Status: RO Alfy's message made me realize that other users might be interested in this generalization of the Map function, which applies a function of n arguments to the corresponding elements of n lists (for any n). MapN::usage = "MapN[function_, lists__] applies function to nth elements of lists, one at a time, returning list of results." MapN[Fn_, Lists__] := Map[Apply[Fn, #]&, Transpose[{Lists}]]; From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Jun 6 23:17:27 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA01220 (5.62+/IDA-1.3.1 for stevec); Wed, 6 Jun 90 23:17:26 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA11196; Wed, 6 Jun 90 23:14:56 CDT Received: by yoda.ncsa.uiuc.edu id AA01051 (5.62+/IDA-1.3.1 for ); Wed, 6 Jun 90 22:51:55 -0500 Received: by yoda.ncsa.uiuc.edu id AA01046 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Wed, 6 Jun 90 22:51:54 -0500 Message-Id: <9006070351.AA01046@yoda.ncsa.uiuc.edu> From: wri!keiper Date: Mon, 4 Jun 90 14:23:53 CDT Subject: Re: Integrating Gaussians To: mathgroup@yoda.ncsa.uiuc.edu Status: RO One way to trick Mathematica into evaluating Erf[] at infinities when the sign of the argument is unknown is to do the following: In[1]:= Unprotect[Erf] Out[1]= {Erf} In[2]:= Erf[DirectedInfinity[1] * ___] = 1 Out[2]= 1 In[3]:= Erf[DirectedInfinity[-1] * ___] = -1 Out[3]= -1 In[4]:= Integrate[Exp[-x^2/(2 sigma^2)],{x,-Infinity,Infinity}] Out[4]= Sqrt[2] Sqrt[Pi] sigma It will still be smart enough to figure out what to do with signed numbers: In[5]:= Erf[DirectedInfinity[1] * (-2)] Out[5]= -1 but if you have in mind a negative value for sigma it will give the wrong answer. From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Jun 7 01:19:59 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA01971 (5.62+/IDA-1.3.1 for stevec); Thu, 7 Jun 90 01:19:58 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA14629; Thu, 7 Jun 90 01:17:26 CDT Received: by yoda.ncsa.uiuc.edu id AA01130 (5.62+/IDA-1.3.1 for ); Wed, 6 Jun 90 22:58:24 -0500 Received: by yoda.ncsa.uiuc.edu id AA01126 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Wed, 6 Jun 90 22:58:23 -0500 Message-Id: <9006070358.AA01126@yoda.ncsa.uiuc.edu> Date: Mon, 4 Jun 90 15:03:26 EDT From: Jim_Wendel@ub.cc.umich.edu To: mathgroup@yoda.ncsa.uiuc.edu Subject: Duplicate mailings Status: RO [My computer went down due to air conditioning problems. This occured in the middle of some mailings. When it came back up, it apparently tried to resent some messages. I am sorry of some of you received more than one copy of some messages. --smc ] I'm getting duplicate transmissions, for instance today two copies of Help with roots and two of Symbolic derivatives and function definition. Can the extra be blocked at your end? Thanks......................Jim Wendel From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Jun 7 00:57:23 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA01918 (5.62+/IDA-1.3.1 for stevec); Thu, 7 Jun 90 00:57:21 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA13894; Thu, 7 Jun 90 00:54:50 CDT Received: by yoda.ncsa.uiuc.edu id AA01051 (5.62+/IDA-1.3.1 for ); Wed, 6 Jun 90 22:51:55 -0500 Received: by yoda.ncsa.uiuc.edu id AA01046 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Wed, 6 Jun 90 22:51:54 -0500 Message-Id: <9006070351.AA01046@yoda.ncsa.uiuc.edu> From: wri!keiper Date: Mon, 4 Jun 90 14:23:53 CDT Subject: Re: Integrating Gaussians To: mathgroup@yoda.ncsa.uiuc.edu Status: RO One way to trick Mathematica into evaluating Erf[] at infinities when the sign of the argument is unknown is to do the following: In[1]:= Unprotect[Erf] Out[1]= {Erf} In[2]:= Erf[DirectedInfinity[1] * ___] = 1 Out[2]= 1 In[3]:= Erf[DirectedInfinity[-1] * ___] = -1 Out[3]= -1 In[4]:= Integrate[Exp[-x^2/(2 sigma^2)],{x,-Infinity,Infinity}] Out[4]= Sqrt[2] Sqrt[Pi] sigma It will still be smart enough to figure out what to do with signed numbers: In[5]:= Erf[DirectedInfinity[1] * (-2)] Out[5]= -1 but if you have in mind a negative value for sigma it will give the wrong answer. From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Jun 7 01:53:18 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA02056 (5.62+/IDA-1.3.1 for stevec); Thu, 7 Jun 90 01:53:16 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA15210; Thu, 7 Jun 90 01:50:47 CDT Received: by yoda.ncsa.uiuc.edu id AA01193 (5.62+/IDA-1.3.1 for ); Wed, 6 Jun 90 23:10:01 -0500 Received: by yoda.ncsa.uiuc.edu id AA01189 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Wed, 6 Jun 90 23:10:00 -0500 Message-Id: <9006070410.AA01189@yoda.ncsa.uiuc.edu> Date: Wed, 6 Jun 90 14:56:23 PDT From: van-bc!kenward%mdivax1 (Gary Kenward) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Superimposed plots Status: RO I have a number of curves that I want to show on one plot. I know that: p1=Plot[f[x], {x,xmin,xmax}] p2=Plot[g[y], {y,ymin,ymax}] Show[p1,p2] Will combine the two plots, but in the process, to extraneous plots are displayed. Is there an easy way to disable the display of p1 and p2? Gary W. Kenward Mobile Data International, Inc Richmond, BC From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Jun 7 02:22:37 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA02144 (5.62+/IDA-1.3.1 for stevec); Thu, 7 Jun 90 02:22:36 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA15787; Thu, 7 Jun 90 02:20:05 CDT Received: by yoda.ncsa.uiuc.edu id AA01139 (5.62+/IDA-1.3.1 for ); Wed, 6 Jun 90 22:58:52 -0500 Received: by yoda.ncsa.uiuc.edu id AA01135 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Wed, 6 Jun 90 22:58:50 -0500 Message-Id: <9006070358.AA01135@yoda.ncsa.uiuc.edu> Date: Mon, 4 Jun 90 21:58:07 PDT From: marchett@cod.nosc.mil (David J. Marchette) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Gaussians Status: RO Thanks again for all those who responded to my query. Here is the simplest solution: (Type the following into mathematica) f[x_,s_] := Exp[-(x/s)^2/2]/(Sqrt[2 Pi] s) Unprotect[Erf] Erf[DirectedInfinity[1] * ___] = 1 Erf[DirectedInfinity[-1] * ___] = -1 Protect[Erf] Integrate[f[x,sigma],{x,-Infinity,Infinity}] (* Yay! *) Integrate[f[x,sigma]^2,{x,-Infinity,Infinity}] (* Yay! *) Integrate[f[x,sigma1] f[x,sigma2],{x,-Infinity,Infinity}] (* Boo! *) As you can see, if you did the above, it's still hosed. Now it seems that I need to tell it that Sqrt[-x] I is -Sqrt[x], and whatall. It is pretty clear that in order to do what I want, I have to know much more about Mathematica. Does anyone out there have access to Macsyma or Maple? Do these also choke on this? I'm not saying that Mathematica is wrong, mind you, it's just not giving me what I want. Am I too demanding? By the way, I apologize for not providing Mathematica output. My email and Mathematica are on different machines, and the networking is at 1200 baud over the phone lines (networked into the 50s we call it). If I come up with any really complicated questions, I'll figure out a way to get the full session. David Marchette marchett@nosc.mil From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Jun 7 02:29:56 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA02149 (5.62+/IDA-1.3.1 for stevec); Thu, 7 Jun 90 02:29:55 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA15882; Thu, 7 Jun 90 02:27:27 CDT Received: by yoda.ncsa.uiuc.edu id AA01199 (5.62+/IDA-1.3.1 for ); Wed, 6 Jun 90 23:11:04 -0500 Received: by yoda.ncsa.uiuc.edu id AA01195 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Wed, 6 Jun 90 23:11:03 -0500 Message-Id: <9006070411.AA01195@yoda.ncsa.uiuc.edu> Date: Wed, 6 Jun 90 19:24:40 EDT From: Jim_Wendel@ub.cc.umich.edu To: mathgroup@yoda.ncsa.uiuc.edu Subject: Two quasi-bugs in Macintosh II Mathematica Status: RO Two quasi-bugs in Macintosh II Mathematica: (1) Plot something that lies wholly in the first quadrant but give option axes ->{0,0} with the intent of seeing the plot with nice axes; you will get partial axes, seemingly defined by the ranges of abscissas and ordinates in the plot. Example:Plot[x^2,{x,2,5},Axes->{0,0}] produces rather an ugly display. (2) DSolve[{y''[x]+y[x]==0,y[0]==1,y'[0]==-1},y[x],x] gives the rule y[x]->Cos[-x]+Sin[-x]. This is correct, but not as natural and nice to see as Cos[x]-Sin[x]. At least such is my opinion! Jim_Wendel@ub.cc.umich.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Jun 6 23:54:10 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA01246 (5.62+/IDA-1.3.1 for stevec); Wed, 6 Jun 90 23:54:09 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA11702; Wed, 6 Jun 90 23:51:41 CDT Received: by yoda.ncsa.uiuc.edu id AA01121 (5.62+/IDA-1.3.1 for ); Wed, 6 Jun 90 22:57:53 -0500 Received: by yoda.ncsa.uiuc.edu id AA01117 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Wed, 6 Jun 90 22:57:52 -0500 Message-Id: <9006070357.AA01117@yoda.ncsa.uiuc.edu> To: mathgroup@yoda.ncsa.uiuc.edu Subject: newsgroup vs. digest vs. status quo Date: Mon, 04 Jun 90 12:45:28 PDT From: jacobson@cello.hpl.hp.com Status: RO I'm against making the mathgroup into a newsgroup. I never get around to looking at news. Things falling into my mailbox get seen. If people are bothered with the number of things, then a digest is the answer (in my opinion). But send out the digest every day or every other day at the most. Three days would slow down interaction too much. -- David From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Jun 7 03:27:28 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA02371 (5.62+/IDA-1.3.1 for stevec); Thu, 7 Jun 90 03:27:26 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA16649; Thu, 7 Jun 90 03:24:56 CDT Received: by yoda.ncsa.uiuc.edu id AA01205 (5.62+/IDA-1.3.1 for ); Wed, 6 Jun 90 23:11:32 -0500 Received: by yoda.ncsa.uiuc.edu id AA01201 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Wed, 6 Jun 90 23:11:29 -0500 Message-Id: <9006070411.AA01201@yoda.ncsa.uiuc.edu> From: macg@SLCS.SLB.COM (Bill Macgregor) Date: Tue, 5 Jun 90 16:22:09 CDT To: mathgroup@yoda.ncsa.uiuc.edu Subject: debugPoint Status: RO This message contains the definition of debugPoint, a small Mathematica function that we find useful for debugging. This function may be obsoleted by new tracing features in Mma 2.0, but meanwhile... The idea for debugPoint was mentioned by Elaine Kant at the Mathematica conference in January. There were enough positive comments at that meeting to justify distribution to the mailing list. How it works ------------ When debugPoint is called, it prints the String passed as its first argument, and then it prints the values of any expressions given as its 2nd or subsequent arguments. Values are printed in the form == so you can tell what is being printed. debugPoint then enters an interactive evaluation loop. Any expression presented will be evaluated and printed in the usual way, except the input string "go" (without the quotes) which terminates the interaction sequence. Example: In[4]:= Block[{e}, e = Expand[(x + y)^4]; debugPoint["after Set[e, ...]", e]; ] debugPoint: after Set[e, ...] 4 3 2 2 3 4 e == y + 4 y x + 6 y x + 4 y x + x debugIn:= x + x debugOut= 2 x debugIn:= go In[5]:= The actions of debugPoint are controlled by two global symbols, debugPrint and debugPause. If either is True, debugPoint prints the label when it is evaluated. If debugPrint is True, debugPoint prints the unevaluated == evaluated forms. If debugPause is True, debugPoint enters the interactive evaluation loop. Hint for its use: if you work with multiple packages, it is a good idea to always include $Context in the debugPoint argument list. Definitions follow. - Bill MacGregor Schlumberger Laboratory for Computer Science ----------------- debugPrint = True; debugPause = True; debugPoint::usage = "debugPoint[s_String] prints the label s if debugPrint or debugPause is True, and pauses for interactive input if debugPause is True. debugPoint[s_String, x__] also prints the unevaluated and evaluated forms of the arguments x, if debugPrint is True."; Off[Hold::argct]; SetAttributes[debugPoint, HoldAll]; debugPoint[s_:"(unlabelled)", x___] := Block[{e}, If[TrueQ[debugPrint] || TrueQ[debugPause], Print["debugPoint: ", s]; ]; If[TrueQ[debugPrint], Scan[Print[" ", StringJoin @@ Drop[Drop[Characters[ToString[InputForm[#]]] ,5], -1], " == ", Release[#]]&, Map[Hold, Hold[x], 1] ] ]; If[TrueQ[debugPause], While[(e = InputString[" debugIn:= "]) != "go", Print[" debugOut= ", ToExpression[e]] ] ]; ]; From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Jun 7 17:17:41 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA03038 (5.62+/IDA-1.3.1 for stevec); Thu, 7 Jun 90 17:17:39 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA01037; Thu, 7 Jun 90 17:15:07 CDT Received: by yoda.ncsa.uiuc.edu id AA02913 (5.62+/IDA-1.3.1 for ); Thu, 7 Jun 90 15:36:20 -0500 Received: by yoda.ncsa.uiuc.edu id AA02909 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Thu, 7 Jun 90 15:36:19 -0500 Message-Id: <9006072036.AA02909@yoda.ncsa.uiuc.edu> Date: Thu, 7 Jun 90 09:04:02 -0700 From: fateman@ucbarpa.Berkeley.EDU (Richard Fateman) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Integrating Gaussians/ making things easier Status: RO You might also see how much slower the system is after adding such information. It could be that Mathematica's clever handling of rules avoids the introduction of inefficiencies. Or maybe not.. I suspect that if you put in too many "improvements" to Mathematica, the whole system would bog down dreadfully. Has anyone studied this? -- Richard Fateman From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Jun 7 19:27:18 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA03243 (5.62+/IDA-1.3.1 for stevec); Thu, 7 Jun 90 19:27:16 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA02992; Thu, 7 Jun 90 19:24:49 CDT Received: by yoda.ncsa.uiuc.edu id AA02918 (5.62+/IDA-1.3.1 for ); Thu, 7 Jun 90 15:36:27 -0500 Received: by yoda.ncsa.uiuc.edu id AA02914 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Thu, 7 Jun 90 15:36:25 -0500 Message-Id: <9006072036.AA02914@yoda.ncsa.uiuc.edu> Date: Thu, 7 Jun 90 09:10 PDT From: JOE@oregon.uoregon.edu Subject: Does anyone have an apparent fix for this mathematica problem? To: mathgroup@yoda.ncsa.uiuc.edu Status: RO Has anyone else heard of the problem my users describe below? Is a patch available to make Mathematica on the NeXT yield the same results as Mathematica on the Mac? If you've any queries Fred needs to see or respond to, please CC: him directly since he's not on the list right now. Thanks, Joe St Sauver (JOE@OREGON.UOREGON.EDU or JOE@OREGON) Statistical Programmer and Consultant University of Oregon Computing Center >From: OREGON::OLNESS "Fredrick Olness (503) 346-5206 OLNESS@OREGON" >To: OREGON::JOE > >Joe, > > .... One of Bob Zimmerman's students >found what appers to be a bug in Mathematica on the Next. >(Yes, I did not believe it until I tried it myself.) > >I attach two examples of the problem below. >(For reference, the Mac gave the correct answer, >so it is not a subtle error pertaining to branch cuts or >anything.) I think he was going to try it on a different Next >machine for comparison. > >Thanks, > >Fred. > >--- example one -- >1% math >Mathematica 1.2 (August 30, 1989) [With pre-loaded data] >by S. Wolfram, D. Grayson, R. Maeder, H. Cejtin, > S. Omohundro, D. Ballman and J. Keiper >with I. Rivin and D. Withoff >Copyright 1988,1989 Wolfram Research Inc. > >In[1]:= InputForm[(b*c*(a + d - (a^2 + 4*b*c - 2*a*d + d^2)^(1/2))^3)/ > (4*(a - d + (a^2 + 4*b*c - 2*a*d + d^2)^(1/2))* > (a^2 + 4*b*c - 2*a*d + d^2)^(1/2)) - > (b*c*(a + d + (a^2 + 4*b*c - 2*a*d + d^2)^(1/2))^3)/ > (4*(a - d - (a^2 + 4*b*c - 2*a*d + d^2)^(1/2))* > (a^2 + 4*b *c - 2*a*d + d^2)^(1/2))] > >Out[1]//InputForm= > (b*c*(a + d - (a^2 + 4*b*c - 2*a*d + d^2)^(1/2))^3)/ > (4*(a^2 + 4*b*c - 2*a*d + d^2)^(1/2)* > (a - d + (a^2 + 4*b*c - 2*a*d + d^2)^(1/2))) - > (b*c*(a + d + (a^2 + 4*b*c - 2*a*d + d^2)^(1/2))^3)/ > (4*(a^2 + 4*b*c - 2*a*d + d^2)^(1/2)* > (a - d - (a^2 + 4*b*c - 2*a*d + d^2)^(1/2))) > >In[2]:= rule={a->1,b->2,c->3,d->4} > >Out[2]= {a -> 1, b -> 2, c -> 3, d -> 4} > >In[3]:= N[res//.rule] > >Out[3]= res > >In[4]:= res=%1; > >In[5]:= N[res//.rule] > >Out[5]= 37. > >In[6]:= N[Together[Expand[res]]//.rule] > >Out[6]= 47.2208 > >In[7]:= N[Simplify[res]//.rule] > >Out[7]= 47.2208 > >-- example two follows -- > >1 % math >Mathematica 1.2 (August 30, 1989) [With pre-loaded data] >by S. Wolfram, D. Grayson, R. Maeder, H. Cejtin, > S. Omohundro, D. Ballman and J. Keiper >with I. Rivin and D. Withoff >Copyright 1988,1989 Wolfram Research Inc. > >In[1]:= InputForm[(b*c*(a + d - (a^2 - 2*a*c + 4*b*c + d^2)^(1/2))^3)/ > (4*(a - d + (a^2 - 2*a*c + 4*b*c + d^2)^(1/2))* > (a^2 - 2*a*c + 4*b*c + d^2)^(1/2)) - > (b*c*(a + d + (a^2 - 2*a*c + 4*b*c + d^2)^(1/2))^3)/ > (4*(a - d - (a^2 - 2*a*c + 4*b*c + d^2)^(1/2))* > (a^2 - 2*a *c + 4*b*c + d^2)^(1/2))] > > >Out[1]//InputForm= > (b*c*(a + d - (a^2 - 2*a*c + 4*b*c + d^2)^(1/2))^3)/ > (4*(a^2 - 2*a*c + 4*b*c + d^2)^(1/2)* > (a - d + (a^2 - 2*a*c + 4*b*c + d^2)^(1/2))) - > (b*c*(a + d + (a^2 - 2*a*c + 4*b*c + d^2)^(1/2))^3)/ > (4*(a^2 - 2*a*c + 4*b*c + d^2)^(1/2)* > (a - d - (a^2 - 2*a*c + 4*b*c + d^2)^(1/2))) > >In[2]:= res=%; > >In[3]:= rule={a->1,b->2,c->3,d->4} > >Out[3]= {a -> 1, b -> 2, c -> 3, d -> 4} > >In[4]:= N[res//.rule] > >Out[4]= 36.9231 > >In[5]:= N[Together[Expand[res]]//.rule] > >Out[5]= 46.9906 > >In[6]:= N[Simplify[res]//.rule] > >Out[6]= 46.9906 From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Jun 7 19:16:38 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA03207 (5.62+/IDA-1.3.1 for stevec); Thu, 7 Jun 90 19:16:31 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA02855; Thu, 7 Jun 90 19:14:04 CDT Received: by yoda.ncsa.uiuc.edu id AA02924 (5.62+/IDA-1.3.1 for ); Thu, 7 Jun 90 15:36:34 -0500 Received: by yoda.ncsa.uiuc.edu id AA02919 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Thu, 7 Jun 90 15:36:32 -0500 Message-Id: <9006072036.AA02919@yoda.ncsa.uiuc.edu> Date: Thu, 7 Jun 90 14:08 EDT From: jpg@ALLEGHENY.SCRC.Symbolics.COM Subject: Re: Gaussians To: mathgroup@yoda.ncsa.uiuc.edu Status: RO Date: Mon, 4 Jun 90 21:58:07 PDT From: marchett@cod.nosc.mil (David J. Marchette) Thanks again for all those who responded to my query. Here is the simplest solution: (Type the following into mathematica) f[x_,s_] := Exp[-(x/s)^2/2]/(Sqrt[2 Pi] s) Unprotect[Erf] Erf[DirectedInfinity[1] * ___] = 1 Erf[DirectedInfinity[-1] * ___] = -1 Protect[Erf] Integrate[f[x,sigma],{x,-Infinity,Infinity}] (* Yay! *) Integrate[f[x,sigma]^2,{x,-Infinity,Infinity}] (* Yay! *) Integrate[f[x,sigma1] f[x,sigma2],{x,-Infinity,Infinity}] (* Boo! *) As you can see, if you did the above, it's still hosed. Now it seems that I need to tell it that Sqrt[-x] I is -Sqrt[x], and whatall. It is pretty clear that in order to do what I want, I have to know much more about Mathematica. Does anyone out there have access to Macsyma or Maple? Do these also choke on this? Since you ask, MACSYMA has no trouble with this. I typed in the problem as you first posed it: (C1) assume(sigma>0)$ (C2) integrate(exp(-x^2/(2*sigma^2)),x,-inf,inf); (D2) sqrt(2) sqrt(%pi) sigma (C3) (forget(sigma>0),assume(sigma<0))$ (C4) integrate(exp(-x^2/(2*sigma^2)),x,-inf,inf); (D4) - sqrt(2) sqrt(%pi) sigma I'm not saying that Mathematica is wrong, mind you, it's just not giving me what I want. Am I too demanding? I don't think so. Jeffrey P. Golden Symbolics MACSYMA Division jpg@ALLEGHENY.SCRC.Symbolics.COM From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Jun 8 00:28:38 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA04351 (5.62+/IDA-1.3.1 for stevec); Fri, 8 Jun 90 00:28:36 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA08483; Fri, 8 Jun 90 00:26:07 CDT Received: by yoda.ncsa.uiuc.edu id AA03707 (5.62+/IDA-1.3.1 for ); Thu, 7 Jun 90 23:20:28 -0500 Received: by yoda.ncsa.uiuc.edu id AA03703 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Thu, 7 Jun 90 23:20:27 -0500 Message-Id: <9006080420.AA03703@yoda.ncsa.uiuc.edu> Date: Thu, 7 Jun 90 22:16:39 MDT From: smithw@mathnx.byu.edu (William V. Smith) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re:Does anyone have an apparent fix for this mathematica problem? Status: RO Yes. There is a fix. It is available from your local friendly NeXT Rep. Here's what happens with the fix: In[1]:= InputForm[(b*c*(a + d - (a^2 + 4*b*c - 2*a*d + d^2)^(1/2))^3)/ (4*(a - d + (a^2 + 4*b*c - 2*a*d + d^2)^(1/2))* (a^2 + 4*b*c - 2*a*d + d^2)^(1/2)) - (b*c*(a + d + (a^2 + 4*b*c - 2*a*d + d^2)^(1/2))^ 3)/ (4*(a - d - (a^2 + 4*b*c - 2*a*d + d^2)^(1/2)) * (a^2 + 4*b *c - 2*a*d + d^2)^(1/2))] Out[1]//InputForm= (b*c*(a + d - (a^2 + 4*b*c - 2*a*d + d^2)^(1/2))^3)/ (4*(a^2 + 4*b*c - 2*a*d + d^2)^(1/2)* (a - d + (a^2 + 4*b*c - 2*a*d + d^2)^(1/2))) - (b*c*(a + d + (a^2 + 4*b*c - 2*a*d + d^2)^(1/2))^3)/ (4*(a^2 + 4*b*c - 2*a*d + d^2)^(1/2)* (a - d - (a^2 + 4*b*c - 2*a*d + d^2)^(1/2))) In[2]:= rule={a->1,b->2,c->3,d->4} Out[2]= {a -> 1, b -> 2, c -> 3, d -> 4} In[3]:= N[res//.rule] Out[3]= res In[4]:= res=%1; In[5]:= N[res//.rule] Out[5]= 37. In[6]:= N[Together[Expand[res]]//.rule] Out[6]= 37. In[7]:= N[Simplify[res]//.rule] Out[7]= 37. The bad result was from a known bug in the Together function which is called by Simplify so both gave the wrong answer. From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Jun 8 22:25:09 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA05094 (5.62+/IDA-1.3.1 for stevec); Fri, 8 Jun 90 22:25:07 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA29330; Fri, 8 Jun 90 22:22:43 CDT Received: by yoda.ncsa.uiuc.edu id AA05064 (5.62+/IDA-1.3.1 for ); Fri, 8 Jun 90 20:58:10 -0500 Received: by yoda.ncsa.uiuc.edu id AA05059 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 8 Jun 90 20:58:09 -0500 Message-Id: <9006090158.AA05059@yoda.ncsa.uiuc.edu> Date: Fri, 8 Jun 90 14:17:14 EDT From: Jim_Wendel@ub.cc.umich.edu To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Superimposed Plots Status: RO Re Superimposed Plots , Gary W. Kenward. I just learned how to disable unwanted plotting displays. On the Plot command give the option DisplayFunction->Identity; cf. pg 109. Then on the Show command give the option DisplayFunction->$DisplayFunction. Jim_Wendel@ub.cc.umich.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Jun 8 23:28:04 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA05177 (5.62+/IDA-1.3.1 for stevec); Fri, 8 Jun 90 23:28:01 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA00396; Fri, 8 Jun 90 23:25:36 CDT Received: by yoda.ncsa.uiuc.edu id AA05058 (5.62+/IDA-1.3.1 for ); Fri, 8 Jun 90 20:58:02 -0500 Received: by yoda.ncsa.uiuc.edu id AA05054 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 8 Jun 90 20:58:01 -0500 Message-Id: <9006090158.AA05054@yoda.ncsa.uiuc.edu> From: wri!withoff@uunet.UU.NET Date: Thu, 7 Jun 90 10:50:21 CDT To: mathgroup@yoda.ncsa.uiuc.edu, uunet!van-bc!kenward%mdivax1@uunet.UU.NET Subject: Re: Superimposed plots Status: RO One way of doing this is included in the Graphics/Graphics.m package. The basic idea is that what appears on the screen (or other output device) is a side effect generated by applying the setting of the DisplayFunction option to the graphics object. Among other things, this feature can be used to produce superimposed plots, as in In[1]:= Show[Plot[Sin[x], {x, 0, 10}, DisplayFunction -> Identity], Plot[Cos[x], {x, 0, 10}, DisplayFunction -> Identity], DisplayFunction :> $DisplayFunction] Dave Withoff Wolfram Research withoff@wri.com From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Jun 12 22:34:24 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA04085 (5.62+/IDA-1.3.1 for stevec); Tue, 12 Jun 90 22:34:22 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA25298; Tue, 12 Jun 90 22:32:03 CDT Received: by yoda.ncsa.uiuc.edu id AA04029 (5.62+/IDA-1.3.1 for ); Tue, 12 Jun 90 21:29:01 -0500 Received: by yoda.ncsa.uiuc.edu id AA04025 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 12 Jun 90 21:29:00 -0500 Message-Id: <9006130229.AA04025@yoda.ncsa.uiuc.edu> Date: Tue, 12 Jun 90 16:52:37 CDT From: fulling@sarastro.tamu.edu (Stephen A. Fulling) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Saying something good, for a change Status: RO Since recent messages of mine were critical of Mathematica and its documentation, let me share my delight over an instance where Mathematica's special features enabled a hard calculation to be done easily. I need to integrate from 0 to Infinity various linear combinations of functions of the form r^a Exp[-b r^2]. (*) All these integrals can be done in closed form, and for a variety of reasons I don't want to use Mathematica's built-in integrator; I must use the formula. I programmed it: gaussParam[alpha_, gamma_] := Block[{beta,answer}, beta = (alpha+1)/2; answer = (1/2) gamma^(-beta) Gamma[beta]; Return[answer] ] The catch is that the integrand emerges as the output of another Mathematica function, and I was wondering if I'd need to write a C program to parse that expression to extract all the a's and b's, or ... That same weekend I was reading through Roman Maeder's book, Programming in Mathematica. I hit page 70: "Often we can avoid programming a loop altogether by applying functions to lists or other expressions. Section[s ...] about mapping of functions over expressions go the heart of Mathematica's programming language. Understanding this material will allow you to write concise programs in the style that the authors of Mathematica think is best to use." Blinding illumination! All I need to do is to write a function defined only on expressions that match the pattern (*), then Map[] it over sums! gauss[ c_. Exp[-gamma_. r^2] r^alpha_. ] := (c/2) gamma^(-(alpha+1)/2) Gamma[(alpha+1)/2] /; FreeQ[c, r] gauss[ c_. Exp[-gamma_. r^2] ] := (c/2) gamma^(-1/2) Gamma[1/2] /; FreeQ[c, r] gauss[expr_] := Map[gauss, expr] That doesn't mean that all is sweetness and light, however. I did run into two bugs-or-features in this little project, which will be reported in later messages. Steve Fulling Texas A&M Math From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Jun 12 23:42:08 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA04131 (5.62+/IDA-1.3.1 for stevec); Tue, 12 Jun 90 23:42:06 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA26287; Tue, 12 Jun 90 23:39:48 CDT Received: by yoda.ncsa.uiuc.edu id AA04041 (5.62+/IDA-1.3.1 for ); Tue, 12 Jun 90 21:30:42 -0500 Received: by yoda.ncsa.uiuc.edu id AA04037 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 12 Jun 90 21:30:41 -0500 Message-Id: <9006130230.AA04037@yoda.ncsa.uiuc.edu> Date: Tue, 12 Jun 90 17:23:15 CDT From: fulling@sarastro.tamu.edu (Stephen A. Fulling) To: mathgroup@yoda.ncsa.uiuc.edu Subject: infinite limits that aren't Status: RO Here is a more serious problem: In[1]:= <0. This can be seen by expanding the exponentials in power series and cancelling all the negative powers of r. *) In[3]:= Limit[%, r->0] Out[3]= ComplexInfinity (* wrong *) In[4]:= %2 /. {a->1, b->2} 2 1 -2 1 ----- - ---- ----- + ---- 6 4 6 4 27 r 9 r 27 r 9 r Out[4]= ------------ - ------------ 2 2 4 r r E E In[5]:= Limit[%, r->0] 1 Out[5]= -(-) (* For a special case, the right answer is obtained. *) 6 In[6]:= Quit I SPECULATE that this is what is happening: Mathematica is trying to evaluate the limit of a quotient, either before or after applying l'Hopital's rule. It simplifies the limit of the denominator to 0. It simplifies the limit of the numerator to an expression (not a "number", in Mathematica's technical sense), which it does not recognize as identically zero, although that expression would indeed simplify to zero if a more powerful simplification procedure were applied. (This, by the way, is the reason I inserted a Together[] inside the Limit[] in the code included in the previous message on "lost" error messages.) So, it gives its "generic" response, expression/0 = ComplexInfinity. But it really should be "Indeterminate" (at worst) in this case. Like the Sqrt[x^2] bug that we recently discussed, this feature can give an unsuspecting user false information. The default behavior of functions and simplification procedures should somehow be made "fail safe". I do appreciate the difficulty of doing so in subtle cases like this, where it may be very hard for the program to know what numerical values an expression might take on. Steve Fulling Texas A&M Math From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Jun 13 00:45:26 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA04865 (5.62+/IDA-1.3.1 for stevec); Wed, 13 Jun 90 00:45:24 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA28450; Wed, 13 Jun 90 00:43:04 CDT Received: by yoda.ncsa.uiuc.edu id AA04035 (5.62+/IDA-1.3.1 for ); Tue, 12 Jun 90 21:30:04 -0500 Received: by yoda.ncsa.uiuc.edu id AA04031 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 12 Jun 90 21:30:03 -0500 Message-Id: <9006130230.AA04031@yoda.ncsa.uiuc.edu> Date: Tue, 12 Jun 90 16:57:39 CDT From: fulling@sarastro.tamu.edu (Stephen A. Fulling) To: mathgroup@yoda.ncsa.uiuc.edu Subject: "Lost" error message Status: RO I have run into two peculiar phenomena. Maybe somebody can tell me whether I'm doing something wrong. The first is a merely aesthetic annoyance. I am calculating a sum of terms involving Gamma functions (see previous message). If the argument of a Gamma is a nonpositive integer, that term is infinite; however, the expression as a whole is guaranteed to be finite -- the infinities must cancel. The finite value can be computed as the limit from noninteger values of the parameter. Mathematica can be told to compute the limit if the first attempt at calculating the function yields Indeterminate: radial[expon_, m1_, m2_, a_, b_] := Block[{answer}, answer = gauss[Expand[r^expon cauchy[m1,m2,a,b]]]; answer = If[answer===Indeterminate, Limit[Together[radial[varexpon,m1,m2,a,b]], varexpon->expon], answer]; Return[answer] ] So far, so good. But of course Mathematica issues a warning message Infinity::indt: Indeterminate expression ComplexInfinity - ComplexInfinity encountered. This is objectionable, since the program is actually performing correctly. So, we turn off the message inside the Block: Off[Infinity::indt] Alas, that turns off the message globally -- which is undesirable, since that message might turn up later in another context where it really does indicate an error. So, at the end of the Block we turn it back on again. Problem should be solved. Unfortunately, the On[] statement, when executed, issues an error message On::none: Message Infinity::indt not found. (It does, however, succeed in turning the indt message back on!) This new message is even more objectionable than the first. So, we have to turn it off, too. Then turn it back on again, and, wondrous to relate, we are NOT caught in an infinite regress: On[] CAN find its OWN message without complaining. So the final version of the function is radial[expon_, m1_, m2_, a_, b_] := Block[{answer}, Off[Infinity::indt]; answer = gauss[Expand[r^expon cauchy[m1,m2,a,b]]]; answer = If[answer===Indeterminate, Limit[Together[radial[varexpon,m1,m2,a,b]], varexpon->expon], answer]; Off[On::none]; On[Infinity::indt]; On[On::none]; Return[answer] ] This does exactly what it is supposed to, but seems needlessly complex. A bit of experimentation revealed: (1) The indt message can be turned off and on interactively without any problem. Only inside a subroutine does it trigger the On::none message. (2) In a virgin Mathematica session -- no radial[] loaded -- Messages[Infinity] does NOT show the indt message. However, Messages[On] DOES turn up the "none" message. Comments? Since this is getting long, I'll describe the second problem in another message. Steve Fulling Texas A&M Math From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Jun 13 01:41:50 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA04979 (5.62+/IDA-1.3.1 for stevec); Wed, 13 Jun 90 01:41:42 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA29673; Wed, 13 Jun 90 01:39:22 CDT Received: by yoda.ncsa.uiuc.edu id AA04885 (5.62+/IDA-1.3.1 for ); Wed, 13 Jun 90 00:47:30 -0500 Received: by yoda.ncsa.uiuc.edu id AA04880 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Wed, 13 Jun 90 00:47:27 -0500 Message-Id: <9006130547.AA04880@yoda.ncsa.uiuc.edu> Date: Wed, 13 Jun 90 01:26:30 EDT From: wsd@cs.brown.edu To: mathgroup@yoda.ncsa.uiuc.edu Subject: Differential Geom Package Status: RO I already made this request on sci.math.symbolic, but this is a better place for it: I am looking for Mathematica code that provides operations from differential geometry such as normal hairs on surfaces, tubes around space curves, and geodesics on surfaces (given initial conditions). any help is appreciated. wsd@cs.brown.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Jun 14 23:46:26 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA06868 (5.62+/IDA-1.3.1 for stevec); Thu, 14 Jun 90 23:46:24 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA14151; Thu, 14 Jun 90 23:43:25 CDT Received: by yoda.ncsa.uiuc.edu id AA06651 (5.62+/IDA-1.3.1 for ); Thu, 14 Jun 90 22:41:23 -0500 Received: by yoda.ncsa.uiuc.edu id AA06647 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Thu, 14 Jun 90 22:41:22 -0500 Message-Id: <9006150341.AA06647@yoda.ncsa.uiuc.edu> Date: Wed, 13 Jun 90 14:32:52 PDT From: jwendel@isdmnl.wr.usgs.gov Subject: Limit To: mathgroup@yoda.ncsa.uiuc.edu Status: RO The function Series can help in some cases where Limit fails or errs. An example is Steve Fulling's cauchy[2,2,a,b]. Apply Series to his complicated function of r,a,b and see directly that no negative powers of r survive. Jim Wendel jwendel@isdmnl.wr.usgs.gov From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Jun 15 01:43:09 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA07668 (5.62+/IDA-1.3.1 for stevec); Fri, 15 Jun 90 01:43:08 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA17537; Fri, 15 Jun 90 01:40:03 CDT Received: by yoda.ncsa.uiuc.edu id AA06656 (5.62+/IDA-1.3.1 for ); Thu, 14 Jun 90 22:41:30 -0500 Received: by yoda.ncsa.uiuc.edu id AA06652 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Thu, 14 Jun 90 22:41:28 -0500 Message-Id: <9006150341.AA06652@yoda.ncsa.uiuc.edu> Date: 14 Jun 90 11:03:00 EST From: buot%estd.decnet@ccf3.nrl.navy.mil Subject: mathematica applied to tight-binding Dyson equation To: mathgroup@yoda.ncsa.uiuc.edu Status: RO I and my colleague,Felix Buot,are interested in exploring the use of the symbolic capabilities of the Mathematica software to generate tight-binding Green's functions via application of Dyson's equation. Please let us know if you have any software products that can do this,or are aware of users of Mathematica who have done something similar. You can contact either Bill Grise at: Bill Grise Electrical Engineering Dept. Anderson Hall,Rm. 699 Univ. of Kentucky Lexington,Ky. 40506-0046 606-257-1971 OR Felix Buot at Felix Buot Code 6852,Naval Research Lab 4555 Overlook Ave.,S.W. Washington ,D.C. 20375-5000 202-767-2535 FAB's email address is: buot%estd.decnet@ccf3.nrl.navy.mil Thanks for your efforts, Felix Buot/Bill Grise From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Jun 15 00:43:13 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA07551 (5.62+/IDA-1.3.1 for stevec); Fri, 15 Jun 90 00:43:11 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA16286; Fri, 15 Jun 90 00:40:11 CDT Received: by yoda.ncsa.uiuc.edu id AA06646 (5.62+/IDA-1.3.1 for ); Thu, 14 Jun 90 22:41:18 -0500 Received: by yoda.ncsa.uiuc.edu id AA06642 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Thu, 14 Jun 90 22:41:16 -0500 Message-Id: <9006150341.AA06642@yoda.ncsa.uiuc.edu> Date: Wed, 13 Jun 90 16:07:21 EDT From: jas@erc-sparc.mc.duke.edu (John Schmidt) To: mathgroup@yoda.ncsa.uiuc.edu Subject: C program Status: RO I am trying to write a C program that can be called from Mathematica that solves a linear set of equations. I would like to be able to have my program return the solution set back to Mathematica for further processing. I would like to be able to pass my matrix and my b vector generated by Mathematica to my C program. I understand that I must use mathlink.c and other related files and commands, but I am not sure if I can pass an array to the C program. Has anyone else done this type of thing that they might be able to help me out? Thanks for any help, John Schmidt Duke University jas@erc-sparc.mc.duke.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Jun 15 01:48:45 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA07686 (5.62+/IDA-1.3.1 for stevec); Fri, 15 Jun 90 01:48:43 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA17645; Fri, 15 Jun 90 01:45:42 CDT Received: by yoda.ncsa.uiuc.edu id AA06636 (5.62+/IDA-1.3.1 for ); Thu, 14 Jun 90 22:41:02 -0500 Received: by yoda.ncsa.uiuc.edu id AA06632 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Thu, 14 Jun 90 22:41:01 -0500 Message-Id: <9006150341.AA06632@yoda.ncsa.uiuc.edu> From: wri!withoff@uunet.uu.net Date: Wed, 13 Jun 90 11:04:51 CDT To: mathgroup@yoda.ncsa.uiuc.edu, fulling@sarastro.tamu.edu Subject: Re: infinite limits that aren't Status: RO The fact that Limit isn't yet up to handling the problem described by Steve Fulling is disappointing. For relatively tricky things like this I often look to other parts of Mathematica for independent confirmation of results. In the case of Limit, I try substituting numerical values, or plotting. Another perhaps less obvious tool is Series, which works reasonably well in this example: 2 1 2 1 ------------- - ------------- ------------- + ------------- 2 2 3 6 2 2 2 4 2 2 3 6 2 2 2 4 (a - b ) r (a - b ) r (a - b ) r (a - b ) r Out[31]= ----------------------------- - ----------------------------- 2 2 2 2 b r a r E E In[32]:= Together /@ Series[%, {r, 0, 2}] 2 2 2 1 (a + b ) r 3 Out[32]= -(-) + ------------ + O[r] 6 12 From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Jun 15 02:29:54 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA07756 (5.62+/IDA-1.3.1 for stevec); Fri, 15 Jun 90 02:29:52 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA18412; Fri, 15 Jun 90 02:26:49 CDT Received: by yoda.ncsa.uiuc.edu id AA06641 (5.62+/IDA-1.3.1 for ); Thu, 14 Jun 90 22:41:11 -0500 Received: by yoda.ncsa.uiuc.edu id AA06637 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Thu, 14 Jun 90 22:41:09 -0500 Message-Id: <9006150341.AA06637@yoda.ncsa.uiuc.edu> Date: Wed, 13 Jun 90 21:08:58 +0200 From: lauten@ds1.cip.physik.tu-muenchen.de Subject: Reordered transformation rules To: mathgroup@yoda.ncsa.uiuc.edu Status: RO I have started to work with Mathematica only recently and I have run into the following trouble: In a file, say "ordered.m", I specify the following ORDERED transformation rules (reduced here to a generic form): f[{a___, X, X, b___}] := 1 f[{a___, X, b_, c___}] := 2 f[{a___, X}] := 3 /; OddQ[ Length[{a}] ] f[{a___}] := 4 /; !MemberQ[{a},X] && OddQ[ Length[{a}] ] f[{X}] := 5 f[{a_,b_,X}] := 6 f[{a_,b_}] := 7 f[{a_,b_,c_,d_,X}] := 8 f[{a_,b_,c_,d_}] := 9 f[{a___, X}] := 10 f[{a___}] := 11 where X is a symbol that shouldn't be used as a normal variable by the later user. I have numbered the rules for use in the discussion below. Then I teach Mathematica my ORDERED transformations rules by entering: In[1]:= < Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA27214; Fri, 15 Jun 90 13:32:28 CDT Received: by yoda.ncsa.uiuc.edu id AA08160 (5.62+/IDA-1.3.1 for ); Fri, 15 Jun 90 12:17:07 -0500 Received: by yoda.ncsa.uiuc.edu id AA08156 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 15 Jun 90 12:17:06 -0500 Message-Id: <9006151717.AA08156@yoda.ncsa.uiuc.edu> From: macg@SLCS.SLB.COM (Bill Macgregor) Date: Fri, 15 Jun 90 08:37:35 CDT To: mathgroup@yoda.ncsa.uiuc.edu Subject: RE rule ordering Status: RO and echoing lauten's request for information. Does anyone know the precise meaning of "match" on page 575 in the book? (See paragraph quoted below.) Anyone from WRI listening? Is there a formal definition of the pattern match relation which determines rule ordering, maybe represented as a Mma program? - Bill MacGregor ----- Begin Included Message ----- >From macg@SLCS.SLB.COM Wed Jun 13 09:25:11 1990 Return-Path: Received: from frank.SLCS.SLB.COM by SLCS.SLB.COM (4.1/SLCS Mailhost 3.2) id AA00233; Wed, 13 Jun 90 09:25:08 CDT From: macg@SLCS.SLB.COM (Bill Macgregor) Received: by frank.SLCS.SLB.COM (4.1/SLCS Subsidiary 1.6) id AA07558; Wed, 13 Jun 90 09:25:05 CDT Date: Wed, 13 Jun 90 09:25:05 CDT Message-Id: <9006131425.AA07558.macg@frank.SLCS.SLB.COM> To: de Subject: confusion reigns Status: RO Amazing what you can find in the book. Our question yesterday on transformation rule ordering has a natural, concise answer on pages 574-575 (but keep reading): .... Each time you make an assignment, the corresponding transformation rule is inserted at the end of the list of transformation rules [the list is searched in order, in principle, during evaluation-MacG] associated with s, except in the following cases: * The left-hand side of the transformation rule is identical to a transformation rule that has already been stored, and any /; conditions on the right-hand side are also identical. In this case, the new transformation rule is inserted in place of the old one. * Transformation rules that are already in the list have left-hand sides which are patterns that match the left- hand side of the transformation rule being inserted. In this case, the new transformation rule is inserted immediately before the first transformation rule that matches it. (Neither new nor old transformation rules can have /; conditions attached in this case.) Subtlety here, I suspect, is in the definition of one pattern "matching" another--I don't think it means MatchQ. Our case in point was the rule set Rule 1: f[h_[a___]] := ... Rule 2: f[x_] := ... Suppose Rule 1 is defined first (i.e., is in the list). When Rule 2 is defined, does h_[a___] match x_? MatchQ says yes, if you try it (see below). So Rule 2 is inserted before Rule 1, right? Suppose Rule 2 is defined first. When Rule 1 is defined, MatchQ[h_[a___], x_] is True, so Rule 1 is inserted before Rule 2, don't you think? However, look over this typescript that shows the opposite actually happens - In[1]:= f[x_] := 7; In[2]:= f[h_[a___]] := 8; In[3]:= ??f f f/: f[x_] := 7 f/: f[(h_)[a___]] := 8 In[3]:= Clear[f] In[4]:= ??f f In[4]:= f[h_[a___]] := 8; In[5]:= f[x_] := 7; In[6]:= ??f f f/: f[(h_)[a___]] := 8 f/: f[x_] := 7 In[6]:= MatchQ[h_[a___], x_] Out[6]= True In[7]:= MatchQ[x_, h_[a___]] Out[7]= True My conclusion: "match" in the text from the Mathematica book does not mean MatchQ. Which leaves the question: what does "match" mean? Meanwhile, the answer to the specific question is clear: the behavior of CasesAll DOES depend upon the order in which the two definitions are made. - Bill PS to readers of mathgroup: we've defined CasesAll (named by analogy with MapAll) by: CasesAll::usage = "CasesAll[expr_, pat_] returns a list of the subexpressions in expr that match pat. CasesAll[expr_, pat_, rhs_] returns Map[(# /. pat :> rhs)&, CasesAll[expr, pat]]." CasesAll[x_, p_, r_] := Map[(# /. p :> r)&, CasesAll[x, p]]; CasesAll[e:h_[a___], p_] := Join[CasesAllmatch[e, p], CasesAll[h, p], Join @@ Map[CasesAll[#, p]&, {a}]]; CasesAll[x_, p_] := CasesAllmatch[x, p]; CasesAllmatch[x_, p_] := Replace[x, {p -> {x}, _ -> {}}]; From mathgroup-adm@yoda.ncsa.uiuc.edu Sat Jun 16 02:29:16 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA09440 (5.62+/IDA-1.3.1 for stevec); Sat, 16 Jun 90 02:29:14 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA11452; Sat, 16 Jun 90 02:26:17 CDT Received: by yoda.ncsa.uiuc.edu id AA09245 (5.62+/IDA-1.3.1 for ); Sat, 16 Jun 90 00:53:09 -0500 Received: by yoda.ncsa.uiuc.edu id AA09240 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Sat, 16 Jun 90 00:53:07 -0500 Message-Id: <9006160553.AA09240@yoda.ncsa.uiuc.edu> Date: Fri, 15 Jun 90 17:06:53 EDT From: oliveria@caen.engin.umich.edu (ROQUE DONIZETE DE OLIVEIRA) To: mathgroup@yoda.ncsa.uiuc.edu Subject: ComplexMap.m Status: RO Has anyone modified ComplexMap.m from the book Roman E. Maeder: Programming in Mathematica, Addison-Wesley, 1989. to handle x and y axes labeling when plotting a function F[x + I y] ? It already draws labels for the Re an Im part of F but it would be nice to keep track of what the corresponding x and y values are. Thanks for any help. Roque oliveria@caen.engin.umich.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Sat Jun 16 01:29:53 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA09363 (5.62+/IDA-1.3.1 for stevec); Sat, 16 Jun 90 01:29:51 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA10434; Sat, 16 Jun 90 01:26:51 CDT Received: by yoda.ncsa.uiuc.edu id AA09239 (5.62+/IDA-1.3.1 for ); Sat, 16 Jun 90 00:53:03 -0500 Received: by yoda.ncsa.uiuc.edu id AA09235 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Sat, 16 Jun 90 00:53:01 -0500 Message-Id: <9006160553.AA09235@yoda.ncsa.uiuc.edu> To: mathgroup@yoda.ncsa.uiuc.edu Subject: meaning of match Date: Fri, 15 Jun 90 13:40:51 PDT From: jacobson@cello.hpl.hp.com Status: RO The meaning of match is apparently very strict. Observer the following: In[1]:= f[x_] := 1 In[2]:= f[y_] := 2 In[3]:= ??f f f/: f[x_] := 1 f/: f[y_] := 2 -- David Jacobson From mathgroup-adm@yoda.ncsa.uiuc.edu Sat Jun 16 02:50:42 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA09468 (5.62+/IDA-1.3.1 for stevec); Sat, 16 Jun 90 02:50:40 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA11693; Sat, 16 Jun 90 02:47:43 CDT Received: by yoda.ncsa.uiuc.edu id AA09234 (5.62+/IDA-1.3.1 for ); Sat, 16 Jun 90 00:52:56 -0500 Received: by yoda.ncsa.uiuc.edu id AA09230 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Sat, 16 Jun 90 00:52:55 -0500 Message-Id: <9006160552.AA09230@yoda.ncsa.uiuc.edu> Date: Fri, 15 Jun 90 10:35:08 PDT From: van-bc!mdivax1!kenward (Gary Kenward) To: mathgroup@yoda.ncsa.uiuc.edu Subject: A question about plotting Status: RO Please excuse my impatience, but I am reposting this question in case it did not get through: I am trying to plot two lists on one plot but with different point styles. I cannot find anything in the documentation on how to specify a point style. "PlotStyle is an option for Plot and ListPlot that specifies the style of lines or points to be plotted", however, like many of the attributes, there is no hint as to how point styles (other than size) are defined. Any suggestions? Thanks, Gary Kenward Mobile Data International, Inc. (a Motorola company) From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Jun 19 23:15:24 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA12960 (5.62+/IDA-1.3.1 for stevec); Tue, 19 Jun 90 23:15:22 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA04730; Tue, 19 Jun 90 23:13:00 CDT Received: by yoda.ncsa.uiuc.edu id AA12772 (5.62+/IDA-1.3.1 for ); Tue, 19 Jun 90 20:18:15 -0500 Received: by yoda.ncsa.uiuc.edu id AA12768 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 19 Jun 90 20:18:14 -0500 Message-Id: <9006200118.AA12768@yoda.ncsa.uiuc.edu> From: mcdonald@quark.umd.edu (Bill MacDonald) Subject: Re: A question about plotting To: mathgroup@yoda.ncsa.uiuc.edu Date: Sat, 16 Jun 90 17:05:42 EDT Status: RO William M. MacDonald Internet : MCDONALD@QUARK.UMD.EDU Bitnet : MCDONALD@CINCOM X-Mailer: ELM [version 2.3 PL0] > > Please excuse my impatience, but I am reposting this > question in case it did not get through: > > I am trying to plot two lists on one plot but with > different point styles. I cannot find anything in > the documentation on how to specify a point style. > > "PlotStyle is an option for Plot and ListPlot that > specifies the style of lines or points to be plotted", > however, like many of the attributes, there is no > hint as to how point styles (other than size) are > defined. > > Any suggestions? > > Thanks, > Gary Kenward > Mobile Data International, Inc. > (a Motorola company) > > > > Look at the alphabetical List of Built-in atheematica Objects, which begins on page 593, under Graphics. (I find this the best place to start when unsure about some Mathematica object.) There you will find listed the primitives Thickness and Dashing listed. In the index under Thickness find a reference to page 142. There the explanation of these two primitives is given. You can also find explanations of both primitives in the L-o-Bi-M-O. Under Dashing finfururther explanations. From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Jun 19 22:25:46 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA12897 (5.62+/IDA-1.3.1 for stevec); Tue, 19 Jun 90 22:25:44 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA03976; Tue, 19 Jun 90 22:23:22 CDT Received: by yoda.ncsa.uiuc.edu id AA12784 (5.62+/IDA-1.3.1 for ); Tue, 19 Jun 90 20:19:57 -0500 Received: by yoda.ncsa.uiuc.edu id AA12780 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 19 Jun 90 20:19:56 -0500 Message-Id: <9006200119.AA12780@yoda.ncsa.uiuc.edu> Date: Mon, 18 Jun 90 11:34:28 CDT From: wri!withoff@uunet.UU.NET (David Withoff) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: A question about plotting Status: RO The only PlotStyle settings I've used for ListPlot are color and PointSize. To get other plotting symbols, the TextListPlot function in Graphics.m is a reasonable starting point. TextListPlot uses character strings instead of points to display data. The same basic idea can be used to display other plotting symbols. For example: SquarePoint[point:{_?NumberQ, _?NumberQ}] := {Line[{Scaled[{.01, .01}, point], Scaled[{.01, -.01}, point], Scaled[{-.01, -.01}, point], Scaled[{-.01, .01}, point], Scaled[{.01, .01}, point]}], Point[point]} SquarePointPlot[data:{{_?NumberQ, _?NumberQ}..}] := Show[Graphics[Map[SquarePoint, data]], Axes -> Automatic] example: data = Table[Random[], {10}, {2}] SquarePointPlot[data] I've seen some partially finished packages (with code fragments like the above), but nothing that seemed finished enough to merit broad distribution. Hopefully a a few code fragments like this will serve the purpose until a more complete solution becomes available. Dave Withoff Wolfram Research withoff@wri.com From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Jun 19 23:25:50 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA13003 (5.62+/IDA-1.3.1 for stevec); Tue, 19 Jun 90 23:25:48 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA04869; Tue, 19 Jun 90 23:23:26 CDT Received: by yoda.ncsa.uiuc.edu id AA12796 (5.62+/IDA-1.3.1 for ); Tue, 19 Jun 90 20:20:53 -0500 Received: by yoda.ncsa.uiuc.edu id AA12792 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 19 Jun 90 20:20:52 -0500 Message-Id: <9006200120.AA12792@yoda.ncsa.uiuc.edu> Date: Tue, 19 Jun 90 14:41:19 MDT From: smithw@mathnx.byu.edu (William V. Smith) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Bug in NullSpace? Status: RO I take it back. Seems there was some kind of machine problem with this computation. I have been able to get it to work twice (at least it gave an answer). It was very slow with the computation however. From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Jun 19 21:33:45 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA12850 (5.62+/IDA-1.3.1 for stevec); Tue, 19 Jun 90 21:33:44 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA03276; Tue, 19 Jun 90 21:31:22 CDT Received: by yoda.ncsa.uiuc.edu id AA12778 (5.62+/IDA-1.3.1 for ); Tue, 19 Jun 90 20:19:10 -0500 Received: by yoda.ncsa.uiuc.edu id AA12774 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 19 Jun 90 20:19:09 -0500 Message-Id: <9006200119.AA12774@yoda.ncsa.uiuc.edu> Date: Sat, 16 Jun 90 15:46:28 PDT From: don@kinghorn.chem.WSU.EDU (Don Kinghorn) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: A question about plotting Status: RO >... >I am trying to plot two lists on one plot but with >different point styles. I cannot find anything in >the documentation on how to specify a point style. >... If you don't mind using ascii characters for your points you could try using the TextListPlot function found in the Graphics.m package. EXAMPLE; In[1]:= < Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA20966; Thu, 21 Jun 90 22:25:21 CDT Received: by yoda.ncsa.uiuc.edu id AA15350 (5.62+/IDA-1.3.1 for ); Thu, 21 Jun 90 20:35:36 -0500 Received: by yoda.ncsa.uiuc.edu id AA15346 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Thu, 21 Jun 90 20:35:34 -0500 Message-Id: <9006220135.AA15346@yoda.ncsa.uiuc.edu> Date: Thu, 21 Jun 90 21:16:47 -0400 (EDT) From: Anand Patwardhan To: mathgroup@yoda.ncsa.uiuc.edu Subject: Remote kernels in Mathematica Status: RO I'd like to run a remote kernel in Mathematica, with the front end on a Macintosh. I do the necessary stuff in the 'Edit Connections' menu and add the hostnames (actually I put in the IP numbers) of the hosts on which I want to run the kernel. Now when I try to actually open a connection, Mathematica complains that it cannot find the 'Hosts' file and leaves MacTCP all confused. I tried to explore and could not find any documentation about this file and/or its syntax etc.. Anybody out there have success in running a remote kernel in Mathematica on the Macintosh? Any suggestions? Thanks in advance Anand ------------------------------------------------------------------------------ Anand Patwardhan |INTERNET : ap10@andrew.cmu.edu Dept. of Engg. and |BITNET : apat@drycas.BITNET Public Policy, C.M.U |(others)..{harvard,psuvax1}!andrew.cmu.edu!ap10 Pittsburgh PA 15213 |VOICE : (412)-268-5617 (office) ------------------------------------------------------------------------------ From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Jun 21 21:30:36 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA15401 (5.62+/IDA-1.3.1 for stevec); Thu, 21 Jun 90 21:30:35 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA20149; Thu, 21 Jun 90 21:28:16 CDT Received: by yoda.ncsa.uiuc.edu id AA15345 (5.62+/IDA-1.3.1 for ); Thu, 21 Jun 90 20:35:28 -0500 Received: by yoda.ncsa.uiuc.edu id AA15341 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Thu, 21 Jun 90 20:35:27 -0500 Message-Id: <9006220135.AA15341@yoda.ncsa.uiuc.edu> Date: Wed, 20 Jun 90 15:30:08 MDT From: smithw@mathnx.byu.edu (William V. Smith) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Plot problem Status: RO We have some NeXT machines in the department and we have run into a difficulty with Plot. Try this on your NeXT if you have one available (the problem does not seem to occur on our MIPS) In[1]:= f[x_]:= x^(5/3) + 5 x^(2/3); g=D[f[x],x] In[2]:= Plot[{f[x],g}, {x, -5, 3}] In[3]:= Show[%,AspectRatio->Automatic] The machine takes an awful long time to compute this and equally long times to copy and paste someplace else (if you can get it to that at all). Worse, the window server seems to lock up so you can't do anything until this compute is done! What's the problem here? When we run this on our MIPS using X-windows graphics (the machines seem about equal in speed on other mathematica stuff) the result comes up FAST! Help! We would like to use some NeXT's in a calculus lab this fall where no doubt problems like this will come up again..... When the machine does finally produce the graphic, just try to PRINT IT! Yikes! Your machine dies! From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Jun 22 19:26:41 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA16686 (5.62+/IDA-1.3.1 for stevec); Fri, 22 Jun 90 19:26:39 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA12471; Fri, 22 Jun 90 19:24:22 CDT Received: by yoda.ncsa.uiuc.edu id AA16628 (5.62+/IDA-1.3.1 for ); Fri, 22 Jun 90 17:49:22 -0500 Received: by yoda.ncsa.uiuc.edu id AA16624 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 22 Jun 90 17:49:20 -0500 Message-Id: <9006222249.AA16624@yoda.ncsa.uiuc.edu> Date: Fri, 22 Jun 90 15:00:52 CST From: "E. Neely Atkinson" Subject: Mathematica bug. To: mathgroup@yoda.ncsa.uiuc.edu Status: RO Please help. I have been muched by a nasty Mathematica bug. I am running version 1.2f33 Enhanced on a Mac II. If I define the function f[x_] := (1/x) (1/x^2)^(1/x^2 -1) and then ask for f[x], I get x^(-1 - 2 (-1 + x^(-2))) Considering the case x=-1 quickly demonstrates that these are not equivalent. E. Neely Atkinson AN123651 at UTHVM1.BITNET neely@mdaali.cancer.utexas.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Jun 22 20:04:13 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA16749 (5.62+/IDA-1.3.1 for stevec); Fri, 22 Jun 90 20:04:11 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA13126; Fri, 22 Jun 90 20:01:53 CDT Received: by yoda.ncsa.uiuc.edu id AA16613 (5.62+/IDA-1.3.1 for ); Fri, 22 Jun 90 17:49:02 -0500 Received: by yoda.ncsa.uiuc.edu id AA16609 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 22 Jun 90 17:49:00 -0500 Message-Id: <9006222249.AA16609@yoda.ncsa.uiuc.edu> Date: Fri, 22 Jun 90 13:30:12 EDT From: riddle@mathcs.emory.edu (Larry Riddle) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Two column printing Status: RO A friend recently showed me a printout from a mathematica session on the NeXt which was in two column landscape mode (at a small font size) similar to what is produced by the Unix command enscript -2r. Unfortunately we were in the midst of grading 77000 Advanced placement calculus exams for ETS and so I didn't get the details on how he did this. What I would like to know is if it is possible to do this on the Macintosh, that is, print a notebook in landscape orientation with two columns. Any suggestions? Larry Riddle | riddle@mathcs.emory.edu PREFERRED Agnes Scott College | {decvax,gatech}!emory!riddle UUCP Dept of Math | riddle@emory.bitnet NON-DOMAIN BITNET Decatur, GA 30030 | (404) 371-6222 AT&T From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Jun 22 20:28:48 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA16778 (5.62+/IDA-1.3.1 for stevec); Fri, 22 Jun 90 20:28:46 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA13477; Fri, 22 Jun 90 20:26:29 CDT Received: by yoda.ncsa.uiuc.edu id AA16633 (5.62+/IDA-1.3.1 for ); Fri, 22 Jun 90 17:49:29 -0500 Received: by yoda.ncsa.uiuc.edu id AA16629 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 22 Jun 90 17:49:27 -0500 Message-Id: <9006222249.AA16629@yoda.ncsa.uiuc.edu> Date: Fri, 22 Jun 90 16:53:27 ED From: sor@cs.williams.edu (Seth O. Rogers) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Mathematica packages Status: RO Dear Math Group, My name is Seth Rogers, and I am a student at Williams College (in Massachusetts). This summer, I am helping to design a course in probability. We are interested in computer programs to compute the various distributions, specifically the discrete distributions (Binomial, Poisson, etc.), and also, if possible, some stochastic pro- cesses, such as discrete branching and random walks. I have been experimenting with Mathematica for the Macintosh as a possible product for use in the course, and it seems like a very appropriate framework. I have written a few of the functions myself, but as I am a novice and I hear that there are many packages available, I thought I would look into a package of probability functions already written better than I can do. Which brings me to the point of the note: do you know of any such package, or anybody else I could ask? I would appreciate any help you may be able to give, as you are my only lead. Please reply as soon as you can, because we are eager to order something and get started. I can be reached at "sor@bull.williams.cs.edu" or "91sor_c@vax.cc.williams.edu" I hope to hear from you soon. Sincerely, Seth Rogers From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Jun 22 21:16:25 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA16883 (5.62+/IDA-1.3.1 for stevec); Fri, 22 Jun 90 21:16:23 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA14131; Fri, 22 Jun 90 21:14:05 CDT Received: by yoda.ncsa.uiuc.edu id AA16608 (5.62+/IDA-1.3.1 for ); Fri, 22 Jun 90 17:48:54 -0500 Received: by yoda.ncsa.uiuc.edu id AA16604 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 22 Jun 90 17:48:52 -0500 Message-Id: <9006222248.AA16604@yoda.ncsa.uiuc.edu> From: mcdonald@quark.umd.edu (Bill MacDonald) Subject: Re: Remote kernels in Mathematica To: mathgroup-adm@yoda.ncsa.uiuc.edu (Anand Patwardhan) Date: Fri, 22 Jun 90 8:13:12 EDT Status: RO William M. MacDonald Internet : MCDONALD@QUARK.UMD.EDU Bitnet : MCDONALD@CINCOM X-Mailer: ELM [version 2.3 PL0] > > > I'd like to run a remote kernel in Mathematica, with the front end on > a Macintosh. I do the necessary stuff in the 'Edit Connections' menu and add > the hostnames (actually I put in the IP numbers) of the hosts on which I > want to run the kernel. Now when I try to actually open a connection, > Mathematica complains that it cannot find the 'Hosts' file and leaves MacTCP > all confused. > > I tried to explore and could not find any documentation about this > file and/or its syntax etc.. > > Anybody out there have success in running a remote kernel in > Mathematica on the Macintosh? Any suggestions? > > Thanks in advance > > Anand > ------------------------------------------------------------------------------ > Anand Patwardhan |INTERNET : ap10@andrew.cmu.edu > Dept. of Engg. and |BITNET : apat@drycas.BITNET > Public Policy, C.M.U |(others)..{harvard,psuvax1}!andrew.cmu.edu!ap10 > Pittsburgh PA 15213 |VOICE : (412)-268-5617 (office) > ------------------------------------------------------------------------------ > > > > I am running from MacIICi to a DECstation 3100 using the frontend on the MAC and the remote kernel on the DECstation. I had the same difficulty, but solved it by deselecting the Host File box (take out the check). I think you must need a local file and Mathematica can not find it. Let me hear from you if this works or if there are other problems. Like many users I don't have time to read every word in the documentation. Bill (William M. MacDonald, Prof of Physics, U of Maryland) From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Jun 22 21:16:40 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA16888 (5.62+/IDA-1.3.1 for stevec); Fri, 22 Jun 90 21:16:38 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA14135; Fri, 22 Jun 90 21:14:22 CDT Received: by yoda.ncsa.uiuc.edu id AA16618 (5.62+/IDA-1.3.1 for ); Fri, 22 Jun 90 17:49:08 -0500 Received: by yoda.ncsa.uiuc.edu id AA16614 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 22 Jun 90 17:49:06 -0500 Message-Id: <9006222249.AA16614@yoda.ncsa.uiuc.edu> Date: Fri, 22 Jun 90 12:44:27 PDT From: don@kinghorn.chem.WSU.EDU (Don Kinghorn) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re:Plot problem Status: RO > We have some NeXT machines in the department and we have run into a difficulty >with Plot. Try this on your NeXT if you have one available (the problem >does not seem to occur on our MIPS) > >In[1]:= f[x_]:= x^(5/3) + 5 x^(2/3); > g=D[f[x],x] > >In[2]:= Plot[{f[x],g}, {x, -5, 3}] > >In[3]:= Show[%,AspectRatio->Automatic] > >The machine takes an awful long time to compute this and equally long times >to copy and paste someplace else (if you can get it to that at all). Worse, >the window server seems to lock up so you can't do anything until this compute >is done! What's the problem here? When we run this on our MIPS using >X-windows graphics (the machines seem about equal in speed on other >mathematica stuff) the result comes up FAST! Help! We would like to use >some NeXT's in a calculus lab this fall where no doubt problems like this >will come up again..... When the machine does finally produce the graphic, >just try to PRINT IT! Yikes! Your machine dies! > I ran your input statements on a minimally configured NeXT running the 1.0 system software and got the following results with ShowTime on. f[x_]:= x^(5/3) + 5 x^(2/3); g=D[f[x],x] 0.0166667 Second Plot[{f[x],g}, {x, -5, 3}] 2.28333 Second Show[%,AspectRatio->Automatic] 0.483333 Second The results seem fine on my machine. Copy and paste into WriteNow worked fine as did printing from the Mathematica window . You didn't say how your NeXT was configured, but if you're running 1.0 with the 40 meg swap drive your swap file may be growing to large. I've had this problem on my machine with the result being symptoms like you described above. System 1.0 does not clean up the swapfile correctly.You can run df from a UNIX prompt to check this out. The easiest work around I know is to power down when the swapdisk is greater than 75% full. The latest upgrade, 1.0a, fixes this problem (I hope) I'm waiting on the upgrade myself. ---Don Kinghorn From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Jun 22 18:26:45 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA16638 (5.62+/IDA-1.3.1 for stevec); Fri, 22 Jun 90 18:26:44 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA11513; Fri, 22 Jun 90 18:24:25 CDT Received: by yoda.ncsa.uiuc.edu id AA16623 (5.62+/IDA-1.3.1 for ); Fri, 22 Jun 90 17:49:14 -0500 Received: by yoda.ncsa.uiuc.edu id AA16619 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 22 Jun 90 17:49:12 -0500 Message-Id: <9006222249.AA16619@yoda.ncsa.uiuc.edu> Date: Fri, 22 Jun 90 14:31:06 MDT From: smithw@mathnx.byu.edu (William V. Smith) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Plot problem Status: RO It looks like I gave out a slightly different problem than the one I originally had. Here is the original problem: f[x_] = x^(5/3) + 5x^(2/3); g = D[f[x], x]; Plot[ {f[x], g}, {x, -6, 2}, PlotStyle -> { GrayLevel[0.2],Dashing[{.05, .05}] } ] Show[%, AspectRatio -> Automatic] But we may have had some corruption introduced by a system problem. See what you can do with this if you can get a moment. Thanks. We had a problem printing this as well. From mathgroup-adm@yoda.ncsa.uiuc.edu Sun Jun 24 20:29:30 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA19060 (5.62+/IDA-1.3.1 for stevec); Sun, 24 Jun 90 20:29:28 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA20353; Sun, 24 Jun 90 20:27:13 CDT Received: by yoda.ncsa.uiuc.edu id AA19053 (5.62+/IDA-1.3.1 for ); Sun, 24 Jun 90 19:34:54 -0500 Received: by yoda.ncsa.uiuc.edu id AA19049 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Sun, 24 Jun 90 19:34:53 -0500 Message-Id: <9006250034.AA19049@yoda.ncsa.uiuc.edu> Date: Sun, 24 Jun 90 15:54:52 PDT From: don@kinghorn.chem.WSU.EDU (Don Kinghorn) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Plot problem / NeXT Mathematica bug in PlotStyle->Dashing Status: RO > >It looks like I gave out a slightly different problem than the one I originally had. >Here is the original problem: > >f[x_] = x^(5/3) + 5x^(2/3); >g = D[f[x], x]; >Plot[ {f[x], g}, {x, -6, 2}, >PlotStyle -> { GrayLevel[0.2],Dashing[{.05, .05}] } ] >Show[%, AspectRatio -> Automatic] > >But we may have had some corruption introduced by a system problem. >See what you can do with this if you can get a moment. Thanks. >We had a problem printing this as well. > I tried this input ---result, locked up system. The problem seems to be with the Dashing option. I sent the following bug report to NeXT inc. along with the original messages describing the problem; ------------------------------------------------------------------------ This bug report concerns; NeXT release 1.0 Mathematica Kernel version 1.2 Front end version 1.2 The PlotStyle option Dashing locks up the window server when used for plotting functions that contain singularities . This seems to be a NeXT only problem.? THIS CRASHES THE SYSTEM; In[1]:= Plot[ 1/x, {x, -10, 10} , PlotStyle-> Dashing[ {.05, .05} ] ] HOWEVER, THIS WORKS FINE; In[1]:= Plot[ 1/x, {x, -11, 10} , PlotStyle-> Dashing[ {.05, .05} ] ] ... etc... ---------------------------------------------------------------------------- The effect this bug has on the system makes it hard to investigate. The only thing I can suggest is avoid using the Dashing option. If NeXT Inc. sends me any "work around" I'll be sure to pass it on. ---Don Kinghorn From mathgroup-adm@yoda.ncsa.uiuc.edu Mon Jun 25 20:28:07 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA20072 (5.62+/IDA-1.3.1 for stevec); Mon, 25 Jun 90 20:28:05 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA12972; Mon, 25 Jun 90 20:25:21 CDT Received: by yoda.ncsa.uiuc.edu id AA20038 (5.62+/IDA-1.3.1 for ); Mon, 25 Jun 90 19:52:37 -0500 Received: by yoda.ncsa.uiuc.edu id AA20034 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Mon, 25 Jun 90 19:52:35 -0500 Message-Id: <9006260052.AA20034@yoda.ncsa.uiuc.edu> Date: Mon, 25 Jun 90 09:32:47 +0200 From: lauten@ds1.cip.physik.tu-muenchen.de Subject: Re: Mathematica packages To: mathgroup@yoda.ncsa.uiuc.edu Status: RO Dear SETH, I am a student and a Mathematica novice, too, so my help will be probably very limited. I remember seeing an example Mathematica program on random walk in the book "Programming Mathematica" by Roman Maeder, published by Addison-Wesley. Since you will probably have to dive deeper into Mathematica having a look at this book might be a good idea anyway. If your finial Mathematica Package is free for distribution I would greatly appreciate a copy of it. Do the right hack, MARKUS From mathgroup-adm@yoda.ncsa.uiuc.edu Mon Jun 25 21:27:24 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA20180 (5.62+/IDA-1.3.1 for stevec); Mon, 25 Jun 90 21:27:22 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA13854; Mon, 25 Jun 90 21:24:39 CDT Received: by yoda.ncsa.uiuc.edu id AA20054 (5.62+/IDA-1.3.1 for ); Mon, 25 Jun 90 19:52:58 -0500 Received: by yoda.ncsa.uiuc.edu id AA20049 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Mon, 25 Jun 90 19:52:56 -0500 Message-Id: <9006260052.AA20049@yoda.ncsa.uiuc.edu> Date: Mon, 25 Jun 90 17:22:53 EST From: irh@baby.bby.oz.au (Ian R Heddle) To: mathgroup@yoda.ncsa.uiuc.edu Subject: mathlink.c bug Status: RO The mathlink.c code used to call external functions contains a programming error. The parameter information linked list is linked in reverse order to the functions actual parameters. This can cause type mismatch. The code is also restricted to using either one or two parameters, which is not mentioned in any Mathematica documentation. If more than two parameters are needed to call a remote funcition you will have to edit the mathlink.c file to include a switch selection statement that will coincide with the parameters you require. From mathgroup-adm@yoda.ncsa.uiuc.edu Mon Jun 25 22:17:12 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA20279 (5.62+/IDA-1.3.1 for stevec); Mon, 25 Jun 90 22:17:10 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA14579; Mon, 25 Jun 90 22:14:26 CDT Received: by yoda.ncsa.uiuc.edu id AA20043 (5.62+/IDA-1.3.1 for ); Mon, 25 Jun 90 19:52:44 -0500 Received: by yoda.ncsa.uiuc.edu id AA20039 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Mon, 25 Jun 90 19:52:43 -0500 Message-Id: <9006260052.AA20039@yoda.ncsa.uiuc.edu> Date: Mon, 25 Jun 90 10:49:20 PDT From: eran@THSUN1.SLAC.STANFORD.EDU Subject: HEP packages To: mathgroup@yoda.ncsa.uiuc.EDU Status: RO I have recently completed, together with Alex Hsieh, a set of packages for performing calculations common in High-Energy Physics, using Mathematica. Specifically, we have written the following packages: NonCommutativeMultiply.m - General utilities for working with non-commutative algebras: declaring objects as non-commutative, automatically factoring out the commuting variables, manually commuting specific objects, and more. RelativisticKinematics.m - Working with four-vectors: constructing four-vectors, extracting invariant mass, energy and momentum from a four-vector, calculating the dot-product of two four-vectors, boosting a four-vector in an arbitrary direction, decaying a four-vector into two four-vectors, working with Mandelstam variables and more. All operations can be done both symbolically and numerically. Spinor.m - Working with Dirac Algebra and Lorentz indices: The space-time metric g, contructing over Lorentz indices, working with spinors U, Ubar, V and Vbar, squaring expressions with spinors to give traces over gamma-matrices, evaluating traces over gamma- matrices in arbitrary space-time dimension and more. CrossSection.m - Automatically evaluating cross-sections and decay- widths from a matrix element squared by constructing the necessary phase-space integrals, and optionally evaluating them. Evaluation can be either symbolic or numeric. Class.m - A very general implementation of some object- oriented programming tools: classes, properties and inheritance. StandardModel.m - A compilation of the Feyman rules of the Standard- Model, together with other useful facts. These packages, together with a small number of sample calculations are now available for beta testing. If you are interested, write to me. Pease indicate explicitly if you are NOT using a Unix-based system. From mathgroup-adm@yoda.ncsa.uiuc.edu Mon Jun 25 22:27:36 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA20285 (5.62+/IDA-1.3.1 for stevec); Mon, 25 Jun 90 22:27:35 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA14727; Mon, 25 Jun 90 22:24:52 CDT Received: by yoda.ncsa.uiuc.edu id AA20048 (5.62+/IDA-1.3.1 for ); Mon, 25 Jun 90 19:52:51 -0500 Received: by yoda.ncsa.uiuc.edu id AA20044 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Mon, 25 Jun 90 19:52:50 -0500 Message-Id: <9006260052.AA20044@yoda.ncsa.uiuc.edu> Date: Mon, 25 Jun 90 14:54:41 CST From: AN123651@uthvm1.bitnet Subject: Mathematica confusion To: mathgroup@yoda.ncsa.uiuc.edu Status: RO Thanks to the many people who have responded to my earlier posting. Let me see if I can be more clear, and refrain from embarassing myself further. When I enter the expression (1/x) (1/x^2)^(1/x^2 -1) mma simplifies it to x^(-1 - 2 (-1 + x^(-2))) Now, consider x = -2 (not -1 as I mistyped previously). In the first expression, x is squared before any roots are taken, so it is natural to expect a real answer. In the second case, a root of -2 is taken and a complex answer is no surprise. mma's simplification effects the choice of the branch cut. This is not a bug. The question of branch cuts is difficult. Instead, let me post this as a query - how can I get mma to take the cut I want? Note that mma is not entirely consistent on this point: (1/x) (1/x^2)^(1/x^2 -1) /. x-> -2 and f[x_] := (1/x) (1/x^2)^(1/x^2 -1) f[-2] return different answers. E. Neely Atkinson AN123651 at UTHVM1.BITNET neely@mdaali.cancer.utexas.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Jun 28 21:36:35 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA23777 (5.62+/IDA-1.3.1 for stevec); Thu, 28 Jun 90 21:36:34 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA15918; Thu, 28 Jun 90 21:33:36 CDT Received: by yoda.ncsa.uiuc.edu id AA23729 (5.62+/IDA-1.3.1 for ); Thu, 28 Jun 90 20:40:30 -0500 Received: by yoda.ncsa.uiuc.edu id AA23725 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Thu, 28 Jun 90 20:40:28 -0500 Message-Id: <9006290140.AA23725@yoda.ncsa.uiuc.edu> Date: Mon, 25 Jun 90 23:30:04 EDT From: wsd@cs.brown.edu To: mathgroup@yoda.ncsa.uiuc.edu Subject: Sqrt[x^2] Status: RO In[6]:= Sqrt[x^2] Out[6]= x why? this leads to the rather dubious distinction: In[13]:= f[x_] := Sqrt[x x] In[15]:= f[-2] Out[15]= 2 In[16]:= g[x_] = Sqrt[x x] In[18]:= g[-2] Out[18]= -2 as well as real problems such as E. Neely Atkinson's. anyone want to defend this? wsd@cs.brown.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Jun 28 22:48:54 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA23843 (5.62+/IDA-1.3.1 for stevec); Thu, 28 Jun 90 22:48:52 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA16989; Thu, 28 Jun 90 22:45:41 CDT Received: by yoda.ncsa.uiuc.edu id AA23734 (5.62+/IDA-1.3.1 for ); Thu, 28 Jun 90 20:40:37 -0500 Received: by yoda.ncsa.uiuc.edu id AA23730 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Thu, 28 Jun 90 20:40:35 -0500 Message-Id: <9006290140.AA23730@yoda.ncsa.uiuc.edu> Date: Tue, 26 Jun 90 12:52:40 +0200 From: lauten@ds1.cip.physik.tu-muenchen.de Subject: New Mathematica release? To: mathgroup@yoda.ncsa.uiuc.edu Status: RO Our physics department wants to buy a new license for Mathematica on a SUN SparcStation. Since recent discussion in this mailing list has shown that there are still some serious bugs in the current release, e.g. the ordering of transformation rules, it would be interesting to know whether there is a new improved version of Mathematica just around the corner. If there is one, how long will it take until it will be available ? MARKUS LAUTENBACHER lauten@ds1.cip.physik.tu-muenchen.de From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Jun 28 23:36:57 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA23917 (5.62+/IDA-1.3.1 for stevec); Thu, 28 Jun 90 23:36:56 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA17677; Thu, 28 Jun 90 23:33:57 CDT Received: by yoda.ncsa.uiuc.edu id AA23744 (5.62+/IDA-1.3.1 for ); Thu, 28 Jun 90 20:40:54 -0500 Received: by yoda.ncsa.uiuc.edu id AA23740 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Thu, 28 Jun 90 20:40:53 -0500 Message-Id: <9006290140.AA23740@yoda.ncsa.uiuc.edu> Date: Thu, 28 Jun 90 06:54:13 EDT From: joe@mathcs.emory.edu (Joe Christy) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Braids Status: RO [The braids packages and other files can be found on the MathGroup archive in the /Symbolic/Mathematica/Packages/BRAIDS directory. -- smc] I have submitted a trio of packages, SymmetricGroup.m, BraidGroup.m, and Braids.m to the archive at ftp.ncsa.uiuc.edu. Together they do some simple algebraic manipulations in the symmetric and braid groups, and draw pictures of framed links, represented as braids. There is also a notebook, WhizzoKeenBraids.ma, which demonstrates how to use the packages to draw some pretty pictures of some interesting knots and links. Joe Joe Christy | joe@mathcs.emory.edu | Time flies like an Emory University | {rutgers,gatech}!emory!joe | arrow, fruit flies Dept of Math and CS | joe@emory.bitnet | like bananas. Atlanta, GA 30322 | Phone: (404) 727-7956 | From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Jun 28 23:45:09 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA23929 (5.62+/IDA-1.3.1 for stevec); Thu, 28 Jun 90 23:45:06 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA17801; Thu, 28 Jun 90 23:42:05 CDT Received: by yoda.ncsa.uiuc.edu id AA23739 (5.62+/IDA-1.3.1 for ); Thu, 28 Jun 90 20:40:44 -0500 Received: by yoda.ncsa.uiuc.edu id AA23735 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Thu, 28 Jun 90 20:40:43 -0500 Message-Id: <9006290140.AA23735@yoda.ncsa.uiuc.edu> Date: Wed, 27 Jun 90 18:59:27 +0200 From: lauten@ds1.cip.physik.tu-muenchen.de Subject: Transformation rules and Conditions To: mathgroup@yoda.ncsa.uiuc.edu Status: RO Suppose you have a Mathematica file called "f.m" that contains the following generic transformation rules: f[ a_ ] := StringJoin[ "< ", ToString[ a ], " >" ] /; ftostring f[ a_,b_ ] := f[a] f[b] ftostring = True Now I give the script of a short Mathematica session using these rules: In[1]:= < < b > In[3]:= ftostring = False Out[3]= False In[4]:= ftest = f[a,b] Out[4]= f[a] f[b] In[5]:= ftostring = True Out[5]= True In[6]:= ftest Out[6]= f[a] f[b] In[7]:= Update[] In[8]:= ftest Out[8]= < a > < b > Now the problem is the result of In[6], since I want Mathematica to use the transformation rule for f[a_] if ftostring is True. Obviously this only works after I do an Update[]. I know what the Mathematica handbook says in connection with Update[] and Condition tests on page 699 and 223, but I am interested in the three following points anyway: 1. Is there a way to avoid the Update[], since e.g. on an AT386/87 the Update[] can take quite a time and I will have to switch the rules several times in my particular application. 2. Can I do just a partial Update[] ? I tried Update[ftostring] but it didn't work. 3. Can anyone (e.g. Wolfram Res. people) explain to me the deeper meaning of "It (Update[]) should not need to be called except under very special circumstances that very rarely occur in practice." (Mathematica book page 699), since I am really interested in Why and What is going on on a deeper level of understanding ? Thanks in advance, MARKUS From mathgroup-adm@yoda.ncsa.uiuc.edu Sat Jul 7 01:30:30 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA05094 (5.62+/IDA-1.3.1 for stevec); Sat, 7 Jul 90 01:30:28 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA23884; Sat, 7 Jul 90 01:28:12 CDT Received: by yoda.ncsa.uiuc.edu id AA04394 (5.62+/IDA-1.3.1 for ); Fri, 6 Jul 90 23:41:00 -0500 Received: by yoda.ncsa.uiuc.edu id AA04390 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 6 Jul 90 23:40:58 -0500 Message-Id: <9007070440.AA04390@yoda.ncsa.uiuc.edu> Date: Tue, 3 Jul 90 15:14:26 MDT From: smithw@mathnx.byu.edu (William V. Smith) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Problems resizing plots Status: RO Some one down the hall brought me this problem and I thought I would ask you people about it. The problem seems to occur on a NeXT (1.0a software, Jan. 1990 Mathematica kernel). They are developing notebooks for honors calculus with alot of plot windows. It seems that after they are working for 10 or 15 minutes on the machine, suddenly plot window resizing goes haywire. When they try to resize a plot, the window suddenly becomes very narrow . Height is still adjustable, but width no longer is adjustable. The problem is temporarily cured by reloading Mathematica.app from an optical. Someone have an idea on this??? smithw@mathnx.byu.edu (William V. Smith) From mathgroup-adm@yoda.ncsa.uiuc.edu Sat Jul 7 01:47:34 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA05127 (5.62+/IDA-1.3.1 for stevec); Sat, 7 Jul 90 01:47:32 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA24158; Sat, 7 Jul 90 01:45:16 CDT Received: by yoda.ncsa.uiuc.edu id AA04399 (5.62+/IDA-1.3.1 for ); Fri, 6 Jul 90 23:41:04 -0500 Received: by yoda.ncsa.uiuc.edu id AA04395 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 6 Jul 90 23:41:03 -0500 Message-Id: <9007070441.AA04395@yoda.ncsa.uiuc.edu> Date: Fri, 6 Jul 90 17:41:58 CDT From: Elaine Kant To: mathgroup@yoda.ncsa.uiuc.edu Subject: forcing printing of error messages Status: RO In theory, you can force Mathematica to print all error messages instead of just the first 3 by turning off General::stop. However, this doesn't seem to work, at least not in our environment (version 1.2 on a Sun4). "...Mathematica keeps track of all messages that are produced during a particular calculation, and stops printing a particular message if it comes up more than three times. Whenever this happens, Mathematica prints the message General::stop to let you know. If you really want to see all the messages that Mathematica tries to print, you can do this by switching off General::stop." If we try the following, Off[General::stop] MathCode::syntax = "Syntax error in ``." Do[Message[MathCode::syntax, foo], {i, 10}] we still only get 3 messages. What's happening? Is this not the proper way to see all the messages? IS there a way? Thanks. -- Elaine From mathgroup-adm@yoda.ncsa.uiuc.edu Mon Jul 9 20:32:20 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA07238 (5.62+/IDA-1.3.1 for stevec); Mon, 9 Jul 90 20:32:17 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA19995; Mon, 9 Jul 90 20:30:03 CDT Received: by yoda.ncsa.uiuc.edu id AA07161 (5.62+/IDA-1.3.1 for ); Mon, 9 Jul 90 18:16:06 -0500 Received: by yoda.ncsa.uiuc.edu id AA07157 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Mon, 9 Jul 90 18:16:04 -0500 Message-Id: <9007092316.AA07157@yoda.ncsa.uiuc.edu> Date: Sun, 8 Jul 90 14:17:42 EST From: marwan@ee.su.oz.au (Marwan Jabri) To: stevec@yoda.ncsa.uiuc.edu Subject: Re: X11 driver Status: RO We have a Mathematica license for Sun 4 and for some reasons we were delivered the X11 driver for Sun 3. We have been trying to get the proper driver now for some months from the Australian distributors of Mathematica without success (The company is in Melbourne and we are not sure if there are still in business or playing the deads!). Is there anyway of getting the X11 driver through ftp? Marwan Jabri marwan@ee.su.oz.au From mathgroup-adm@yoda.ncsa.uiuc.edu Mon Jul 9 21:33:53 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA07312 (5.62+/IDA-1.3.1 for stevec); Mon, 9 Jul 90 21:33:50 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA20916; Mon, 9 Jul 90 21:31:38 CDT Received: by yoda.ncsa.uiuc.edu id AA07166 (5.62+/IDA-1.3.1 for ); Mon, 9 Jul 90 18:16:13 -0500 Received: by yoda.ncsa.uiuc.edu id AA07162 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Mon, 9 Jul 90 18:16:12 -0500 Message-Id: <9007092316.AA07162@yoda.ncsa.uiuc.edu> Date: Sat, 7 Jul 90 20:08:50 +0200 From: lie@itk.unit.no To: mathgroup@yoda.ncsa.uiuc.edu Subject: ParametricPlot Status: RO k Plotting of several curves in ParametricPlot -------------------------------------------- I want to make a routine that plots several curves in one window with ParametricPlot. The problem is that I don't want to specify the number of functions in advance - the routine should detect the number. To be more specific: Let: h[s] be a vector where each element is a "transferfunction", {h[s]}(i,j) = a(s)/b(s) (a, b may be polynomials in s) I want to plot each element of Abs[h[s]] in a log-log coordinate system. A simple way is to use ParametricPlot. ParametricPlot[ { {d, 20 Log[10, Abs[ h[I 10^d] [[1,1]] ] ]}, {d, 20 Log[10, Abs[ h[I 10^d] [[2,1]] ] ]}, .............}, {d, dmin, dmax} ] This is, however, rather inconvenient. I want the list of elements of h[s] to be made automatically. I tried the following solution: list={}; Do[ list=Append[list, {d, f[i]}], {i, Dimensions[h[s]] [[1,1]] } ]; ParametricPlot[ f[i_]=20 Log[10, Abs[ h[I 10^d] [[i,1]] ] ]; list, {d,dmin,dmax} ] What I actually tried was the following: I wanted to plot all the Singular values of a *matrix* h[I w] as a function of "frequency" w, in one plot. The function f[i_] above thus got rather involved, and I got an error message that said that I tried to calculate the Singur values of a non-numeric matrix. How should I solve my problem? -Bernt Lie lie@itk.unit.no From mathgroup-adm@yoda.ncsa.uiuc.edu Mon Jul 9 19:45:18 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA07219 (5.62+/IDA-1.3.1 for stevec); Mon, 9 Jul 90 19:45:15 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA19293; Mon, 9 Jul 90 19:43:03 CDT Received: by yoda.ncsa.uiuc.edu id AA07156 (5.62+/IDA-1.3.1 for ); Mon, 9 Jul 90 18:16:00 -0500 Received: by yoda.ncsa.uiuc.edu id AA07152 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Mon, 9 Jul 90 18:15:59 -0500 Message-Id: <9007092315.AA07152@yoda.ncsa.uiuc.edu> Date: Mon, 9 Jul 90 12:03:19 EST From: irh@melba.bby.oz.au (Ian R Heddle) To: mathgroup@yoda.ncsa.uiuc.edu Subject: AnalysisofVariance package Status: RO I've just been reading the 1990 Mathematica conference notes on Data Analysis by Dave Withoff. On page 30 he mentions the packages AnalysisofVariance and LinearRegression. We did not receive these packages with our copy of Mathematica. Are they available, and if so from who ? Thanks in advance Ian Heddle irh@melba.bby.oz.au From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Jul 10 12:48:43 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA08431 (5.62+/IDA-1.3.1 for stevec); Tue, 10 Jul 90 12:48:41 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA11559; Tue, 10 Jul 90 12:46:32 CDT Received: by yoda.ncsa.uiuc.edu id AA08342 (5.62+/IDA-1.3.1 for ); Tue, 10 Jul 90 11:27:14 -0500 Received: by yoda.ncsa.uiuc.edu id AA08338 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 10 Jul 90 11:27:13 -0500 Message-Id: <9007101627.AA08338@yoda.ncsa.uiuc.edu> Date: Mon, 9 Jul 90 18:33:28 PDT From: campbell@garnet.berkeley.edu (Robert I. Campbell) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: mathematica in the classroom Status: RO Some contacts you might try: Prof Ken Ribet at UCBerkeley has been teaching freshman calc w/ Mathematica. Prof Stan Devitt at Univ of Saskatchewan " " " " w/ MAPLE Prof Don Small at Colby College publishes a newsletter on the subject. - Robert Campbell - From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Jul 10 13:45:53 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA08444 (5.62+/IDA-1.3.1 for stevec); Tue, 10 Jul 90 13:45:50 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA29959; Tue, 10 Jul 90 13:43:30 CDT Received: by yoda.ncsa.uiuc.edu id AA08337 (5.62+/IDA-1.3.1 for ); Tue, 10 Jul 90 11:27:07 -0500 Received: by yoda.ncsa.uiuc.edu id AA08333 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 10 Jul 90 11:27:06 -0500 Message-Id: <9007101627.AA08333@yoda.ncsa.uiuc.edu> Date: Sun, 8 Jul 90 14:17:42 EST From: marwan@ee.su.oz.au (Marwan Jabri) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: X11 driver Status: RO We have a Mathematica license for Sun 4 and for some reasons we were delivered the X11 driver for Sun 3. We have been trying to get the proper driver now for some months from the Australian distributors of Mathematica without success (The company is in Melbourne and we are not sure if there are still in business or playing the deads!). Is there anyway of getting the X11 driver through ftp? Marwan Jabri marwan@ee.su.oz.au From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Jul 10 14:48:14 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA08556 (5.62+/IDA-1.3.1 for stevec); Tue, 10 Jul 90 14:48:12 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA09206; Tue, 10 Jul 90 14:46:02 CDT Received: by yoda.ncsa.uiuc.edu id AA08353 (5.62+/IDA-1.3.1 for ); Tue, 10 Jul 90 11:28:53 -0500 Received: by yoda.ncsa.uiuc.edu id AA08349 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 10 Jul 90 11:28:52 -0500 Message-Id: <9007101628.AA08349@yoda.ncsa.uiuc.edu> Date: Tue, 10 Jul 90 08:21:24 EDT From: gregor@oit.itd.umich.edu To: mathgroup@yoda.ncsa.uiuc.edu Subject: Mathematica Materials for 3rd Semester Multi-Variable Calculus Status: RO Hello, I am at the University of Michigan. There is a project here about ready to get under way which involves the creation of Mathematica materials for a 3rd semester multi-variable calculus course. We are wondering if there are any such materials available already which we could use as a springboard for our work, or possibly incorporate as-is. Can anyone out there help us? --Gregor From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Jul 10 15:25:27 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA08631 (5.62+/IDA-1.3.1 for stevec); Tue, 10 Jul 90 15:25:21 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA09995; Tue, 10 Jul 90 15:23:10 CDT Received: by yoda.ncsa.uiuc.edu id AA08358 (5.62+/IDA-1.3.1 for ); Tue, 10 Jul 90 11:29:00 -0500 Received: by yoda.ncsa.uiuc.edu id AA08354 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 10 Jul 90 11:28:59 -0500 Message-Id: <9007101628.AA08354@yoda.ncsa.uiuc.edu> Date: Tue, 10 Jul 90 17:05:41 +0200 From: lie@itk.unit.no To: mathgroup@yoda.ncsa.uiuc.edu Subject: Bug ? Status: RO BUG in evaluation of iteration functions? ----------------------------------------- According to the Mathematica book, "Iteration functions such as *Table* and *Sum*, as well as *Plot* and *Plot3D*, evaluate their arguments in a slightly complicated way...". Then follows a discussion of how *Table* works. *Plot* and *Table* does, however, not evaluate the argument in the same way, as the following example shows: Example: (Comments and questions follow the example). ----------------------------------------------------------------------- In[225]:= MatrixForm[h[s]] 1 - s 1 + 3 s ------ ------- 3 3 1 + s 1 + s 2 2 5 + s 5 + 3 s + s ------ ------------ 3 3 Out[225]//MatrixForm= 1 + s 1 + s In[226]:= Table[ sv[d_]:= N[ SingularValues[ h[ I 10^d] ] ]; Table[sv[d][[2,i]], {i, 2}], {d, -2, 3, .5}] Out[226]= {{7.21106, 0.0235744}, {7.21065, 0.0745382}, {7.20658, 0.235377}, > {7.16454, 0.733152}, {4.96973, 1.34229}, {0.461212, 0.170416}, > {0.138501, 0.0277379}, {0.0446215, 0.00282351}, {0.014139, 0.000282794}, > {0.00447204, 0.0000282838}, {0.00141421, 0.00000282842}} In[227]:= Plot[ sv[d_]:= N[ SingularValues[ h[I 10^d] ] ]; Table[ sv[d][[2,i]], {i, 2}], {d, -2,3}, PlotPoints->11] d Plot::notnum: sv[d_] := N[SingularValues[h[I 10 ]]]; Table[sv[d][[2,i]], {i, 2}] does not evaluate to a real number at d=-2.. d Plot::notnum: sv[d_] := N[SingularValues[h[I 10 ]]]; Table[sv[d][[2,i]], {i, 2}] does not evaluate to a real number at d=-1.5. d Plot::notnum: sv[d_] := N[SingularValues[h[I 10 ]]]; Table[sv[d][[2,i]], {i, 2}] does not evaluate to a real number at d=-1.. General::stop: Further output of Plot::notnum will be suppressed during this calculation. Out[227]= -Graphics- In[228]:= -------------------- The table in Out[226] shows the singular values of h[I 10^d], d in {-2, -1.5, ..., 3}. This will only work as long as the *outermost* iterator is evaluated first. (See Maeder: Programming in Math..., p. 78-79). The command in In[227] was meant to plot these same singular values. The error messages seem to indicate that in In[227], the *innermost* iterator (i of Table) is sought evaluated *before* the *outermost* iterator (d of Plot). In that case, the Singular Values can not be evaluated, and sv[d][[2,i]] has no meaning. Question: 1) Is my interpretation of the error messages correct? If so, is this a bug? ********* 2) If it isn't a bug, what is the purpose of this feature? How can I override the order of evaluation? -Bernt Lie, lie@itk.unit.no Question: In Plot: How can I make the iterator receive a value *before* the iterator in Table is evaluated, i.e., the way Table works. From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Jul 10 15:43:42 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA08643 (5.62+/IDA-1.3.1 for stevec); Tue, 10 Jul 90 15:43:41 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA10399; Tue, 10 Jul 90 15:41:30 CDT Received: by yoda.ncsa.uiuc.edu id AA08398 (5.62+/IDA-1.3.1 for ); Tue, 10 Jul 90 12:11:02 -0500 Received: by yoda.ncsa.uiuc.edu id AA08394 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 10 Jul 90 12:11:01 -0500 Message-Id: <9007101711.AA08394@yoda.ncsa.uiuc.edu> From: mcdonald@wmm-wks.umd.edu (Bill MacDonald) Subject: Sqrt[x^2] "bug" To: mathgroup@yoda.ncsa.uiuc.edu Date: Tue, 10 Jul 90 12:23:52 EDT Status: RO The "bug" is that if f[x_] = Sqrt[x*x] and g[x_]:=Sqrt[x*x] then f[-2] returns -2 and g[-2] returns 2. Look at f with ?f . You learn that f[x_] = x while g[x_]:=Sqrt[x*x] . So that immediate evaluation causes Mathematica to say that the Sqrt[] is the inverse of the operation of squaring. However, in the delayed evaluation the creators have chosen to take only the positive square root ? -- William M. MacDonald Professor of Physics University of Maryland Internet: mcdonald@quark.umd.edu Bitnet:mAcdonald@cincom From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Jul 12 00:39:22 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA11024 (5.62+/IDA-1.3.1 for stevec); Thu, 12 Jul 90 00:39:21 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA14171; Thu, 12 Jul 90 00:37:42 CDT Received: by yoda.ncsa.uiuc.edu id AA10362 (5.62+/IDA-1.3.1 for ); Thu, 12 Jul 90 00:00:39 -0500 Received: by yoda.ncsa.uiuc.edu id AA10351 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Wed, 11 Jul 90 23:59:45 -0500 Message-Id: <9007120459.AA10351@yoda.ncsa.uiuc.edu> Date: Tue, 10 Jul 90 15:49:32 EDT From: fran@jim.cam.nist.gov (Francis Sullivan) To: mathgroup-adm@yoda.ncsa.uiuc.edu Subject: Mathematica in the classroom. Status: RO An additional contact for Mathematica in the classroom is: Calculus&Mathematica H. Porta and J.J. Uhl University of Illinois -Francis Sullivan- From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Jul 12 01:29:26 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA11049 (5.62+/IDA-1.3.1 for stevec); Thu, 12 Jul 90 01:29:22 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA15396; Thu, 12 Jul 90 01:27:43 CDT Received: by yoda.ncsa.uiuc.edu id AA10363 (5.62+/IDA-1.3.1 for ); Thu, 12 Jul 90 00:00:41 -0500 Received: by yoda.ncsa.uiuc.edu id AA10355 (5.62+/IDA-1.3.1 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Wed, 11 Jul 90 23:59:53 -0500 Message-Id: <9007120459.AA10355@yoda.ncsa.uiuc.edu> Date: Wed, 11 Jul 90 15:35:02 +0200 From: lie@itk.unit.no To: mathgroup@yoda.ncsa.uiuc.edu Subject: Framed Plots Status: RO Framed plots with axes on the frame. --------------------------------------- Question: How can I create framed plots with axes on the frame?? I have tried to write: Show[%, Framed->True, Axes->Scaled[{0,0}] ] but Mathematica doesn't seem to recognize the function Scaled (which is supposed to scale coordinates to run from 0 to 1 in each direction). -Bernt Lie, lie@itk.unit.no PS: The scaled command is briefly described on p. 146 in the Mathematica book. From mathgroup-adm@yoda.ncsa.uiuc.edu Sat Jul 28 23:13:13 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA07032 (5.64+/IDA-1.3.4 for stevec); Sat, 28 Jul 90 23:13:09 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA18067; Sat, 28 Jul 90 23:11:53 CDT Received: by yoda.ncsa.uiuc.edu id AA06957 (5.64+/IDA-1.3.4 for ); Sat, 28 Jul 90 22:01:37 -0500 Received: by yoda.ncsa.uiuc.edu id AA06953 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Sat, 28 Jul 90 22:01:35 -0500 Message-Id: <9007290301.AA06953@yoda.ncsa.uiuc.edu> To: mathgroup@yoda.ncsa.uiuc.edu Subject: Mathematica packages Date: Fri, 27 Jul 90 11:47:19 PDT From: jacobson@cello.hpl.hp.com Status: RO I've heard rumors of a collection of Mathematica packages available via anonymous ftp from somewhere at Stanford. I solicit more information about this. -- David Jacobson From mathgroup-adm@yoda.ncsa.uiuc.edu Sun Jul 29 03:11:40 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA07805 (5.64+/IDA-1.3.4 for stevec); Sun, 29 Jul 90 03:11:38 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA23673; Sun, 29 Jul 90 03:10:09 CDT Received: by yoda.ncsa.uiuc.edu id AA06947 (5.64+/IDA-1.3.4 for ); Sat, 28 Jul 90 22:01:06 -0500 Received: by yoda.ncsa.uiuc.edu id AA06943 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Sat, 28 Jul 90 22:01:04 -0500 Message-Id: <9007290301.AA06943@yoda.ncsa.uiuc.edu> From: btbg1194@uxa.cso.uiuc.edu (Bradley T Banko) Subject: Mathematica needs a Trig capability... Date: Wed, 25 Jul 90 17:07:42 GMT To: mathgroup@yoda.ncsa.uiuc.edu Status: RO Mathematica needs the capability to perform ComplexToTrig and TrigToComplex operations with respect to only one particular angular variable. I often get expressions like: cos(phi) + i sin(phi) + cos(omega)(cos(phi) + i sin(phi)), ...etc. Also, for more fun and games, try to simplify the following expression: (I have 8 more where this one comes from.) 2 -1 5 Sqrt[2] Sqrt[5] (-1 + 3 Cos[theta] ) ---------- + -------------------------------------- - 6 Sqrt[Pi] 4 Sqrt[15] Sqrt[30] Sqrt[Pi] Cos[omega] + -I Sin[omega] -------------------------- + 6 Sqrt[Pi] Sqrt[3] Cos[theta] (Cos[omega] + -I Sin[omega]) ----------------------------------------------- - 4 Sqrt[Pi] 2 Sqrt[5] (-1 + 3 Cos[theta] ) (Cos[omega] + -I Sin[omega]) --------------------------------------------------------- - 24 Sqrt[Pi] Cos[omega] + I Sin[omega] ------------------------- - 6 Sqrt[Pi] Sqrt[3] Cos[theta] (Cos[omega] + I Sin[omega]) ---------------------------------------------- - 4 Sqrt[Pi] 2 Sqrt[5] (-1 + 3 Cos[theta] ) (Cos[omega] + I Sin[omega]) -------------------------------------------------------- 24 Sqrt[Pi] Finally,... Is it possible to "cut and paste" in Mathematica on a Mac II from Mathematica into an NCSA Telnet window running VI or Emacs? (I would imagine that people at Wolfram would have a quick answer to this.) Thanks! Brad Banko Theoretical Biophysics -- Bradley T. Banko Dept of Physics, Univ. of Illinois at Urbana-Champaign btbg1194@uxa.cso.uiuc.edu >From jacobson@cello.hpl.hp.com Fri Jul 27 13:47:18 1990 Received: from hplms2.hpl.hp.com by yoda.ncsa.uiuc.edu with SMTP id AA05175 (5.62+/IDA-1.3.1 for stevec); Fri, 27 Jul 90 13:47:08 -0500 Received: from cello.hpl.hp.com by hplms2.hpl.hp.com with SMTP (15.11.1.3/15.5+IOS 3.20) id AA06142; Fri, 27 Jul 90 11:47:40 pdt Received: from localhost by cello.hpl.hp.com with SMTP (15.11/15.5+IOS 3.14) id AA26559; Fri, 27 Jul 90 11:47:21 pdt To: mathgroup@yoda.ncsa.uiuc.edu Subject: Mathematica packages Date: Fri, 27 Jul 90 11:47:19 PDT Message-Id: <26557.649104439@cello.hpl.hp.com> From: jacobson@cello.hpl.hp.com Status: RO I've heard rumors of a collection of Mathematica packages available via anonymous ftp from somewhere at Stanford. I solicit more information about this. -- David Jacobson From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Aug 7 02:58:59 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA04939 (5.64+/IDA-1.3.4 for stevec); Tue, 7 Aug 90 02:58:56 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA23462; Tue, 7 Aug 90 02:57:10 CDT Received: by yoda.ncsa.uiuc.edu id AA04853 (5.64+/IDA-1.3.4 for ); Tue, 7 Aug 90 01:30:51 -0500 Received: by yoda.ncsa.uiuc.edu id AA04849 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 7 Aug 90 01:30:49 -0500 Message-Id: <9008070630.AA04849@yoda.ncsa.uiuc.edu> To: mathgroup@yoda.ncsa.uiuc.edu Subject: Derivative "feature" Date: Mon, 30 Jul 90 10:50:33 PDT From: jacobson@cello.hpl.hp.com Status: RO Beware of differentiation of functions defined on more than one piece using "/;" operator. In[1]:= f[x_] := x^2 /; x <=1 In[2]:= f[x_] := 2 x -1 Plotting this shows a parabola to the left smoothly connecting to a straight line at x = 1. However, if we ask for the derivative, we get a surprise: In[3]:= f' Out[3]= 2 & This is wrong for x < 1. Does anyone know how to write a function composed of multiple segments that can be differentiated? I tried to teach Mathematica how to differentiate the If[cond,expr1,expr2] function, without success. -- David Jacobson From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Aug 7 05:02:51 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA05146 (5.64+/IDA-1.3.4 for stevec); Tue, 7 Aug 90 05:02:48 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA27079; Tue, 7 Aug 90 05:01:01 CDT Received: by yoda.ncsa.uiuc.edu id AA04858 (5.64+/IDA-1.3.4 for ); Tue, 7 Aug 90 01:30:58 -0500 Received: by yoda.ncsa.uiuc.edu id AA04854 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 7 Aug 90 01:30:56 -0500 Message-Id: <9008070630.AA04854@yoda.ncsa.uiuc.edu> Date: Mon, 30 Jul 90 13:57:44 EDT From: royster@unccvax.uncc.edu (David Royster) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Relative Speed of Mathematica on a MacII Status: RO I have been learning to use Mathematica on a MacII for a couple of months now. I quite often run into problems of the speed with which Mathematica performs its operations. For example, I wanted to compute the determinant of the n x n Hilbert matrix, the matrix whose ij th entry is \frac{1}{i+j-1}. I was able to compute the determinant of the 12 x 12 matrix in a matter of 4 minutes, whereas DERIVE was able to compute the determinant of the 40 x 40 in 153 seconds. I was never able to compute the determinant of the 13 x 13 matrix in Mathematica. Last week we saw the form to graph using SphericalPlot3D to graph a cornucopia. Mathematica on my Mac refused to graph the surface. I left it running all night and all that happened was that the Mac froze---completely! Should I be expecting this type of behavior from Mathematica on a MacII? Should I send the MacII back to Siberia and use something else? I would really like to get some benchmarks with which to compare the performance on my machine. Thanks, dcroyster -------------------------------------------------------------------------- David C. Royster royster@unccvax.uncc.edu (128.143.109.1) Mathematics Department fma00dcr@unccvm.bitnet UNC Charlotte, Charlotte NC Augustus Moebius Wedding Band Co.---Rings to fit every finger! From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Aug 7 05:04:50 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA05157 (5.64+/IDA-1.3.4 for stevec); Tue, 7 Aug 90 05:04:47 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA27093; Tue, 7 Aug 90 05:03:01 CDT Received: by yoda.ncsa.uiuc.edu id AA04868 (5.64+/IDA-1.3.4 for ); Tue, 7 Aug 90 01:31:12 -0500 Received: by yoda.ncsa.uiuc.edu id AA04864 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 7 Aug 90 01:31:10 -0500 Message-Id: <9008070631.AA04864@yoda.ncsa.uiuc.edu> Date: Tue, 31 Jul 90 14:42:49 CDT From: johnsonj@phobos.mathcs.carleton.edu To: mathgroup@yoda.ncsa.uiuc.edu Subject: Strange results with the Integrate function Status: RO In our research this summer, many different statistical applications have been successfully carried out using NeXT Mathematica version 1.2, with the irksome exception of the following exercise: Exact density functions representing sums of n uniforms (on [-.5, .5]) may be calculated exactly by means of Fourier tranforms, using the formula (expressed in Mathematica syntax): f[x_, n_Integer] := (1 / Pi) * Integrate[(Sin[t / 2] / (t / 2)) ^ n * Cos[x * t], {t, 0, Infinity}] /; n > 1 We are replacing the infinite expression for the upper limit by a calculated error function, 2 / epsilon ^ (1 / (n - 1)). Made in the interest of simplification and speed, this step may not be necessary. The question is, why is this (relatively) straightforward integral impossible to express for, say, n = 2 ? When given the input f[x, 2], Mathematica responds with an "Indeterminate" output. BUT...if we change the formula by putting an N[] function about the integrand, the function operates normally, and the time needed to make a Plot of the function f[x, 2] drops considerably, since it is possible to preevaluate the expression before plotting. Still, WHY DOES THIS MAKE A DIFFERENCE? There is nothing numerical in the integrand expression besides the n exponent, and that ought to be simplified anyway -- and if it were not, it would not have an indeterminate result. WHY? Jonathan Johnson, Carleton College, Northfield, MN (Mathematica group member Mike Tie, mtie@mathcs.carleton.edu) From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Aug 7 05:46:17 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA05298 (5.64+/IDA-1.3.4 for stevec); Tue, 7 Aug 90 05:46:14 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA27613; Tue, 7 Aug 90 05:44:28 CDT Received: by yoda.ncsa.uiuc.edu id AA04863 (5.64+/IDA-1.3.4 for ); Tue, 7 Aug 90 01:31:05 -0500 Received: by yoda.ncsa.uiuc.edu id AA04859 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 7 Aug 90 01:31:03 -0500 Message-Id: <9008070631.AA04859@yoda.ncsa.uiuc.edu> Date: Mon, 30 Jul 90 12:26:45 PDT From: eran@THSUN1.SLAC.STANFORD.EDU Subject: Fourier Transform Package To: mathgroup@yoda.ncsa.uiuc.EDU Status: RO I am currently in the process of writing a package for performing analytic Fourier transform with Mathematica. This package is being written for Wolfram Research, and will be bundled with the next major Mathematica release. I am now seeking input from potential users as to their needs and wants on the subject. Particularly: 1) What methods do you currently use? a) Evaluating transform numerically. (With what method and/or computational tools?) b) Consulting tables. (Which?) c) Working transforms from 'first principles'. d) Using a different symbolic algebra software for the purpose. (Which one?) e) Have written a Mathematica package. (Great! Could you enclose it?) 2) Which particular classes of functions (please give specific examples) do you usually work with? Do you transform these functions analytically? If not, do you know whether an analytical formula exists or not? 3) What convention for the Fourier integral do you usually use? a) F[f, t, w] := Integrate[f Exp[-2 Pi I t w], {t, -Infinity, Infinity}] b) F[f, t, w] := Integrate[f Exp[2 Pi I t w], {t, -Infinity, Infinity}] c) F[f, t, w] := Integrate[f Exp[-I t w], {t, -Infinity, Infinity}] d) F[f, t, w] := Integrate[f Exp[I t w], {t, -Infinity, Infinity}] e) One of the above, multiplied by an additional constant coefficient. f) Other? 4) What other, related, operations would you find useful a) Finding Fourier Series coefficients analytically. b) Calculating Fourier Series coefficients numerically. c) Fourier Sin and Cos transforms. d) Others? 5) What is your field of work? 6) What is your favorite literature on the subject? 7) Any other comments, suggestions, warnings, etc.? I will send a copy of the package to anybody who answers this questionnaire, and who so wishes. 8) Would you be interested in becoming a beta tester for the package, once it is completed? Please send your replies to eran@thsun1.slac.stanford.edu Thanks, Eran Yehudai From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Aug 7 05:48:22 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA05305 (5.64+/IDA-1.3.4 for stevec); Tue, 7 Aug 90 05:48:19 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA27669; Tue, 7 Aug 90 05:46:31 CDT Received: by yoda.ncsa.uiuc.edu id AA04878 (5.64+/IDA-1.3.4 for ); Tue, 7 Aug 90 01:31:26 -0500 Received: by yoda.ncsa.uiuc.edu id AA04874 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 7 Aug 90 01:31:24 -0500 Message-Id: <9008070631.AA04874@yoda.ncsa.uiuc.edu> To: mathgroup@yoda.ncsa.uiuc.edu Subject: Mathematica Errors 386 version 1.2 Date: Tue, 07 Aug 90 09:41:21 +1000 From: Peter Horan Status: RO ERROR #1: I sent you mail yesterday about a problem with Hardcopy[]/HARDCOPY.BAT. However, I did not have the details. Here they are. When I run HARDCOPY DIS or do < 0.03 or larger. e.g. ListPlot[Point[{{x1, y1},{x2, y2},....}]] does not appear. The axes are correct if they are turned on. Similarly, ListPlot[Line[......]] works. The contents of dis are as follows: ---------cut here---------------- %! %%Creator: Mathematica %%AspectRatio: 0.61803 MathPictureStart % Scaling calculations 0.02381 1.36054 0.01472 0.02247 [ [(0.1)] 0.15986 0.00222 0 1 Msboxa [(0.2)] 0.29592 0.00222 0 1 Msboxa [(0.3)] 0.43197 0.00222 0 1 Msboxa [(0.4)] 0.56803 0.00222 0 1 Msboxa [(0.5)] 0.70408 0.00222 0 1 Msboxa [(0.6)] 0.84014 0.00222 0 1 Msboxa [(0.7)] 0.97619 0.00222 0 1 Msboxa [(5)] 0.01131 0.12705 1 0 Msboxa [(10)] 0.01131 0.23939 1 0 Msboxa [(15)] 0.01131 0.35172 1 0 Msboxa [(20)] 0.01131 0.46406 1 0 Msboxa [(25)] 0.01131 0.57639 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 0.61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath %%Object: Graphics [ ] 0 setdash 0 setgray gsave gsave 0.002 setlinewidth 0 0.01472 moveto 1 0.01472 lineto stroke 0.15986 0.00847 moveto 0.15986 0.02097 lineto stroke 0 setgray [(0.1)] 0.15986 0.00222 0 1 Mshowa 0.29592 0.00847 moveto 0.29592 0.02097 lineto stroke 0 setgray [(0.2)] 0.29592 0.00222 0 1 Mshowa 0.43197 0.00847 moveto 0.43197 0.02097 lineto stroke 0 setgray [(0.3)] 0.43197 0.00222 0 1 Mshowa 0.56803 0.00847 moveto 0.56803 0.02097 lineto stroke 0 setgray [(0.4)] 0.56803 0.00222 0 1 Mshowa 0.70408 0.00847 moveto 0.70408 0.02097 lineto stroke 0 setgray [(0.5)] 0.70408 0.00222 0 1 Mshowa 0.84014 0.00847 moveto 0.84014 0.02097 lineto stroke 0 setgray [(0.6)] 0.84014 0.00222 0 1 Mshowa 0.97619 0.00847 moveto 0.97619 0.02097 lineto stroke 0 setgray [(0.7)] 0.97619 0.00222 0 1 Mshowa 0.02381 0 moveto 0.02381 0.61803 lineto stroke 0.01756 0.12705 moveto 0.03006 0.12705 lineto stroke 0 setgray [(5)] 0.01131 0.12705 1 0 Mshowa 0.01756 0.23939 moveto 0.03006 0.23939 lineto stroke 0 setgray [(10)] 0.01131 0.23939 1 0 Mshowa 0.01756 0.35172 moveto 0.03006 0.35172 lineto stroke 0 setgray [(15)] 0.01131 0.35172 1 0 Mshowa 0.01756 0.46406 moveto 0.03006 0.46406 lineto stroke 0 setgray [(20)] 0.01131 0.46406 1 0 Mshowa 0.01756 0.57639 moveto 0.03006 0.57639 lineto stroke 0 setgray [(25)] 0.01131 0.57639 1 0 Mshowa grestore grestore 0 0 moveto 1 0 lineto 1 0.618034 lineto 0 0.618034 lineto closepath clip newpath 0 setgray gsave gsave 0.004 setlinewidth 0.02381 0.01472 moveto 0.15986 0.05258 lineto 0.29592 0.06206 lineto 0.43197 0.07578 lineto 0.56803 0.10049 lineto 0.70408 0.13357 lineto 0.84014 0.33573 lineto 0.97619 1.55231 lineto stroke 0.02381 0.01472 moveto 0.15986 0.0492 lineto 0.29592 0.06416 lineto 0.43197 0.07757 lineto 0.56803 0.09354 lineto 0.70408 0.14035 lineto 0.84014 0.29292 lineto 0.97619 1.72971 lineto stroke 0.02381 0.01472 moveto 0.15986 0.0443 lineto 0.29592 0.06278 lineto 0.43197 0.08044 lineto 0.56803 0.0926 lineto 0.70408 0.14652 lineto 0.84014 0.26867 lineto 0.97619 3.69698 lineto stroke 0.02381 0.01472 moveto 0.15986 0.06042 lineto 0.29592 0.06128 lineto 0.43197 0.0757 lineto 0.56803 0.09951 lineto 0.70408 0.1395 lineto 0.84014 0.24426 lineto 0.97619 2.25076 lineto stroke 0.02381 0.01472 moveto 0.15986 0.05597 lineto 0.29592 0.07083 lineto 0.43197 0.08251 lineto 0.56803 0.10293 lineto 0.70408 0.15091 lineto 0.84014 0.25367 lineto 0.97619 5.30671 lineto stroke 0.02381 0.01472 moveto 0.15986 0.0474 lineto 0.29592 0.0635 lineto 0.43197 0.07212 lineto 0.56803 0.09685 lineto 0.70408 0.14807 lineto 0.84014 0.3351 lineto 0.97619 3.10699 lineto stroke 0.02381 0.01472 moveto 0.15986 0.05136 lineto 0.29592 0.06013 lineto 0.43197 0.08808 lineto 0.56803 0.09617 lineto 0.70408 0.15339 lineto 0.84014 0.26884 lineto 0.97619 6.18006 lineto stroke 0.02381 0.01472 moveto 0.15986 0.04769 lineto 0.29592 0.05937 lineto 0.43197 0.07788 lineto 0.56803 0.10776 lineto 0.70408 0.14501 lineto 0.84014 0.28565 lineto stroke 0.02381 0.01472 moveto 0.15986 0.0578 lineto 0.29592 0.05782 lineto 0.43197 0.07248 lineto 0.56803 0.09655 lineto 0.70408 0.16965 lineto 0.84014 0.45957 lineto stroke 0.02381 0.01472 moveto 0.15986 0.0541 lineto 0.29592 0.06017 lineto 0.43197 0.08065 lineto 0.56803 0.11142 lineto 0.70408 0.2381 lineto 0.84014 2.41422 lineto stroke 0.02381 0.01472 moveto 0.15986 0.05256 lineto 0.29592 0.06632 lineto 0.43197 0.08874 lineto 0.56803 0.11721 lineto 0.70408 0.27084 lineto 0.84014 7.00296 lineto stroke 0.02381 0.01472 moveto 0.15986 0.05054 lineto 0.29592 0.06732 lineto 0.43197 0.08488 lineto 0.56803 0.14505 lineto 0.70408 0.54387 lineto stroke 0.02381 0.01472 moveto 0.15986 0.05703 lineto 0.29592 0.06625 lineto 0.43197 0.09412 lineto 0.56803 0.17113 lineto 0.70408 3.02084 lineto stroke 0.02381 0.01472 moveto 0.15986 0.0641 lineto 0.29592 0.06542 lineto 0.43197 0.11169 lineto 0.56803 0.19959 lineto 0.70408 10.2614 lineto stroke 0.02381 0.01472 moveto 0.15986 0.05343 lineto 0.29592 0.07059 lineto 0.43197 0.12167 lineto 0.56803 0.33076 lineto stroke grestore grestore % End of Graphics MathPictureEnd -----------cut here--------------- Peter Horan peter@aragorn.cm.deakin.oz From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Aug 7 03:55:28 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA05016 (5.64+/IDA-1.3.4 for stevec); Tue, 7 Aug 90 03:55:25 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA25996; Tue, 7 Aug 90 03:53:39 CDT Received: by yoda.ncsa.uiuc.edu id AA04873 (5.64+/IDA-1.3.4 for ); Tue, 7 Aug 90 01:31:19 -0500 Received: by yoda.ncsa.uiuc.edu id AA04869 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 7 Aug 90 01:31:17 -0500 Message-Id: <9008070631.AA04869@yoda.ncsa.uiuc.edu> From: fed!m1ejb00@uunet.UU.NET To: mathgroup@yoda.ncsa.uiuc.edu Subject: Cholesky Decomposition Date: Wed, 01 Aug 90 17:14:46 -0400 Status: RO I have the following problem: I am looking for a matrix R such that A = R`R, where A is a positive definite symmetric matrix. This is called the Cholesky decomposition in most linear algebra texts. How can I do such a thing, symbolically, in Mathematica. I thought that decomposing with: eigval=Eigensystem[A] would do the trick since, if Q are the eigenvalues and L is a diagonal matrix of eigenvectors, then: A = Q L Q`, and one can take the square root of L to get A=R`R, where R=Sqrt[L] Transpose[Q]. However, this identity doesn't work in Mathematica, although the manual says it should. (I even tried both permutations with Transpose, in case I got row eigenvectors instead of column eigenvectors.) Does anyone have suggestions. Thank you. Eric Bartelsman email: m1ejb00@fed.FRB.GOV (202) 452-2530 From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Aug 8 04:43:34 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA06886 (5.64+/IDA-1.3.4 for stevec); Wed, 8 Aug 90 04:43:31 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA05389; Wed, 8 Aug 90 04:41:47 CDT Received: by yoda.ncsa.uiuc.edu id AA06855 (5.64+/IDA-1.3.4 for ); Wed, 8 Aug 90 02:09:24 -0500 Received: by yoda.ncsa.uiuc.edu id AA06851 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Wed, 8 Aug 90 02:09:23 -0500 Message-Id: <9008080709.AA06851@yoda.ncsa.uiuc.edu> Date: Tue, 7 Aug 90 17:52:41 -0400 From: fink@acf5.NYU.EDU (Howard Fink) To: mathgroup@yoda.ncsa.uiuc.edu Subject: 386 Hardcopy error Status: RO I too got the memory error using Hardcopy, but only occasionally. It's my belief that the error is due to insufficient memory in the printer. I have a 640k laserjet II, and the install program for mathematica 386 calls for one meg of memory in the printer. Perhaps when Hardcopy tries to image an area that's more than the standard graphics area the memory required exeeds that in the printer. Howard Fink fink@acf5.nyu.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Aug 8 05:30:08 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA06921 (5.64+/IDA-1.3.4 for stevec); Wed, 8 Aug 90 05:30:06 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA06033; Wed, 8 Aug 90 05:28:23 CDT Received: by yoda.ncsa.uiuc.edu id AA06850 (5.64+/IDA-1.3.4 for ); Wed, 8 Aug 90 02:09:16 -0500 Received: by yoda.ncsa.uiuc.edu id AA06846 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Wed, 8 Aug 90 02:09:15 -0500 Message-Id: <9008080709.AA06846@yoda.ncsa.uiuc.edu> Date: Tue, 7 Aug 90 08:40:19 EDT From: zaccone@sol.bucknell.edu (Rick Zaccone) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Cornucopia Status: RO A couple of weeks ago I asked how to produce a graph of a cornucopia. Several people respond (thanks). I've played around with it a bit, and this seems to produce the best result. <{0, 1.8, -3.6}, Boxed -> False ] Be patient! It takes about 40 minutes on a Mac IIci. It also needs a 5MB Multifinder partition. Get rid of Pi/24 if you don't have enough memory. Mathematica may quietly die if it runs out of memory. Rick Zaccone zaccone@sol.bucknell.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Aug 14 19:46:48 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA13372 (5.64+/IDA-1.3.4 for stevec); Tue, 14 Aug 90 19:46:47 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA06738; Tue, 14 Aug 90 19:44:59 CDT Received: by yoda.ncsa.uiuc.edu id AA13336 (5.64+/IDA-1.3.4 for ); Tue, 14 Aug 90 18:49:44 -0500 Received: by yoda.ncsa.uiuc.edu id AA13332 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 14 Aug 90 18:49:43 -0500 Message-Id: <9008142349.AA13332@yoda.ncsa.uiuc.edu> Date: Sun, 12 Aug 90 21:43 EDT From: "Lawrence M. Seiford, IEOR, UMass, (413) 545-2851." Subject: Video course on Mathematica To: mathgroup@yoda.ncsa.uiuc.edu Status: RO The following may be of interest: The Video Instructional Program of the College of Engineering at the University of Massachusetts is offering a two day course - "Mathematica for Engineers: Numeric, Symbolic and Graphical Computation" on August 15-16, 1990 from 11:00am to 5:00pm EST. The course will be broadcast live over the NTU Satellite Network and will provide an intensive introduction to Mathematica. For further information, contact Merilee Hill, Video Instructional Program, University of Massachusetts, phone: (413) 545-0063 FAX: (413) 545-1277 email: MHILL@UMAECS.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Aug 14 20:43:33 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA13463 (5.64+/IDA-1.3.4 for stevec); Tue, 14 Aug 90 20:43:31 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA07543; Tue, 14 Aug 90 20:41:48 CDT Received: by yoda.ncsa.uiuc.edu id AA13325 (5.64+/IDA-1.3.4 for ); Tue, 14 Aug 90 18:49:17 -0500 Received: by yoda.ncsa.uiuc.edu id AA13321 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 14 Aug 90 18:49:16 -0500 Message-Id: <9008142349.AA13321@yoda.ncsa.uiuc.edu> Date: Thu, 9 Aug 90 17:38:55 CDT From: johnsonj@phobos.mathcs.carleton.edu To: mathgroup@yoda.ncsa.uiuc.edu Subject: Is N[10^-11,16] = a. 99999999999999e-12 a known bug? Status: RO There is a curious bug in the N[] function, involving (as far as I can tell) only calculations at sixteen decimal places. I did a quick check with Table[Table[{i, j, N[10^-i, j]}, {j, 1, 2 * i}], {i, 1, 50}] and got errors for i = {11, 20, 25, 32, 36, 40}, all at i = 16. Is this a bug in the most recent release? (If so, better let Wolfram know!) Also, is there a way around it besides avoiding the use of sixteen? It just so happens that CForm[N[x, 16]] is absolutely ideal for sending data to a C program with double precision reals... Jonathan johnsonj@mathcs.carleton.edu Mathematica user Mike Tie, mtie@mathcs.carleton.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Aug 14 21:41:29 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA13584 (5.64+/IDA-1.3.4 for stevec); Tue, 14 Aug 90 21:41:27 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA07785; Tue, 14 Aug 90 21:39:43 CDT Received: by yoda.ncsa.uiuc.edu id AA13341 (5.64+/IDA-1.3.4 for ); Tue, 14 Aug 90 18:49:51 -0500 Received: by yoda.ncsa.uiuc.edu id AA13337 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 14 Aug 90 18:49:50 -0500 Message-Id: <9008142349.AA13337@yoda.ncsa.uiuc.edu> Date: Tue, 14 Aug 90 14:09:56 EDT From: dmg@dash.mitre.org (David M Goblirsch) To: steve@yoda.ncsa.uiuc.edu Subject: Mathematica Status: RO [If you are interested in the applications in the message below, please contact the sender. -smc] Hello, Your name was given to me by Dr. Richard Fateman at Berkeley. He said that you had been helpful to him in locating Mathematica libraries. My personal interest is in signal processing; in particular, speech coding and processing. I am not really looking for packages; I have written much of what I need myself. My goal is to find out who else is writing Mathematica stuff for speech/signal processing who might want to share ideas. Do you know of anyone? Perhaps yourself? Thanks for your time. David M. Goblirsch dmgob@mitre.org (703) 883-5450 The MITRE Corporation Washington C3I Division 7525 Colshire Drive McLean, VA 22102-3481 From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Aug 14 21:54:06 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA13618 (5.64+/IDA-1.3.4 for stevec); Tue, 14 Aug 90 21:54:05 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA08025; Tue, 14 Aug 90 21:52:22 CDT Received: by yoda.ncsa.uiuc.edu id AA13330 (5.64+/IDA-1.3.4 for ); Tue, 14 Aug 90 18:49:25 -0500 Received: by yoda.ncsa.uiuc.edu id AA13326 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 14 Aug 90 18:49:24 -0500 Message-Id: <9008142349.AA13326@yoda.ncsa.uiuc.edu> Date: Fri, 10 Aug 90 13:39:31 MDT From: smithw@mathnx.byu.edu (William V. Smith) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Bug in Integrate? Status: RO This problem came up in some instructional materials being developed here. If any of you know what's going on here let me know. I told the person who handed it to me, that it might be related to the rather awkward way Mathematica handles square roots. So, try doing this integration problem: In[1]:= a Integrate[Sqrt[(1-Cos[theta])^2+Sin[theta]^2],{theta,0,2 Pi}] Out[1]:= 0 (*this is incorrect*) In[2]:= a NIntegrate[Sqrt[(1-Cos[theta])^2+Sin[theta]^2],{theta,0,2 Pi}] Out[2]:= 8. a (*this is correct*) Date: Fri, 10 Aug 90 23:24:01 MDT From: smithw@mathnx.byu.edu (William V. Smith) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Another mathematica bug? Whoops! I just got a chance to look at this one again and it appears that NEITHER Integrate nor NIntegrate give the correct answer. I get 4aSqrt[2] working it out by hand. Sorry about that. Its been a busy day. Somebody want to check this? From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Aug 15 19:50:31 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA15019 (5.64+/IDA-1.3.4 for stevec); Wed, 15 Aug 90 19:50:29 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA22003; Wed, 15 Aug 90 19:48:46 CDT Received: by yoda.ncsa.uiuc.edu id AA14931 (5.64+/IDA-1.3.4 for ); Wed, 15 Aug 90 18:17:47 -0500 Received: by yoda.ncsa.uiuc.edu id AA14927 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Wed, 15 Aug 90 18:17:46 -0500 Message-Id: <9008152317.AA14927@yoda.ncsa.uiuc.edu> Date: Wed, 15 Aug 90 16:01:35 CDT From: johnsonj@phobos.mathcs.carleton.edu To: mathgroup@yoda.ncsa.uiuc.edu Subject: The N[10^-11,16] bug: machine and version information Status: RO You responded to my original question with a counter question: "What machine and what version...?" GOOD question. I am using Mathematica on the NeXT, NeXT Release 1.0 (Kernel version 1.2, Front End version 1.2). I apologize for the oversight. From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Aug 15 20:54:22 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA15145 (5.64+/IDA-1.3.4 for stevec); Wed, 15 Aug 90 20:54:20 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA22993; Wed, 15 Aug 90 20:52:37 CDT Received: by yoda.ncsa.uiuc.edu id AA14936 (5.64+/IDA-1.3.4 for ); Wed, 15 Aug 90 18:17:55 -0500 Received: by yoda.ncsa.uiuc.edu id AA14932 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Wed, 15 Aug 90 18:17:53 -0500 Message-Id: <9008152317.AA14932@yoda.ncsa.uiuc.edu> From: wri!pea@uunet.uu.net Date: Wed, 15 Aug 90 17:09:52 CDT To: mathgroup@yoda.ncsa.uiuc.edu Subject: Position Available Status: RO SOFTWARE QUALITY ASSURANCE MANAGER Wolfram Research, Inc. is the developer of Mathematica, a system for doing mathematics by computer. We have an opening for a Software Quality Assurance Manager to further develop and implement a software quality assurance plan. This position requires a mathematics/computer science background, and 2-5 years experience with a software company. Management and previous SQA experience are preferred. Wolfram Research, Inc. is located in Champaign, Illinois, and currently has over 100 employees. For consideration, send resume to: Wolfram Research, Inc. 100 Trade Center Drive Champaign, IL 61820 FAX: 217-398-0747 Email: resumes@wri.com From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Aug 16 00:33:50 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA16221 (5.64+/IDA-1.3.4 for stevec); Thu, 16 Aug 90 00:33:49 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA26918; Thu, 16 Aug 90 00:32:03 CDT Received: by yoda.ncsa.uiuc.edu id AA15268 (5.64+/IDA-1.3.4 for ); Wed, 15 Aug 90 21:38:04 -0500 Received: by yoda.ncsa.uiuc.edu id AA15264 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Wed, 15 Aug 90 21:38:02 -0500 Message-Id: <9008160238.AA15264@yoda.ncsa.uiuc.edu> Date: Wed, 15 Aug 90 10:32:05 PDT From: decide!bobk@uunet.UU.NET (Bob Korsan) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Bug in Integrate? Status: RO You write ----- Begin Included Message ----- >From saxony!uunet!yoda.ncsa.uiuc.edu!mathgroup-adm Tue Aug 14 20:59:55 1990 From: uunet!mathnx.byu.edu!smithw (William V. Smith) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Bug in Integrate? This problem came up in some instructional materials being developed here. If any of you know what's going on here let me know. I told the person who handed it to me, that it might be related to the rather awkward way Mathematica handles square roots. So, try doing this integration problem: In[1]:= a Integrate[Sqrt[(1-Cos[theta])^2+Sin[theta]^2],{theta,0,2 Pi}] Out[1]:= 0 (*this is incorrect*) In[2]:= a NIntegrate[Sqrt[(1-Cos[theta])^2+Sin[theta]^2],{theta,0,2 Pi}] Out[2]:= 8. a (*this is correct*) Date: Fri, 10 Aug 90 23:24:01 MDT From: smithw@mathnx.byu.edu (William V. Smith) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Another mathematica bug? Whoops! I just got a chance to look at this one again and it appears that NEITHER Integrate nor NIntegrate give the correct answer. I get 4aSqrt[2] working it out by hand. Sorry about that. Its been a busy day. Somebody want to check this? ----- End Included Message ----- Well, you are correct, the trouble is with Sqrt. If you look at the integrand and simplify In[1]:=Simplify[Sqrt[(1-Cos[t])^2+Sin[t]^2]/.Sin[t]^2->1-Cos[t]^2] Out[1]:=Sqrt[2 - 2 Cos[t]] and then In[2]:=Integrate[Sqrt[1-Cos[t]],t] Out[2]:= -2 Sqrt[2] ----------------------- 2 Sin[t] Sqrt[1 + -------------] 2 (1 + Cos[t]) If you plot this you will notice that since Mathematica always (EVEN WHEN IT SHOULDN'T) takes the positive square root, the result is always negative in the interval [0,2Pi]. Thus, the integrand evaluated at both end points is the same and subtracts to zero. This is a MAJOR BUG in version 1.2.1 and should be corrected immediately. Peace/Bob =============================================================================== | "The range of what we think and do | Bob Korsan | | is limited by what we fail to notice. | Decisions, Decisions! | | And because we fail to notice that we | 2136 Lyon Avenue | | fail to notice there is little we can | Belmont, CA 94002-1639 | | do to change until we notice how | 1(415) 595-1206 | | failing to notice shapes our thoughts | bobk@decide.UUCP | | and deeds." | korsan@pa.reuter.com | | -- R. D. Laing | {sun,uunet}!saxony!decide!bobk | =============================================================================== From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Aug 16 05:03:21 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA16510 (5.64+/IDA-1.3.4 for stevec); Thu, 16 Aug 90 05:03:19 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA03336; Thu, 16 Aug 90 05:01:38 CDT Received: by yoda.ncsa.uiuc.edu id AA16469 (5.64+/IDA-1.3.4 for ); Thu, 16 Aug 90 03:19:43 -0500 Received: by yoda.ncsa.uiuc.edu id AA16465 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Thu, 16 Aug 90 03:19:41 -0500 Message-Id: <9008160819.AA16465@yoda.ncsa.uiuc.edu> From: wri!ab@uunet.uu.net Date: Thu, 16 Aug 90 01:20:02 CDT To: mathgroup@yoda.ncsa.uiuc.edu Subject: N[10^-11,16] Status: RO Mathematica (sun4) 2.0pre-alpha (August 15, 1990) Copyright 1988,1989,1990 Wolfram Research, Inc. In[3]:= N[10^-11,16] -11 Out[3]= 1. 10 --------------- In[2]:= Table[Table[{i, j, N[10^-i, j]}, {j, 1, 2 * i}], {i, 1, 50}] Produced a long long output where everything was OK. From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Aug 16 05:55:53 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA16574 (5.64+/IDA-1.3.4 for stevec); Thu, 16 Aug 90 05:55:51 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA04167; Thu, 16 Aug 90 05:54:10 CDT Received: by yoda.ncsa.uiuc.edu id AA16477 (5.64+/IDA-1.3.4 for ); Thu, 16 Aug 90 03:20:35 -0500 Received: by yoda.ncsa.uiuc.edu id AA16473 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Thu, 16 Aug 90 03:20:34 -0500 Message-Id: <9008160820.AA16473@yoda.ncsa.uiuc.edu> To: mathgroup@yoda.ncsa.uiuc.edu Subject: PointSize Problem Date: Thu, 16 Aug 90 17:26:39 +1000 From: Peter Horan Status: RO I got no reaction to ERROR #2 last week: >Subject: Mathematica Errors 386 version 1.2 >ERROR #1: [ This one deleted. Referred to an error in hardcopy. ] >ERROR #2: >When I do ListPlot[] points are not displayed unless >PointSize -> 0.03 or larger. e.g. >ListPlot[Point[{{x1, y1},{x2, y2},....}]] does not appear. The >axes are correct if they are turned on. Similarly, >ListPlot[Line[......]] works. Peter Horan peter@aragorn.cm.deakin.oz From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Aug 16 16:05:40 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA17070 (5.64+/IDA-1.3.4 for stevec); Thu, 16 Aug 90 16:05:38 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA19234; Thu, 16 Aug 90 16:03:56 CDT Received: by yoda.ncsa.uiuc.edu id AA17017 (5.64+/IDA-1.3.4 for ); Thu, 16 Aug 90 14:28:42 -0500 Received: by yoda.ncsa.uiuc.edu id AA17013 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Thu, 16 Aug 90 14:28:41 -0500 Message-Id: <9008161928.AA17013@yoda.ncsa.uiuc.edu> Date: Thu, 16 Aug 90 14:12:17 -0400 From: blachman%gtewd.dnet@gte.com (NELSON M. BLACHMAN) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Bug in Integrate? Status: RO Using the well knwon formula for the sine of half of an angle, I notice that Integrate[ Sqrt[(1 - Cos[theta])^2 + Sin[theta]^2 ], {theta, 0, 2 Pi}] = Integrate[ Sqrt[2 - 2 Cos[theta] ], {theta, 0, 2 Pi}] = Integrate[ 2 Sin[theta/2], {theta, 0, 2 Pi}] = Integrate[ 4 Sin[theta/2], {theta/2, 0, Pi}] = Integrate[ 4 Sin[phi], {phi, 0, Pi}] = -4 Cos[Pi] + 4 Cos[0] = 8 . There seems to be nothing wrong with NIntegrate. Why does Integrate get the value 0?? It's troubles could be sured by a high-school course in trigonometry so that it might carry out the foregoing simplification. A different problem: We recently got VAX-VMS Mathematica but haven't figured out yet how to get its Edit...[ ] features to work; the suggestions in the User's Guide regarding assigning EDITOR the value EDIT/EDT, etc., don't succeed. Nelson M. Blachman blachman%gtewd.dnet@gte.com GTE Government Systems Corp. Mountain View, California From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Aug 16 23:47:04 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA17366 (5.64+/IDA-1.3.4 for stevec); Thu, 16 Aug 90 23:47:02 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA26156; Thu, 16 Aug 90 23:45:21 CDT Received: by yoda.ncsa.uiuc.edu id AA17337 (5.64+/IDA-1.3.4 for ); Thu, 16 Aug 90 21:13:33 -0500 Received: by yoda.ncsa.uiuc.edu id AA17333 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Thu, 16 Aug 90 21:13:32 -0500 Message-Id: <9008170213.AA17333@yoda.ncsa.uiuc.edu> Date: Thu, 16 Aug 90 16:22:14 PDT From: eran@THSUN1.SLAC.STANFORD.EDU Subject: Mathematica Help Package To: mathgroup@yoda.ncsa.uiuc.EDU Status: RO Variable Symbols Inc. has just completed the development of Mathematica Package that extends the on-line help facilities of Mathematica. The package is designed to run under Unix. The package provides, among other things, 1) Complete categorization of the built-in commands in Mathematica 2) For each built-in command in Mathematica: a) Extended usage message b) Example(s) of usage c) Reference to related commands d) Templates for using the command 3) Support for user notes The package uses the same information provided by our HyperCard based Mathematica Help Stack. We are now looking for people to beta-test the package. Ready for beta testing is the information relating to all the built-in Mathematica commands starting with the letters A-C. Additional sections of the Help Package will be made available to beta-testers in the near future. If you are interested, please answer the enclosed questionnaire, and send to eran@thsun1.slac.stanford.edu ------------------------------------------------------------------------------- 1) How long have you been using Mathematica a) Less than a week b) A week to a month c) A month to 3 months d) 3 months to a year e) More than a year 2) How much do you use Mathematica a) Less than two hours a week b) 2 to 8 hours a week c) 8 to 24 hours a week d) More than 24 hours a week 3) If you have used Mathematica, what have you done with it? a) Used interactively (built-in functions only) b) Used interactively (built-in functions and bundled packages) c) Written your own functions d) Written your own packages/notebooks 4) At what level of expertise would you place yourself? a) Novice b) Intermediate c) Expert 5) What are the things you like best about Mathematica? 6) What are the things you like least about Mathematica? 7) On what platform do you usually run Mathematica? a) Computer make and model? b) Memory? c) Hard-drive (how much free space is available now?) d) How many other users are typically using the same system? 8) Who paid for the Mathematica you are currently using? a) Contributed b) You personally c) A work-place budget controlled by you personally d) A departmental budget e) An institution-wide budget f) Bundled (NeXT or Apollo) 9) How much (to your knowledge) was paid for the copy of Mathematica you are usually using? 10) If the help package was to suit your needs IDEALLY, how much, in your estimate, would people around you be willing to pay for it? a) Less than $50 a) $50-$100 b) $100-$250 c) $250-$400 d) More than $400 11) What is your field of work? 12) What type of institute do you usually use Mathematica in? a) Privately b) University (student) c) University (faculty or staff) d) Government research institute e) Private company 13) How many people in your company/department use Mathematica? 14) What features would you like to see in a help package? 15) How much time do you anticipate being able to dedicate to beta testing? a) For initial study? b) As part of your everyday use of Mathematica? 16) Would you be interested in information about Variable Symbols Inc., its products and services? 17) Anything else you wanted to tell us? From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Aug 21 02:36:03 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA00998 (5.64+/IDA-1.3.4 for stevec); Tue, 21 Aug 90 02:36:01 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA15317; Tue, 21 Aug 90 02:34:26 CDT Received: by yoda.ncsa.uiuc.edu id AA00934 (5.64+/IDA-1.3.4 for ); Tue, 21 Aug 90 01:18:19 -0500 Received: by yoda.ncsa.uiuc.edu id AA00930 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 21 Aug 90 01:18:17 -0500 Message-Id: <9008210618.AA00930@yoda.ncsa.uiuc.edu> Date: Mon, 20 Aug 90 17:48:34 CDT From: John Mitchell To: mathgroup@yoda.ncsa.uiuc.edu Subject: Possible Collect bug Status: RO I would like to relate a recent calculation I ran across which I believe represents a bug in Mathematica 1.2.1 (Macintosh II version). I have not seen this bug reported elsewhere, but it may have been. The sample ouput below shows a comparison of Collect with Factor on what seems like a straightforward expression. Note, however, that two different answers result. I would appreciate anyone's comments on this. (Note that this output has been "cut and pasted" from Mathematica into a word-processing program before transfer, explaining the missning In[##] and Out[##] ) expr = -((-1)^(2n) y^2)/8 - ((-1)^(-1 + 2n) y^2)/8 + ((-1)^(1 + 2n) y^2)/8 2 n 2 -1 + 2 n 2 1 + 2 n 2 -((-1) y ) (-1) y (-1) y ------------- - ----------------- + ----------------- 8 8 8 Collect[expr,y] 2 n 2 -3 (-1) y ------------- 8 (* This is incorrect *) Factor[expr] 2 n 2 -((-1) y ) ------------- 8 (* This is correct *) ***************************** John Mitchell Univ. of Chicago 5735 South Ellis Ave. Chicago, IL 60637 (312) 702-7253 mitchell@pico.uchicago.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Aug 23 21:22:52 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA03436 (5.64+/IDA-1.3.4 for stevec); Thu, 23 Aug 90 21:22:50 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA07533; Thu, 23 Aug 90 21:21:16 CDT Received: by yoda.ncsa.uiuc.edu id AA03355 (5.64+/IDA-1.3.4 for ); Thu, 23 Aug 90 20:17:26 -0500 Received: by yoda.ncsa.uiuc.edu id AA03351 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Thu, 23 Aug 90 20:17:25 -0500 Message-Id: <9008240117.AA03351@yoda.ncsa.uiuc.edu> To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Possible Collect bug Date: Thu, 23 Aug 90 13:33:02 +1000 From: Peter Horan Status: RO Fcc: - - -------- Re: 2 n 2 -1 + 2 n 2 1 + 2 n 2 -((-1) y ) (-1) y (-1) y ------------- - ----------------- + ----------------- 8 8 I got the same incorrect result on a 386 Compatible. I traced it to the middle term which lost a minus sign Collect[((-1)^(-1+2 n) y^2, y] gives 2 n 2 (-1) y ------------ Wrong sign. 8 Peter Horan peter@aragorn.cm.deakin.oz From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Aug 23 22:17:36 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA03504 (5.64+/IDA-1.3.4 for stevec); Thu, 23 Aug 90 22:17:35 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA08346; Thu, 23 Aug 90 22:16:03 CDT Received: by yoda.ncsa.uiuc.edu id AA03370 (5.64+/IDA-1.3.4 for ); Thu, 23 Aug 90 20:17:53 -0500 Received: by yoda.ncsa.uiuc.edu id AA03366 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Thu, 23 Aug 90 20:17:51 -0500 Message-Id: <9008240117.AA03366@yoda.ncsa.uiuc.edu> Subject: Plotting Experimental Data To: att!mathgroup Date: Tue, 21 Aug 90 11:27:05 EDT From: Avi Y. Feldblum Status: RO Hello all, I am a novice Mathematica user, and could use some help from some of you more experienced users out there. Here is what I am trying to do: I have a file which contains experimental data that I've taken. I have a mathematical function that I wish to compare and fit the data to. I can read in the data from the file into a list. I've defined the function, and can display a graph of the function. My problem (currently) is how to plot the data. The x-values are N*(step variable), the y-values are from the data file. I can generate a list of each, but I don't know how to generate the form {{x1,y1},{x2,y2},..} that I think I need to plot the data. I am running on a MacIIcx. If anyone has Mathematica Notebook examples that do anything like this I would appreciate it. If anyone is willing to answer simple questions by email or phone, please let me know. Thanks in advance for any help. -- Avi Feldblum ayf@pruxk.att.com or avi_feldblum@att.com 609-639-2474 From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Aug 23 23:04:56 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA03694 (5.64+/IDA-1.3.4 for stevec); Thu, 23 Aug 90 23:04:54 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA09096; Thu, 23 Aug 90 23:03:14 CDT Received: by yoda.ncsa.uiuc.edu id AA03365 (5.64+/IDA-1.3.4 for ); Thu, 23 Aug 90 20:17:45 -0500 Received: by yoda.ncsa.uiuc.edu id AA03361 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Thu, 23 Aug 90 20:17:43 -0500 Message-Id: <9008240117.AA03361@yoda.ncsa.uiuc.edu> Date: Tue, 21 Aug 90 13:25:00 -0400 From: fink@acf5.NYU.EDU (Howard Fink) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Possible Collect bug II Status: RO The following are the findings of John Mitchell reporting to mathgroup August 21. expr = -((-1)^(2n) y^2)/8 - ((-1)^(-1 + 2n) y^2)/8 + ((-1)^(1 + 2n) y^2)/8 2 n 2 -1 + 2 n 2 1 + 2 n 2 -((-1) y ) (-1) y (-1) y ------------- - ----------------- + ----------------- 8 8 8 Collect[expr,y] 2 n 2 -3 (-1) y ------------- 8 (* This is incorrect *) Factor[expr] 2 n 2 -((-1) y ) ------------- 8 (* This is correct *) ***************************** John Mitchell Univ. of Chicago 5735 South Ellis Ave. Chicago, IL 60637 (312) 702-7253 mitchell@pico.uchicago.edu *********************************** I tried a few things and found this: FixedPoint[Simplify, (expr - Simplify[expr])] 0 FixedPoint[Simplify, (expr - Collect[expr,y])] 2 n 2 (-1) y ------------ 4 *********************************** Howard Fink fink@acf5.nyu.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Aug 23 23:18:24 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA03720 (5.64+/IDA-1.3.4 for stevec); Thu, 23 Aug 90 23:18:23 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA09343; Thu, 23 Aug 90 23:16:51 CDT Received: by yoda.ncsa.uiuc.edu id AA03360 (5.64+/IDA-1.3.4 for ); Thu, 23 Aug 90 20:17:37 -0500 Received: by yoda.ncsa.uiuc.edu id AA03356 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Thu, 23 Aug 90 20:17:36 -0500 Message-Id: <9008240117.AA03356@yoda.ncsa.uiuc.edu> Subject: Need help with creating a List To: mathgroup@yoda.ncsa.uiuc.edu (Mathematica Mailing List) Date: Wed, 22 Aug 90 12:57:13 EDT From: Avi Y. Feldblum Status: RO I am having some trouble with creating a list for plotting with ListPlot. As I understand it, what is needed is a list of lists, where each element of the main list is a list of two values, the x and y positions to be plotted. In my case, the x values are just a set of evenly spaced values, while the y values are the difference between some data I have and a functional form for the data. What I have is: func[x_] = "some long function" The data is in a list called "data" diff[x_] := data[[x]] - func[.05x] difftable = Table[ {.05i, diff[i]}, {i, Length[data]} ] My problem is the output of difftable. It looks like: {{.05, {value1}}, {.01, {value2}}, ....} What it needs to be for ListPlot to work (I think) is: {{.05, value1}, {.01, value2}, ....} I tried to make a test file with a simple func[x_] and just put in some datapoints, and there it did work. So I'm confused as to when and why mathematica is giving me {{xval1,yval1},{xval2,yval2}, ..} in one case and {{xval1,{yval1}}, {xval2,{yval2}}, ..} in the other case. Any ideas or suggestions? -- Avi Feldblum ayf@pruxk.att.com or avi_feldblum@att.com From wri!pea@uunet.UU.NET Fri Aug 24 11:30:28 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA04693 (5.64+/IDA-1.3.4 for stevec); Fri, 24 Aug 90 11:30:26 -0500 Return-Path: Received: from uunet.uu.net by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA25220; Fri, 24 Aug 90 11:31:02 CDT Received: from wri.UUCP by uunet.uu.net (5.61/1.14) with UUCP id AA25166; Fri, 24 Aug 90 12:30:33 -0400 From: wri!pea@uunet.uu.net Received: by WRI.com (3.2/SMI-3.0DEV3) id AA13461; Fri, 24 Aug 90 11:28:26 CDT Message-Id: <9008241628.AA13461@WRI.com> Date: Fri, 24 Aug 90 11:28:23 CDT To: steve@ncsa.uiuc.edu Subject: Mathematica Graphics Competition Cc: joe@uunet.UU.NET, pea@uunet.UU.NET Status: RO ***************************************************************************** ** ** ** Mathematica Graphics Competition Deadline ** ** Extended To October 6, 1990 ** ** ** ***************************************************************************** Wolfram Research Sponsors Mathematica Graphics Competition The Competition Wolfram Research, Inc. is sponsoring a competition to recognize outstanding graphics generated with Mathematica in 1990. Graphics can be two- or three-dimensional, black-and-white or color, abstract or representational. The only criterion is that they be produced with Mathematica. Entries will be judged by an independent panel of leading designers and Mathematica users. Winning entries will be published in the full-color 1991 Mathematica Calendar and may be included in other Mathematica material. Competition prizes will include $1,000 for first place and free registration at the second annual Mathematica Conference in San Francisco, January 1991. All entries will be acknowledged, and all entrants will receive a complimentary gift. The Rules All entries must be received by October 6, 1990 Entries must be submitted as Mathematica Notebooks or PostScript files. Electronic mail, or any standard disk or tape format is acceptable. All disks or tapes must be labeled with your name and title of work. Media will not be returned. Each entry must be accompanied by a separate entry form (or facsimile), and must include a short description of how it was produced. Give Mathematica code when possible. By submitting an entry to the competition, you are warranting that you are the owner of all rights associated with the entry, and you are granting to Wolfram Research the nonexclusive right to publish or exhibit your entry in any way. Employees of Wolfram Research and their relatives are not eligible to participate. Send entries to: Mathematica Graphics Competition Wolfram Research, Inc. P.O. Box 6059 Champaign, Illinois 61826-6059, USA Telephone: 217-398-0700 Fax: 217-398-0747 Email: competition@wri.com From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Aug 24 13:24:34 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA04807 (5.64+/IDA-1.3.4 for stevec); Fri, 24 Aug 90 13:24:32 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA27320; Fri, 24 Aug 90 13:22:59 CDT Received: by yoda.ncsa.uiuc.edu id AA04740 (5.64+/IDA-1.3.4 for ); Fri, 24 Aug 90 12:08:26 -0500 Received: by yoda.ncsa.uiuc.edu id AA04736 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 24 Aug 90 12:08:25 -0500 Message-Id: <9008241708.AA04736@yoda.ncsa.uiuc.edu> To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Possible Collect bug Date: Fri, 24 Aug 90 07:54:41 -0500 From: mds@mark.stat.purdue.edu Status: RO If I understand the recent messages from Howard Fink , Peter Horan , and John Mitchell ,and am not confused now :-), below is a simple example demonstrating a problem with the Collect[] function. Mathematica (sun3.fpa) 1.2 (November 6, 1989) [With pre-loaded data] In[1]:= Collect[(-1)^(-1+2n),x] (* note no x in first argument *) 2 n Out[1]= (-1) Mark Senn Purdue University mds@pop.stat.purdue.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Aug 24 14:30:09 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA04924 (5.64+/IDA-1.3.4 for stevec); Fri, 24 Aug 90 14:30:07 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA28653; Fri, 24 Aug 90 14:28:36 CDT Received: by yoda.ncsa.uiuc.edu id AA04735 (5.64+/IDA-1.3.4 for ); Fri, 24 Aug 90 12:08:18 -0500 Received: by yoda.ncsa.uiuc.edu id AA04731 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 24 Aug 90 12:08:17 -0500 Message-Id: <9008241708.AA04731@yoda.ncsa.uiuc.edu> From: wri!pea@uunet.uu.net Date: Fri, 24 Aug 90 11:28:23 CDT To: mathgroup@yoda.ncsa.uiuc.edu Subject: Mathematica Graphics Competition Status: RO ***************************************************************************** ** ** ** Mathematica Graphics Competition Deadline ** ** Extended To October 6, 1990 ** ** ** ***************************************************************************** Wolfram Research Sponsors Mathematica Graphics Competition The Competition Wolfram Research, Inc. is sponsoring a competition to recognize outstanding graphics generated with Mathematica in 1990. Graphics can be two- or three-dimensional, black-and-white or color, abstract or representational. The only criterion is that they be produced with Mathematica. Entries will be judged by an independent panel of leading designers and Mathematica users. Winning entries will be published in the full-color 1991 Mathematica Calendar and may be included in other Mathematica material. Competition prizes will include $1,000 for first place and free registration at the second annual Mathematica Conference in San Francisco, January 1991. All entries will be acknowledged, and all entrants will receive a complimentary gift. The Rules All entries must be received by October 6, 1990 Entries must be submitted as Mathematica Notebooks or PostScript files. Electronic mail, or any standard disk or tape format is acceptable. All disks or tapes must be labeled with your name and title of work. Media will not be returned. Each entry must be accompanied by a separate entry form (or facsimile), and must include a short description of how it was produced. Give Mathematica code when possible. By submitting an entry to the competition, you are warranting that you are the owner of all rights associated with the entry, and you are granting to Wolfram Research the nonexclusive right to publish or exhibit your entry in any way. Employees of Wolfram Research and their relatives are not eligible to participate. Send entries to: Mathematica Graphics Competition Wolfram Research, Inc. P.O. Box 6059 Champaign, Illinois 61826-6059, USA Telephone: 217-398-0700 Fax: 217-398-0747 Email: competition@wri.com From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Aug 24 15:29:26 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA05050 (5.64+/IDA-1.3.4 for stevec); Fri, 24 Aug 90 15:29:24 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA00154; Fri, 24 Aug 90 15:27:53 CDT Received: by yoda.ncsa.uiuc.edu id AA04871 (5.64+/IDA-1.3.4 for ); Fri, 24 Aug 90 13:58:23 -0500 Received: by yoda.ncsa.uiuc.edu id AA04867 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 24 Aug 90 13:58:21 -0500 Message-Id: <9008241858.AA04867@yoda.ncsa.uiuc.edu> Date: Fri, 24 Aug 90 10:40:23 PDT From: don@kinghorn.chem.WSU.EDU (Don Kinghorn) Subject: Re:Need help with creating a List To: mathgroup@yoda.ncsa.uiuc.edu (Mathematica Mailing List) Status: RO Begin recieved message: ************************************************************************************ . . . I am having some trouble with creating a list for plotting with ListPlot. As I understand it, what is needed is a list of lists, where each element of the main list is a list of two values, the x and y positions to be plotted. In my case, the x values are just a set of evenly spaced values, while the y values are the difference between some data I have and a functional form for the data. What I have is: func[x_] = "some long function" The data is in a list called "data" diff[x_] := data[[x]] - func[.05x] difftable = Table[ {.05i, diff[i]}, {i, Length[data]} ] My problem is the output of difftable. It looks like: {{.05, {value1}}, {.01, {value2}}, ....} What it needs to be for ListPlot to work (I think) is: {{.05, value1}, {.01, value2}, ....} I tried to make a test file with a simple func[x_] and just put in some datapoints, and there it did work. So I'm confused as to when and why mathematica is giving me {{xval1,yval1},{xval2,yval2}, ..} in one case and {{xval1,{yval1}}, {xval2,{yval2}}, ..} in the other case. Any ideas or suggestions? --Avi Feldblum ayf@pruxk.att.com or avi_feldblum@att.com *********************************************************************************** Look at your y data. I suspect that its in the form of a list of lists ( an nx1 matrix) and as a result your function diff is returning a vector. Try applying Flatten[] to your y data to put it in the form {y1,y2,y3, . . .}. This should give the result you want. Example: In[1]:= data=Transpose[{{1,2,3,4}}] Out[1]= {{1}, {2}, {3}, {4}} In[2]:= fcn[x_] := x-1/2 In[3]:= dif[x_] := data[[x]]-fcn[.05x] In[4]:= Table[{.05i,dif[i]},{i,Length[data]}] Out[4]= {{0.05, {1.45}}, {0.1, {2.4}}, {0.15, {3.35}}, {0.2, {4.3}}} In[5]:= data = Flatten[data] Out[5]= {1, 2, 3, 4} In[6]:= Table[{.05i,dif[i]},{i,Length[data]}] Out[6]= {{0.05, 1.45}, {0.1, 2.4}, {0.15, 3.35}, {0.2, 4.3}} I hope this helps. (this is only one of many possible solutions) Don Kinghorn From mathgroup-adm@yoda.ncsa.uiuc.edu Sun Aug 26 00:31:22 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA07256 (5.64+/IDA-1.3.4 for stevec); Sun, 26 Aug 90 00:31:20 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA06278; Sun, 26 Aug 90 00:29:51 CDT Received: by yoda.ncsa.uiuc.edu id AA06536 (5.64+/IDA-1.3.4 for ); Sat, 25 Aug 90 23:14:24 -0500 Received: by yoda.ncsa.uiuc.edu id AA06532 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Sat, 25 Aug 90 23:14:22 -0500 Message-Id: <9008260414.AA06532@yoda.ncsa.uiuc.edu> To: mathgroup@yoda.ncsa.uiuc.edu Subject: Graphics primitives Date: Fri, 24 Aug 90 15:53:28 PDT From: jacobson@cello.hpl.hp.com Status: RO I'm trying to make Mathematica draw custom error-bars for statistical data. The problem is that I can't figure out how to make Mathematica draw little lines for ticks at the confidence limits, etc. I want the *position* to be in application coordinates, but the length of the ticks to be in terms of the width of the plot. I figured if I could track down how Mathematica does axes, I'd be able to figure out what I want, but the axes code seems to be hidden from users. -- David Jacobson From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Aug 28 11:46:39 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA09476 (5.64+/IDA-1.3.4 for stevec); Tue, 28 Aug 90 11:46:37 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA27964; Tue, 28 Aug 90 11:44:26 CDT Received: by yoda.ncsa.uiuc.edu id AA09357 (5.64+/IDA-1.3.4 for ); Tue, 28 Aug 90 10:18:11 -0500 Received: by yoda.ncsa.uiuc.edu id AA09353 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 28 Aug 90 10:18:10 -0500 Message-Id: <9008281518.AA09353@yoda.ncsa.uiuc.edu> Date: Tue, 28 Aug 90 09:37:42 CDT From: carl@crazyman.med.ge.com (Carl Crawford) To: mathgroup@yoda.ncsa.uiuc.edu Subject: eqn and tex Status: RO does anyone have a filter to convert mathematica's tex output to eqn? Carl R. Crawford, Ph.D. Voice: 414-521-6572 GE Medical Systems Fax: 414-521-6575 P.O. Box 414, W-875 Uucp: {sun!sunbird,uunet!crdgw1}!gemed!carl Milwaukee, WI 53201 Internet: carl@gemed.ge.com From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Aug 30 22:29:28 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA12216 (5.64+/IDA-1.3.4 for stevec); Thu, 30 Aug 90 22:29:26 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA12028; Thu, 30 Aug 90 22:27:21 CDT Received: by yoda.ncsa.uiuc.edu id AA12097 (5.64+/IDA-1.3.4 for ); Thu, 30 Aug 90 21:05:19 -0500 Received: by yoda.ncsa.uiuc.edu id AA12093 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Thu, 30 Aug 90 21:05:18 -0500 Message-Id: <9008310205.AA12093@yoda.ncsa.uiuc.edu> Date: Thu, 30 Aug 90 15:58 EDT From: PMCGUIRE@coral.bucknell.edu Subject: Bug in Plot To: mathgroup@yoda.ncsa.uiuc.edu Status: RO Has anyone else noticed the plethora of vertical lines that occurs when Mathematica executes the command Plot[x/x,{x,1,2}] or similar plots? This problem seems to be machine independent. I have tried it on a MacIIcx and an IBM 386 machine with the same result. Does anyone have an explanation? From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Aug 30 23:28:55 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA12301 (5.64+/IDA-1.3.4 for stevec); Thu, 30 Aug 90 23:28:53 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA12965; Thu, 30 Aug 90 23:26:48 CDT Received: by yoda.ncsa.uiuc.edu id AA12102 (5.64+/IDA-1.3.4 for ); Thu, 30 Aug 90 21:05:26 -0500 Received: by yoda.ncsa.uiuc.edu id AA12098 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Thu, 30 Aug 90 21:05:25 -0500 Message-Id: <9008310205.AA12098@yoda.ncsa.uiuc.edu> Date: Thu, 30 Aug 90 13:23:37 PDT From: limes@cs.nps.navy.mil (Robert Limes x3216) To: mathgroup@yoda.ncsa.uiuc.edu Subject: mathematica Status: RO Steve Christianson: I am searching for printer drivers for Mathematica graphics output ... specifically for HP LJ and HP pen-plotters. Wolfram can not help us; they suggested I try to contact you. Bob Limes Dept. of Electrical and Computer Eng. Naval Postgraduate School Monterey, CA 93943 (408) 646-3216 limes@cs.nps.navy.mil From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Aug 31 01:23:35 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA13228 (5.64+/IDA-1.3.4 for stevec); Fri, 31 Aug 90 01:23:33 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA16421; Fri, 31 Aug 90 01:21:26 CDT Received: by yoda.ncsa.uiuc.edu id AA12086 (5.64+/IDA-1.3.4 for ); Thu, 30 Aug 90 21:04:59 -0500 Received: by yoda.ncsa.uiuc.edu id AA12082 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Thu, 30 Aug 90 21:04:57 -0500 Message-Id: <9008310204.AA12082@yoda.ncsa.uiuc.edu> Date: Wed, 29 Aug 90 14:11:57 JST From: Hideaki Aoyama Subject: Mathematica To: mathgroup@yoda.ncsa.uiuc.edu Status: RO Dear Dir, I recently learned that you collect and distribute list of bugs in Mathematica. As its regular user, I would appreciate if you could add me to the mailing list. Although it helps my research a great deal, I suffer from its shortcomings, wasting a few hours at a time. A trouble I encountered recently; Integrate[2(1+E^(i p)), {p, 0, 2Pi}] You may have already known this. Mathematica does not know the right branch. Greetings, Hideaki Aoyama Associate Professor Physics Department College of Liberal Arts and Sciences Kyoto Univesity Yoshida, Kyoto 606, JAPAN tel: 075-753-6785 fax: 075-753-6804 From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Aug 31 01:32:01 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA13275 (5.64+/IDA-1.3.4 for stevec); Fri, 31 Aug 90 01:31:59 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA16502; Fri, 31 Aug 90 01:29:53 CDT Received: by yoda.ncsa.uiuc.edu id AA12081 (5.64+/IDA-1.3.4 for ); Thu, 30 Aug 90 21:04:53 -0500 Received: by yoda.ncsa.uiuc.edu id AA12077 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Thu, 30 Aug 90 21:04:51 -0500 Message-Id: <9008310204.AA12077@yoda.ncsa.uiuc.edu> Subject: oh come on!! To: mathgroup@yoda.ncsa.uiuc.edu (mathgroup for mathematica) Date: Tue, 28 Aug 90 19:06:03 PDT From: Steven Warwick Status: RO Another case of "does this make sense?" Let's experiment with Limit.... In[36]:= 1 + 1/(x+a) 1 Out[36]= 1 + - x In[37]:= Limit[%,x->Infinity] Out[37]= 1 ********* ho hum ********** In[38]:= 1 + 1/(1+a) 1 Out[38]= 1 + ----- 1 + x In[39]:= Limit[%,x->Infinity] Out[39]= 1 ************** yawn ********** In[42]:= 1 + 1/( x+a) 1 Out[42]= 1 + ----- a + x In[43]:= Limit[%,x->Infinity] Out[43]= 1 **************** zzzzzzz *********** In[45]:= 1 + 1/(b x) 1 Out[45]= 1 + ------- a + b x In[46]:= Limit[%,x->Infinity] 1 Out[46]= 1 + ---------------- ************** what???? ************* a + b (Infinity) *** so, maybe the multiplication's ** *** got mma upset ** In[47]:= 1 + 1/(b x) 1 Out[47]= 1 + --- b x In[48]:= Limit[%,x->Infinity] Out[48]= 1 ***** nope, just another one of those days **** Is there a consistantcy problem here, or is this just a new form of computer generated cream of wheat (with the lumps like mom used to make.. ) - Steven Warwick Hewlett-Packard sdw@hpsad From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Aug 31 00:55:34 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA13116 (5.64+/IDA-1.3.4 for stevec); Fri, 31 Aug 90 00:55:32 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA15598; Fri, 31 Aug 90 00:53:23 CDT Received: by yoda.ncsa.uiuc.edu id AA12091 (5.64+/IDA-1.3.4 for ); Thu, 30 Aug 90 21:05:04 -0500 Received: by yoda.ncsa.uiuc.edu id AA12087 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Thu, 30 Aug 90 21:05:03 -0500 Message-Id: <9008310205.AA12087@yoda.ncsa.uiuc.edu> To: mathgroup@yoda.ncsa.uiuc.edu Subject: Tick labels Date: Wed, 29 Aug 90 09:20:29 PDT From: jacobson@cello.hpl.hp.com Status: RO In Plot[], the default tick labels for the Y axis have the trailing zeros chopped off, then are right justified. Here is a tty picture of one I just did: 0.0175 + | 0.015 + | 0.0125 + | 0.01 + | 0.0075 + | 0.005 + | 0.0025 + | +-------... I'd much prefer a constant number of places past the decimal point. Or if not that, at least line the decimal points up. Does any one know how to make this happen? Thank you, -- David Jacobson From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Aug 31 02:28:12 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA13416 (5.64+/IDA-1.3.4 for stevec); Fri, 31 Aug 90 02:28:10 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA17504; Fri, 31 Aug 90 02:26:04 CDT Received: by yoda.ncsa.uiuc.edu id AA12076 (5.64+/IDA-1.3.4 for ); Thu, 30 Aug 90 21:04:47 -0500 Received: by yoda.ncsa.uiuc.edu id AA12072 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Thu, 30 Aug 90 21:04:45 -0500 Message-Id: <9008310204.AA12072@yoda.ncsa.uiuc.edu> Subject: consistantcy To: mathgroup@yoda.ncsa.uiuc.edu (mathgroup for mathematica) Date: Tue, 28 Aug 90 16:44:09 PDT From: Steven Warwick Status: RO This one really bugs me... I get the results of an expression of the form: I Sqrt[Pi] Out[]= ---------------------------------- 2 2 2 v /(s1 + s2 ) -2 -2 E Sqrt[-s1 - s2 ] I want to simplify it by giving the hint to pull oout -1 from the Sqrt.. In[] = % /. Sqrt[ -x1_ - x2_] -> I Sqrt[x1+x2] I get... No Change!!! After alot of soul searching, Fullform tells me that it's really not a Sqrt at all I'm looking at: Out[46]//FullForm= > Times[Complex[0, 1], Power[E, > Times[-1, Power[Plus[Power[s1, 2], Power[s2, 2]], -1], Power[v, 2]]], > Power[Pi, Rational[1, 2]], > Power[Plus[Times[-1, Power[s1, -2]], Times[-1, Power[s2, -2]]], > Rational[-1, 2]]] ^^^^^^^^^^^^^^^ it's a 1/Sqrt !!! so my match expression of the form: In[47]:= FullForm[Sqrt[ -x1_ - x2_]] Out[47]//FullForm= > Power[Plus[Times[-1, Pattern[x1, Blank[]]], > Times[-1, Pattern[x2, Blank[]]]], Rational[1, 2]] ^^^^^^^^^^^^^^ will not work.. This is totally non-intuitive. Let's try to coerce the Sqrt form to be positive rational in all cases!! In[59]:= Sqrt /: 1/Sqrt[x__] := (x^Rational[1, 2])^(-1) 1 TagSetDelayed::notag: Tag Sqrt not found in ---------. Sqrt[x__] 1 -1 Out[59]= Sqrt/: --------- := Sqrt[x] Sqrt[x__] ....nope.... O.K., how about Power??? In[] = Power /: 1/Sqrt[x_] := Power[Sqrt[x],-1] now try it: 1/Sqrt[y] Out[]//FullForm= Power[y, Rational[-1, 2]] ^^^^^^^^^^^^^^^^ Nope... I've tried everything I can think of to get Sqrt to give me positive rational powers but mathematica seems to say "no way" How about a more reasonable definition for us "Radical" pattern matchers! -- Steven Warwick Hewlett-Packard sdw@hpsad From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Aug 31 00:28:58 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA13077 (5.64+/IDA-1.3.4 for stevec); Fri, 31 Aug 90 00:28:56 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA15220; Fri, 31 Aug 90 00:26:49 CDT Received: by yoda.ncsa.uiuc.edu id AA12071 (5.64+/IDA-1.3.4 for ); Thu, 30 Aug 90 21:04:41 -0500 Received: by yoda.ncsa.uiuc.edu id AA12067 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Thu, 30 Aug 90 21:04:39 -0500 Message-Id: <9008310204.AA12067@yoda.ncsa.uiuc.edu> Subject: infix inputs To: mathgroup@yoda.ncsa.uiuc.edu (mathgroup for mathematica) Date: Tue, 28 Aug 90 11:06:55 PDT From: Steven Warwick Status: RO I want to define a function which has the characteristics of the "Or" or And semantics i.e. In[] = a ||| b ||| c Out[] = ..Something useful.. I can define a function, but I must use the tilde's to indicate that it's a function i.e. a ~|||~ b ~|||~ c but I can't seem to define a alias such that ||| maps into ~|||~ Clearly, mathematica has this ability since || exists so how do I get to do it too?? -- Steven Warwick Hewlett-Packard sdw@hpsad From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Aug 31 13:27:14 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA13816 (5.64+/IDA-1.3.4 for stevec); Fri, 31 Aug 90 13:27:12 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA00557; Fri, 31 Aug 90 13:24:58 CDT Received: by yoda.ncsa.uiuc.edu id AA13724 (5.64+/IDA-1.3.4 for ); Fri, 31 Aug 90 12:02:47 -0500 Received: by yoda.ncsa.uiuc.edu id AA13720 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 31 Aug 90 12:02:46 -0500 Message-Id: <9008311702.AA13720@yoda.ncsa.uiuc.edu> Date: Fri, 31 Aug 90 08:56 EDT From: "Lawrence M. Seiford, IEOR, UMass, (413) 545-2851." Subject: Re: Bug in Plot To: PMCGUIRE@coral.bucknell.edu, mathgroup@yoda.ncsa.uiuc.edu Status: RO PMCGUIRE writes: Has anyone else noticed the plethora of vertical lines that occurs when Mathematica executes the command Plot[x/x,{x,1,2}] or similar plots? This problem seems to be machine independent. I have tried it on a MacIIcx and an IBM 386 machine with the same result. Does anyone have an explanation? This is a result of the automatic scaling feature of Plot. If you'll use InputForm you'll notice that not all of the y-values are exactly 1. Adding PlotRange->{0,2} or even PlotRange->{.9,1.1} gives the line you're looking for. larry From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Aug 31 14:42:18 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA13941 (5.64+/IDA-1.3.4 for stevec); Fri, 31 Aug 90 14:42:17 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA01981; Fri, 31 Aug 90 14:40:10 CDT Received: by yoda.ncsa.uiuc.edu id AA13729 (5.64+/IDA-1.3.4 for ); Fri, 31 Aug 90 12:02:59 -0500 Received: by yoda.ncsa.uiuc.edu id AA13725 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 31 Aug 90 12:02:57 -0500 Message-Id: <9008311702.AA13725@yoda.ncsa.uiuc.edu> From: ags@seaman.cc.purdue.edu (Dave Seaman) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Bug in Plot Date: Fri, 31 Aug 90 11:13:32 +0500 Status: RO >Has anyone else noticed the plethora of vertical lines that occurs when >Mathematica executes the command Plot[x/x,{x,1,2}] or similar plots? >This problem seems to be machine independent. I have tried it on a MacIIcx >and an IBM 386 machine with the same result. Does anyone have an explanation? If you try Plot[x/x,{x,1,2},PlotRange->{0,2}], I think you'll find that the plot looks normal. The problem appears to be that x/x evaluates to something slightly different from 1 for some x, and the automatic scaling algorithm chooses the maximum and minimum values found for x/x. I got no tick marks or values on the vertical axis at all, probably because the values were something like 1 +/- 10^(-n) for some suitably large n, which wouldn't fit in the plot. It's also interesting to compare Plot[1,{x,1,2}], which produces a horizontal line with tick marks on the vertical axis. Apparantly, the case max=min is a special case, and no allowance is made for the case max-min < epsilon, for suitably small epsilon. Dave Seaman From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Aug 31 15:42:45 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA14050 (5.64+/IDA-1.3.4 for stevec); Fri, 31 Aug 90 15:42:43 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA03013; Fri, 31 Aug 90 15:40:37 CDT Received: by yoda.ncsa.uiuc.edu id AA13719 (5.64+/IDA-1.3.4 for ); Fri, 31 Aug 90 12:02:41 -0500 Received: by yoda.ncsa.uiuc.edu id AA13715 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 31 Aug 90 12:02:39 -0500 Message-Id: <9008311702.AA13715@yoda.ncsa.uiuc.edu> Date: Fri, 31 Aug 90 15:53:10 +1000 From: jimr@maths.su.oz.au (Jim Richardson) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Apollo Mathematica bugs Status: RO We have a version of Mathematica 1.2 running on Apollo workstations. It identifies itself as follows: Mathematica (Apollo SR10) 1.2 (January 5, 1990) [With pre-loaded data] by S. Wolfram, D. Grayson, R. Maeder, H. Cejtin, S. Omohundro, D. Ballman and J. Keiper with I. Rivin and D. Withoff Copyright 1988,1989 Wolfram Research Inc. -- Display Manager graphics initialized -- Does anyone have a later version? I am interested in particular to find out whether two Apollo-specific bugs have been fixed in the latest version. a) Mathematica will not run while one is connected to another node via the Apollo crp (create remote process) utilitity. It prints the banner (shown above) then dies with a segmentation fault. b) The postscript viewer dmps, supplied with Mathematica for use under the Apollo Display Manager, has a bug which displaces dashed line plots upwards. For example, the result of Plot[x,{x,-3,3}, PlotStyle->Dashing[{0.01,0.01}]] looks as if the function being plotted were y = x + 0.7 instead of y = x. This bug is not present in the X windows postscript viewer, only the Display Manager one. -- Jim Richardson Department of Pure Mathematics, University of Sydney, NSW 2006, Australia Internet: jimr@maths.su.oz.au Phone: +61 2 692 2232 FAX: +61 2 692 4534 From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Aug 31 15:46:37 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA14070 (5.64+/IDA-1.3.4 for stevec); Fri, 31 Aug 90 15:46:35 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA03039; Fri, 31 Aug 90 15:44:31 CDT Received: by yoda.ncsa.uiuc.edu id AA13880 (5.64+/IDA-1.3.4 for ); Fri, 31 Aug 90 14:16:34 -0500 Received: by yoda.ncsa.uiuc.edu id AA13876 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 31 Aug 90 14:16:32 -0500 Message-Id: <9008311916.AA13876@yoda.ncsa.uiuc.edu> Date: Fri, 31 Aug 90 14:10:14 -0400 From: lwyse@thalamus.bu.edu To: mathgroup@yoda.ncsa.uiuc.edu Subject: binary io Status: RO Is there anyway to read and write large blocks of data from and to arrays in Mathematica analogous to fread and fwrite in C? This would save a lot of time! thanks, lonce XXX XXX Lonce Wyse | X X Center for Adaptive Systems \ | / X X Boston University \ / 111 Cummington St. Boston,MA 02215 ---- ---- X X X X "The best things in life / \ XXX XXX are emergent." / | \ | From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Aug 31 21:23:07 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA14456 (5.64+/IDA-1.3.4 for stevec); Fri, 31 Aug 90 21:23:05 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA27722; Fri, 31 Aug 90 21:20:54 CDT Received: by yoda.ncsa.uiuc.edu id AA14360 (5.64+/IDA-1.3.4 for ); Fri, 31 Aug 90 19:53:03 -0500 Received: by yoda.ncsa.uiuc.edu id AA14356 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 31 Aug 90 19:53:02 -0500 Message-Id: <9009010053.AA14356@yoda.ncsa.uiuc.edu> To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Bug in plot Date: Fri, 31 Aug 90 13:52:42 PDT From: jacobson@cello.hpl.hp.com Status: RO > The problem appears to be that x/x evaluates to something > slightly different from 1 for some x, and the automatic scaling algorithm > chooses the maximum and minimum values found for x/x. This is a "feature" of IEEE floating point. x/x is not requried to evaluate to 1. You can collect a set of values for which this happens with Select[Table[Random[],{100}],#/#-1 != 0&] -- David Jacobson From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Aug 31 23:42:11 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA14754 (5.64+/IDA-1.3.4 for stevec); Fri, 31 Aug 90 23:42:09 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA10184; Fri, 31 Aug 90 23:40:05 CDT Received: by yoda.ncsa.uiuc.edu id AA14370 (5.64+/IDA-1.3.4 for ); Fri, 31 Aug 90 19:53:21 -0500 Received: by yoda.ncsa.uiuc.edu id AA14366 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 31 Aug 90 19:53:20 -0500 Message-Id: <9009010053.AA14366@yoda.ncsa.uiuc.edu> Date: Fri, 31 Aug 90 17:12:51 EDT From: dmg@dash.mitre.org (David M Goblirsch) To: mathgroup@yoda.ncsa.uiuc.edu Subject: binary io Status: RO Is there anyway to read and write large blocks of data from and to arrays in Mathematica analogous to fread and fwrite in C? This would save a lot of time! I have a good way to get binary data IN to Mathematica, but not a very good way to get it out. The fastest way is in fact to write a C program that reads a binary file using fread and writes ascii output to the standard output, and read this into Mathematica through a pipe using the Mathematica built-in function ReadList. For example, create a C program like the following. NOTES: (1) This program is for short ints, which is typical of the speech files that I work with. If you want to read binary floats or long ints, make the appropriate changes. (2) This is a skeleton program FOR EXAMPLE PURPOSES ONLY and does not show all of the error checking that I would normally do (for example, checking for a return of a NULL pointer by fopen), so don't use this program as is without adding the error checks. Use at your own risk. (3) It may even be faster to read more than one data value at a time which is what this program does. ---------- Example C program (simplified) --------------------------- #include "stdio.h" main(int argc, char *argv[]) { short int orig_data_value; FILE *fopen(), *fpi; fpi = fopen( argv[1], "rb"); while( fread( &orig_data_value, sizeof(short int), 1, fpi) ) { printf("%d\n", orig_data_value); } fclose(fpi); } ---------- End of Example C program ------------- Suppose that you call the executable version of this program "convert" and that it is in the directory /you/bin. Now create a Mathematica function like the following (note the space between convert and the quote): ReadBinaryFile[filename_String] := ReadList[ StringJoin[ "!/you/bin/convert ", filename ], Number ] Now to read your data into a list, just type listname = ReadBinaryFile["datafilename"]; Don't forget the semi-colon unless you like watching data speed by on your screen! Of course, you may want to take the usual precautions of sticking this in a Package and protecting it, etc. On a SUN SPARC under 4.0.3, this approach takes 7 secs to read a file with 13421 data points and 18.4 seconds to read a file with 43828 data points. I do not have a good way to get binary data out. That appears to involve the creation the dual program to this one AND the creation of a temporary file in the corresponding Mathematica function (ugh), so I will be most interested in a clean way to do this. David M. Goblirsch dmgob@mitre.org (703) 883-5450 The MITRE Corporation Washington C3I Division 7525 Colshire Drive McLean, VA 22102-3481 From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Aug 31 23:09:46 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA14704 (5.64+/IDA-1.3.4 for stevec); Fri, 31 Aug 90 23:09:44 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA09735; Fri, 31 Aug 90 23:07:33 CDT Received: by yoda.ncsa.uiuc.edu id AA14355 (5.64+/IDA-1.3.4 for ); Fri, 31 Aug 90 19:52:55 -0500 Received: by yoda.ncsa.uiuc.edu id AA14351 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 31 Aug 90 19:52:53 -0500 Message-Id: <9009010052.AA14351@yoda.ncsa.uiuc.edu> Date: Fri, 31 Aug 90 16:22 EDT From: PMCGUIRE@coral.bucknell.edu Subject: Followup to Bug in Plot To: MATHGROUP@YODA.NCSA.UIUC.EDU Status: RO This is a followup to my request for an explanation of what occurs when Mathematica executes the command Plot[x/x,{x,1,2}] . From the responses (for which I thank one and all) I was able to get a clear picture of what is happening. On executing the command InputForm[%] after the plot, one can see that x/x is not always evaluated to 1. Since the values are very close to 1 the automatic scaling function compresses the scale for the range to an interval about 1 of radius roughly 10^-18 . Relative to this s cale the graph is correct and the tick marks are rubbed out of existence. To get a clear indication of what is happening, it is worthwhile looking at the plot with the following plot range specified: Plot[x/x,{x,1,2},PlotRange->{.999999999999999999,1.000000000000000001}]. As was pointed out in one of the responses, it would be more appropriate for Mathematica to make an allowance in the automatic scaling for the case when the difference between the max and min is very very small. This was an eye opening example for me. Thanks, Paul McGuire From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Aug 31 22:47:11 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA14664 (5.64+/IDA-1.3.4 for stevec); Fri, 31 Aug 90 22:47:10 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA09368; Fri, 31 Aug 90 22:45:05 CDT Received: by yoda.ncsa.uiuc.edu id AA14365 (5.64+/IDA-1.3.4 for ); Fri, 31 Aug 90 19:53:11 -0500 Received: by yoda.ncsa.uiuc.edu id AA14361 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 31 Aug 90 19:53:10 -0500 Message-Id: <9009010053.AA14361@yoda.ncsa.uiuc.edu> From: ags@seaman.cc.purdue.edu (Dave Seaman) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Bug in plot Date: Fri, 31 Aug 90 16:00:16 +0500 Status: RO >This is a "feature" of IEEE floating point. x/x is not requried to >evaluate to 1. You can collect a set of values for which this happens >with > >Select[Table[Random[],{100}],#/#-1 != 0&] > > -- David Jacobson On the other hand, Plot[Release[x/x],{x,1,2}] gives the desired straight line, because Release[x/x] evaluates to exactly 1 (without a decimal point). Dave Seaman From mathgroup-adm@yoda.ncsa.uiuc.edu Sat Sep 8 22:56:11 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA08190 (5.64+/IDA-1.3.4 for stevec); Sat, 8 Sep 90 22:56:09 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA08595; Sat, 8 Sep 90 22:54:16 CDT Received: by yoda.ncsa.uiuc.edu id AA08095 (5.64+/IDA-1.3.4 for ); Sat, 8 Sep 90 21:13:09 -0500 Received: by yoda.ncsa.uiuc.edu id AA08091 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Sat, 8 Sep 90 21:13:08 -0500 Message-Id: <9009090213.AA08091@yoda.ncsa.uiuc.edu> Subject: solve hangs on Arc Functions To: mathgroup@yoda.ncsa.uiuc.edu (mathgroup for mathematica) Date: Wed, 5 Sep 90 9:11:48 PDT From: Steven Warwick Status: RO There appears to be a bug in solve in which expressions involving Arc Trig functions cause Mma to hang with no return... ***************** This hangs In[3]:= ww==ArcCos[ (4-ts^2 wc^2)/ (4+ts^2 wc^2)] 2 2 4 - ts wc Out[3]= ww == ArcCos[-----------] 2 2 4 + ts wc In[4]:= Solve[%,wc] *********** this doesn't ********** In[4]:= Cos[wt] == (4-ts^2 wc^2)/ (4+ts^2 wc^2) 2 2 4 - ts wc Out[4]= Cos[wt] == ----------- 2 2 4 + ts wc In[5]:= Solve[%,wc] Sqrt[4 - 4 Cos[wt]] Sqrt[4 - 4 Cos[wt]] Out[5]= {{wc -> -----------------------}, {wc -> -(-----------------------)}} 2 2 2 2 Sqrt[ts + ts Cos[wt]] Sqrt[ts + ts Cos[wt]] ********************************** Watch out..... -- Steven Warwick Hewlett-Packard sdw@hpsad From mathgroup-adm@yoda.ncsa.uiuc.edu Sat Sep 8 23:50:39 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA08304 (5.64+/IDA-1.3.4 for stevec); Sat, 8 Sep 90 23:50:37 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA25480; Sat, 8 Sep 90 23:48:31 CDT Received: by yoda.ncsa.uiuc.edu id AA08100 (5.64+/IDA-1.3.4 for ); Sat, 8 Sep 90 21:13:19 -0500 Received: by yoda.ncsa.uiuc.edu id AA08096 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Sat, 8 Sep 90 21:13:17 -0500 Message-Id: <9009090213.AA08096@yoda.ncsa.uiuc.edu> To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: binary io Date: Wed, 05 Sep 90 11:50:35 -0700 From: xinwei@jessica.stanford.edu Status: RO As for getting binary data out from Mathematica, one workaround for simple functions (without control structures), is to apply CForm[], then cut & paste the result into a C program] to generate the data. Of course, you might have to write a small set of atomic C glue functions for those functions produced by CForm which aren't in the standard C libraries. Here's a test example for producing binary data for a NeXT app (I stripped out the functions originally generated by CForm, to save space.): #include #include #include #include #import #import #import #define FLOATSIZE (sizeof(float)) #define NUMPOINTS 20 #define PI 3.14159265359 main() { int fd; fd = setupfile(); if (fd >=0) { writepts(fd); close(fd); } } int setupfile() { int numpts; int fd; fd = open("/xinwei/mobjunk.top", O_CREAT | O_RDWR, 777 ); if (fd < 0) { /* char message[256]; sprintf(message,"Cannot open file."); NXRunAlertPanel(NULL,message,"OK",NULL,NULL); */ return fd; } numpts = NUMPOINTS; write(fd, &numpts, sizeof(int)); return fd; } float Sqrt(float x) { float xx; xx = (float) sqrt(x); return (xx); } float Sign(float x) { return ((x < 0) ? -1.0 : 1.0) ; } float Power(float x, int n) { float xx; xx = (float) pow((double) x, (double) n); return (xx); } float mob1(float t,float s) { return(t); } float mob2(float t,float s) { return (s); } float mob3(float t,float s) { return(Power(2.7,- Power(t,2) - Power(s,2))); } int writepts(fd) int fd; /* file descriptor */ { int i,j; float t,s,x; int cc; for (i= 0; i < NUMPOINTS; i++) { for (j = 0; j < NUMPOINTS; j++) { t = (i / (float) NUMPOINTS) * 1.6 - 0.8; s = (j / (float) NUMPOINTS) * 2 * PI; /* write point to file */ x = mob1(t,s); cc = write(fd,&x , FLOATSIZE); x = mob2(t,s); cc = write(fd,&x , FLOATSIZE); x = mob3(t,s); cc = write(fd,&x , FLOATSIZE); } } } From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Sep 19 01:58:48 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA22470 (5.64+/IDA-1.3.4 for stevec); Wed, 19 Sep 90 01:58:46 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA10294; Wed, 19 Sep 90 01:56:42 CDT Received: by yoda.ncsa.uiuc.edu id AA21779 (5.64+/IDA-1.3.4 for ); Tue, 18 Sep 90 23:53:53 -0500 Received: by yoda.ncsa.uiuc.edu id AA21775 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 18 Sep 90 23:53:51 -0500 Message-Id: <9009190453.AA21775@yoda.ncsa.uiuc.edu> Date: Thu, 13 Sep 90 15:45:13 PDT From: limes@cs.nps.navy.mil (Robert Limes x3216) To: mathgroup-request@yoda.ncsa.uiuc.edu Subject: printer drivers Status: RO Steven Warwick: I am searching for printer and plotter drivers for Mathematica graphics output; specifically for HPLJ and HP pen-plotters. Computer is Sun Sparcstation 1. Bob Limes Dept. of Electrical and Computer Engineering Code EC Naval Postgraduate School Monterey, CA 93943 (408) 646-3216 limes@cs.nps.navy.mil From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Sep 19 02:41:39 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA22521 (5.64+/IDA-1.3.4 for stevec); Wed, 19 Sep 90 02:41:37 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA11024; Wed, 19 Sep 90 02:39:34 CDT Received: by yoda.ncsa.uiuc.edu id AA21784 (5.64+/IDA-1.3.4 for ); Tue, 18 Sep 90 23:53:59 -0500 Received: by yoda.ncsa.uiuc.edu id AA21780 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 18 Sep 90 23:53:58 -0500 Message-Id: <9009190453.AA21780@yoda.ncsa.uiuc.edu> Date: Mon, 17 Sep 1990 12:22:45.71 GMT From: amaro@ptifm.bitnet Subject: Various Questions To: mathgroup@yoda.ncsa.uiuc.edu Status: RO From: Amaro Jose' Rica da Silva, Instituto Superior Tecnico, Physics Dep., Av. Rovisco Pais, 1096 Lisboa, PORTUGAL email: AMARO@PTIFM.BITNET I am a faculty member in the Physics Dept. of the Instituto Superior Tecnico, I am engaged in a research project in the area of Dynamical Systems/Cellular Automata. I have proposed here the use of Mathematica as a general unifying basic interface for the software development related with this project, having most particularly in mind its ability to control external processes (e.g. data acquisition, processing and device control). Having used Mathematica on the Macintosh only, I cannot as yet gauge this ability (no multitasking environment) so I would like to get as much info as I can on this before deciding on the best hardware/software combination for us. Some of the questions are : -- I can't get `FontForm[expr, fontname, size]' to work on the Mac (neither `fontname' nor `size' are effective)! Is this to be expected? I have also tried `ResetMedium[file, options]' for -stdout- using the option `GraphicsFont ->"myfont\&size"' but that didn'd work either. Only `Define Style' of Axes Labels seems to work, but then every text in Graphics has the same font & size. -- Adding `math.record' path name to `init.m' doesn't do any good, nor does adding a file name to the `$Echo' list in order to record input lines ! Is this also inherent to the Mac interface ? -- How can I produce animation of the kind you get when you open the ``About Mathematica''window? Is it a compiled routine, and can one add a function whose definition involves an independently compiled program? From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Sep 25 03:07:45 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA00311 (5.64+/IDA-1.3.4 for stevec); Tue, 25 Sep 90 03:07:43 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA19931; Tue, 25 Sep 90 03:05:31 CDT Received: by yoda.ncsa.uiuc.edu id AA00114 (5.64+/IDA-1.3.4 for ); Tue, 25 Sep 90 00:32:09 -0500 Received: by yoda.ncsa.uiuc.edu id AA00110 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 25 Sep 90 00:32:08 -0500 Message-Id: <9009250532.AA00110@yoda.ncsa.uiuc.edu> Date: Thu, 20 Sep 90 10:33:48 EDT From: prs@cook.whoi.edu (Peter R. Shaw) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Spherical Harmonic Status: RO Hi, folks, I'm using spherical harmonics ... I want to access Ylm for l=2, m=0. No azimuthal dependence, so I set phi=0, and want to look at the theta dependence. So, when I type: SphericalHarmonicY[2,0,theta,0] I get the satisfying result: 2 Sqrt[5] (-1 + 3 Cos[theta] ) ---------------------------- 4 Sqrt[Pi] BUT, when I try to access theta=0, what I get is SphericalHarmonicY[2,0,0,0] 0 General::ind: Indeterminate expression 0 encountered. 0 0 Sqrt[5] ---------- 2 Sqrt[Pi] Am I nuts or what? Cos[0]=1, so Cos[theta]^2 = 1, so I should get Sqrt[5] (-1 + 3 ) ------------------ 4 Sqrt[Pi] which evaluates to 1/2 Sqrt[5/Pi], and does not involve anything like 0^0. None of the constants are dependent on theta. --------------------------------------------- Peter R. Shaw pshaw@aqua.whoi.edu Woods Hole Oceanographic Institution --------------------------------------------- From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Sep 25 02:03:50 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA00237 (5.64+/IDA-1.3.4 for stevec); Tue, 25 Sep 90 02:03:48 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA18662; Tue, 25 Sep 90 02:01:46 CDT Received: by yoda.ncsa.uiuc.edu id AA00109 (5.64+/IDA-1.3.4 for ); Tue, 25 Sep 90 00:32:01 -0500 Received: by yoda.ncsa.uiuc.edu id AA00105 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 25 Sep 90 00:32:00 -0500 Message-Id: <9009250532.AA00105@yoda.ncsa.uiuc.edu> Date: Wed, 19 Sep 90 14:33 N From: SURF203@kub.nl To: mathgroup@yoda.ncsa.uiuc.EDU Subject: Simplify Status: RO Is there a way by which MATHEMATICA can factor (simplify) expressions in which the extracted parts contain differential operators. For instance, we know that a substitution of u = 2 (d/dx v)/v in Burgers' equation (d/dt u + u d/dx u + d2/dx2 u = 0) leads to an equation in which we can extract the operator O = 2 (-1/v^2 (d/dx v) + 1/v d/dx ) such that it becomes O (d/dt + d2/dx2)) v = 0. Also, a substitution of u = v^2 + d/dx v in Korteweg-de Vries equation (d/dt u + u d/dx u + d3/dx3 u = 0), can be written as (2 v + d/dx) (d/dt v + v^2 d/dx v + d3/dx3 v) = 0, which splits off the operator O = (2 v + d/dx). Is there a way by which MATHEMATICA can single out the operator O in the previous examples? This, presumably, requires the treat- ment of operators as non-commuting products: i.e when D = d/dx, then D f(x) = f(x) D + d/dx f. I would appreciate comments on the previous! Yours sincerely, Leo R.M. Maas From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Sep 25 04:40:47 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA00517 (5.64+/IDA-1.3.4 for stevec); Tue, 25 Sep 90 04:40:45 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA23014; Tue, 25 Sep 90 04:38:43 CDT Received: by yoda.ncsa.uiuc.edu id AA00119 (5.64+/IDA-1.3.4 for ); Tue, 25 Sep 90 00:32:18 -0500 Received: by yoda.ncsa.uiuc.edu id AA00115 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 25 Sep 90 00:32:16 -0500 Message-Id: <9009250532.AA00115@yoda.ncsa.uiuc.edu> From: dan@chem.bu.edu (Dan Dill) Date: Thu, 20 Sep 90 14:03:52 -0400 To: mathgroup@yoda.ncsa.uiuc.edu Subject: Efficiency in Mathematica Status: RO While Mathematica allows things to be done in different ways, the procedural way can be a real dog. On page 104 of Volume 1, Issue 1 of The Mathematica Jounral, is written "procedural programming is less efficient, longer and more difficult to understand". The following example amply demonstrates for me at least the first two of these assertions, and, in hindsight, the third too. The Journal goes on to say that "sometimes it can take awhile to see how to do it. The time spent is almost always worth it." I certainly did have to play around a bit to see how to come up with a functional scheme, but it certainly was worth it. I have a nested list real numbers (generated by an external program and read in with ReadList) of structure data = {{e1, {{m1, {u1, ..., u30}}, {m2, { ... }}, ... {m30, { ... }}}}, ... {e50, {{m1, {u1, ..., u30}}, {m2, { ... }}, ... {m30, { ... }}}}} I want to replace the elements m1, m2, ... with their unit modulus, to 8 decimal-digits precision. The straightforward, "traditional" way (ne = 30 and nkmat = 30) oldmod := Block[{i,j}, For[i = 1, i < ne + 1, i++, For[j = 1, j < nkmat + 1, j++, data[[i,2,j,1]] = N[Mod[data[[i,2,j,1]], 1], 8] ] ] ]; gives Timing[oldmod] Out[205]= {869.683 Second, Null} A head-scratchingly less-straightforward, "functional" way mod[i_Integer, n_Integer] := Transpose[ MapAt[N[Mod[#, 1], n]&, Transpose[data[[i, 2]]], {1}] ] gives Timing[data = Array[{data[[#, 1]], mod[#, 8]}&, ne];]; Out[212]= {3.56667 Second, Null} about 240 times faster. From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Sep 25 04:37:37 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA00508 (5.64+/IDA-1.3.4 for stevec); Tue, 25 Sep 90 04:37:35 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA22993; Tue, 25 Sep 90 04:35:33 CDT Received: by yoda.ncsa.uiuc.edu id AA00129 (5.64+/IDA-1.3.4 for ); Tue, 25 Sep 90 00:32:28 -0500 Received: by yoda.ncsa.uiuc.edu id AA00120 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 25 Sep 90 00:32:26 -0500 Message-Id: <9009250532.AA00120@yoda.ncsa.uiuc.edu> From: Alfy_N_Riddle@cup.portal.com To: mathgroup@yoda.ncsa.uiuc.edu Subject: equation manipulation Date: Mon, 24 Sep 90 01:25:03 PDT Status: RO Dear Mathematica users, I do a fair amount of manipulating equations and am always searching for tools to help me do this better. Since Solve can have problems at times I have found the following set of functions useful for manually solving an equation. All these functions do is allow one to operate on both sides of the equals mark at once, and format the result. This ensures a correct solution is obtained, and is useful for tutorials. If anyone out there has any comments on this, or has found better ways of doing this I would appreciate hearing from you. I will send a summary to the net if there are enough replies. Sincerely, -- Alfy ================================= EqnForm::usage= "EqnForm[x,y] returns an equation formatted as x=y. Mathematical operations can be performed directly on this form and are passed to each side of the equation. This is very useful for manual equation simplification and tutorials. Normal[EqnForm[x,y]] returns {x,y}." Format[EqnForm[x_,y_]] := SequenceForm[x," = ",y] Normal[EqnForm[x_,y_]] ^= {x,y} f_[ EqnForm[x_,y_]] ^= EqnForm[f[x],f[y]] Times[ a_, EqnForm[x_,y_]] ^= EqnForm[a x,a y] ======================== end of functions From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Sep 25 19:27:41 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA01615 (5.64+/IDA-1.3.4 for stevec); Tue, 25 Sep 90 19:27:39 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA11785; Tue, 25 Sep 90 19:25:40 CDT Received: by yoda.ncsa.uiuc.edu id AA01347 (5.64+/IDA-1.3.4 for ); Tue, 25 Sep 90 16:54:01 -0500 Received: by yoda.ncsa.uiuc.edu id AA01342 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 25 Sep 90 16:53:59 -0500 Message-Id: <9009252153.AA01342@yoda.ncsa.uiuc.edu> Date: Tue, 25 Sep 90 09:12:05 -0700 From: fateman@ucbarpa.Berkeley.EDU (Richard Fateman) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Efficiency in Mathematica Status: RO I think that Dan's efficiency issue is not related to procedural vs. functional, but a data-accessing problem. Repeatedly accessing the nth, (n+1)st, (n+2)nd, ... element of a data structure by repeatedly scanning the same structure, starting from the first location, is a real waste of time. I think that is what the procedural version is doing. A procedure that explicitly takes into account the list-nature of the structure may be just fine. The general advice that using some built-in function (implemented in C) in Mathematica, vs. writing your own "do loop" which will be interpreted slowly, is reasonable, and probably contributes somewhat to the difference in speed, but replacing an O(n^2) algorithm by an O(n) algorithm is usually a big win. -- Richard Fateman From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Sep 25 20:12:21 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA01679 (5.64+/IDA-1.3.4 for stevec); Tue, 25 Sep 90 20:12:19 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA12449; Tue, 25 Sep 90 20:10:18 CDT Received: by yoda.ncsa.uiuc.edu id AA01352 (5.64+/IDA-1.3.4 for ); Tue, 25 Sep 90 16:54:09 -0500 Received: by yoda.ncsa.uiuc.edu id AA01348 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 25 Sep 90 16:54:08 -0500 Message-Id: <9009252154.AA01348@yoda.ncsa.uiuc.edu> Date: Tue, 25 Sep 90 09:19:51 -0700 From: ilan@Gang-of-Four.Stanford.EDU (Ilan Vardi) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Efficiency in Mathematica Status: RO From: dan@chem.bu.edu (Dan Dill) Date: Thu, 20 Sep 90 14:03:52 -0400 While Mathematica allows things to be done in different ways, the procedural way can be a real dog. On page 104 of Volume 1, Issue 1 of The Mathematica Jounral, is written "procedural programming is less efficient, longer and more difficult to understand". The following example amply demonstrates for me at least the first two of these assertions, and, in hindsight, the third too. The Journal goes on to say that "sometimes it can take awhile to see how to do it. The time spent is almost always worth it." I certainly did have to play around a bit to see how to come up with a functional scheme, but it certainly was worth it. This is basically wrong. First, there are some algorithms which don't seem to have efficient functional implementations. A good example is ToCycles, i.e., a program which finds the cycle decomposition of a permutation in linear time. I thought about doing this for a long time and I don't think it can be done though I don't know how to prove it's impossible either. In any case I challenge anybody to do this. Here is a quadratic functional implementation of ToCycles. Frankly, I think this code is rather obscure ToCycles[a_] := Select[Take[#, Length[Union[#]]]& /@ Map[NestList[a[[#]]&, #, Length[a]] &, a], #[[1]] == Min[#]&] The second point is that Functional programming (in Mathematica anyway) uses a lot of parallel constructs like Map which end up being memory intensive. An iterative loop is more memory efficient. As a toy example, finding the sum of the first n integers directly is most efficient as sum[n_]:= Plus @@ Range[n] for n < 50,000 on most computers. However, this probably won't work on sum[10^7] so the following procedural method works by breaking it up into smaller chunks and iterating. This seems the clearest way to do it. sum2[n_, k_]:= Block[{total = 0, i}, Do[total += Plus @@ Range[i, i + k - 1], {i, 1, n, k}]; total + Plus @@ Range[n - Mod[n, k] + 1, n]] On my computer sum2[10^5, 10^4] was also 10% faster than sum[10^5]. I would say that the way Mathematica was designed usually favors functional programming, but that choice of style is a personal decision ultimately. From mathgroup-adm@yoda.ncsa.uiuc.edu Mon Oct 1 02:58:21 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA08967 (5.64+/IDA-1.3.4 for stevec); Mon, 1 Oct 90 02:58:19 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA06019; Mon, 1 Oct 90 02:56:26 CDT Received: by yoda.ncsa.uiuc.edu id AA08114 (5.64+/IDA-1.3.4 for ); Sun, 30 Sep 90 23:14:19 -0500 Received: by yoda.ncsa.uiuc.edu id AA08110 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Sun, 30 Sep 90 23:14:18 -0500 Message-Id: <9010010414.AA08110@yoda.ncsa.uiuc.edu> From: dan@chem.bu.edu (Dan Dill) Date: Thu, 27 Sep 90 12:56:13 -0400 To: mathgroup@yoda.ncsa.uiuc.edu Subject: Efficiency in Mathematica. Part 2 Status: RO Richard (fateman@ucbarpa.Berkeley.EDU) comments that the essence of the speed up is to have accessed, by whatever means, internal algorithms that take advantage of the list structure of the data. David Jacobson (jacobson@cello.hpl.hp.com) sent me a suggestion that may do just this, in the context of "traditional" subscripting. By itself David's method reduced the time from 870 seconds to 9.6 seconds, only about twice as slow as the fastest scheme I have been able to achieve. I include David's text below, but the idea is to prevent Mathematica from knowing it is dealing with a list until all subscripting is done: SetAttributes[HoldList,HoldAll]; ne = 50; nkmat = 18; (* The values were used earlier, too *) oldmodhold := Block[{i,j}, data = Apply[HoldList, Apply[HoldList,data,4]]; For[i = 1, i < ne + 1, i++, For[j = 1, j < nkmat + 1, j++, data[[i,2,j,1]] = N[Mod[data[[i,2,j,1]], 1], 8] ] ]; data = Apply[List, Apply[List,data,4]]; ]; Timing[oldmodhold;] Out[137]= {9.58333 Second, Null} Recall that oldmod differs from the above by the absence of the Apply[...] before and after the double loop, and the timing is then 870 seconds. So David must be onto something. Here's David's message: ------------------------------- >From jacobson@cello.hpl.hp.com Tue Sep 25 13:45:14 1990 Return-Path: Received: from hplms2.hpl.hp.com by chem.bu.edu (5.61+++/JLK-4.0.3) id AA11645; Tue, 25 Sep 90 13:45:10 -0400 Received: from cello.hpl.hp.com by hplms2.hpl.hp.com with SMTP (15.11.1.3/15.5+IOS 3.20) id AA17661; Tue, 25 Sep 90 10:47:20 pdt Received: from localhost by cello.hpl.hp.com with SMTP (15.11/15.5+IOS 3.14) id AA25443; Tue, 25 Sep 90 10:46:41 pdt To: dan@chem.bu.edu (Dan Dill) Subject: Re: Efficiency in Mathematica In-Reply-To: Your message of "Thu, 20 Sep 90 14:03:52 PDT." <9009250532.AA00115@yoda.ncsa.uiuc.edu> Date: Tue, 25 Sep 90 10:46:35 PDT Message-Id: <25441.654284795@cello.hpl.hp.com> From: jacobson@cello.hpl.hp.com Status: RO I've also noticed that programs that munge on just part of a list using subscripting run like molassas. I'm suspicious that a good part of the performance problem lies in the subscript operation. It evaluates both arguments, and the first is the whole giant list. So, in principle, the whole list gets scanned on each reference to see if there is anything that will evaluate. Internally, Mathematica seems to have some bunch of flags to avoid multiple evalutations, but when you are using subscripting on the left hand side, it may clear the flag. I've found that the following trick will often speed such things up by an order of magnitude. First do this. SetAttributes[HoldList,HoldAll] HoldList will be a "function" that works about like List, except that it does not evaluate its arguments. You can easily replace the outmost List with HoldList with Apply[HoldList,<<>>] Then you do all the subscripting, then let it all evaluate at one swoop with Apply[List,<<>>]. In your case, you might want to use HoldList at 2 levels. If you see fit, I'd appreciate you trying this trick and reporting to the mathgroup what the performance was. -- David Jacobson From mathgroup-adm@yoda.ncsa.uiuc.edu Mon Oct 1 04:27:37 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA09061 (5.64+/IDA-1.3.4 for stevec); Mon, 1 Oct 90 04:26:39 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA09092; Mon, 1 Oct 90 04:23:51 CDT Received: by yoda.ncsa.uiuc.edu id AA08104 (5.64+/IDA-1.3.4 for ); Sun, 30 Sep 90 23:14:02 -0500 Received: by yoda.ncsa.uiuc.edu id AA08100 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Sun, 30 Sep 90 23:14:01 -0500 Message-Id: <9010010414.AA08100@yoda.ncsa.uiuc.edu> Date: Wed, 26 Sep 1990 10:21:41 MDT From: MARZKE@ASUCP1.LA.ASU.EDU Subject: Fitting data with Mathematica To: mathgroup@yoda.ncsa.uiuc.edu Status: RO Novak at Mathematica referred me to your group for this question. If I want to fit data to an expression which I already know the functional form of, but which contains adjustable parameters such as the value of a magnetic field, initial angle of a nuclear spin with respect to that field, etc., how do I use Mathematica to find least-squares "best" values of these parameters to fit the data? In other words, how do I use Mathematica to obtain non-linear, parametric, least-squares fits to experimental data? There are large, cumbersome FORTRAN programs like CERN's MINUIT which do this for Nuclear and Particle Physics data, I know. But one thing which is generally lacking is a powerful, easy-to-use FIT routine of this kind running on workstations. I have been advised by an expert on MacSyma that one does not want to do this kind of thing with symbolic algebra programs, because they will be very slow. My reply to that thought is that often one needs to fit data somewhat roughly, at least, and be able to look at it immediately on screen in the form of a plot, or do other calculations and plots based which involve some processing of the data, etc. For these the capabilities of the packages make up for the slowness of the calculations, in many ways. Does your group know of any Mathematica-based approaches to this question? The FIT command in Mathematica is far too limited. Bob Marzke Physics Department Arizona State University Bitnet: MARZKE@ASUCPS Phone: 602-965-6197 Department Phone: 602-965-3561 FAX: 602-965-7954 From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Oct 2 23:43:35 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA11947 (5.64+/IDA-1.3.4 for stevec); Tue, 2 Oct 90 23:43:33 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA22619; Tue, 2 Oct 90 23:41:43 CDT Received: by yoda.ncsa.uiuc.edu id AA11798 (5.64+/IDA-1.3.4 for ); Tue, 2 Oct 90 21:11:35 -0500 Received: by yoda.ncsa.uiuc.edu id AA11794 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 2 Oct 90 21:11:34 -0500 Message-Id: <9010030211.AA11794@yoda.ncsa.uiuc.edu> To: mathgroup@yoda.ncsa.uiuc.edu Subject: LISP/Mathematica Interface Date: Mon, 01 Oct 90 10:00:54 +0100 From: Ron I. Herman Status: RO Does anyone have any information about an interface between LISP and Mathematica? Ron Herman From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Oct 3 02:37:12 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA12944 (5.64+/IDA-1.3.4 for stevec); Wed, 3 Oct 90 02:37:11 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA20775; Wed, 3 Oct 90 02:35:20 CDT Received: by yoda.ncsa.uiuc.edu id AA11808 (5.64+/IDA-1.3.4 for ); Tue, 2 Oct 90 21:11:48 -0500 Received: by yoda.ncsa.uiuc.edu id AA11804 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 2 Oct 90 21:11:46 -0500 Date: Tue, 2 Oct 90 21:11:46 -0500 Message-Id: <9010030211.AA11804@yoda.ncsa.uiuc.edu> To: mathgroup@yoda.ncsa.uiuc.EDU From: ONM010@de0hrz1a.bitnet Subject: Non-linear fitting in Mathematica Status: RO It is indeed possible to perform non-linear fits with Mathematica, however, it seems to be very slow indeed. Some time ago I tried a simple 4-parameter fit involving 2 Gaussians. I first specified the function with the parameters to be fitted max, g, s1, and s1: f[x_]:=max ( g Exp[-1/2 x^2/s1^2] + (1-g) Exp[-1/2 x^2/s2^2] ) Then I put the 128 (experimental) data points into 2 tables: x=Table[data[[i,1]],{i,1,ndat}] y=Table[data[[i,2]],{i,1,ndat}] I defined the least-squares function to be minimized: chisq=Sum[(y[[i]]-f[x[[i]]])^2,{i,1,ndat}] FindMinimum can be used to perform the non-linear fitting operation: FindMinimum[chisq, {g,ginit}, {max,maxinit}, {s1,s1init}, {s2,s2init}, Gradient -> {D[chisq,g], D[chisq,max], D[chisq,s1], D[chisq,s2]}, AccuracyGoal -> 4, MaxIterations -> 50 ] There were about 128 data points and I used initial guesses which were close to the final parameter values at the solution. I remember that it took over an hour to converge to a solution on a Macintosh SE/30 with 8 MB memory using the enhanced version of Mathematica 1.2.1. For comparison, I fitted in double precision FORTRAN using NL2SOL (Dennis JE, Gay DM, Welsch RE. An adaptive nonlinear least-squares algorithm. ACM Trans Math Software 7:348-368, 1981) for the minimization. I compiled with Microsoft Fortran v. 2.2 which doesn+t even use the floating point hardware of the SE/30. The fit took about 2 or 3 seconds for the same number of datapoints and not much longer even for worse initial parameter guesses. The above formulation of the problem im Mathematica is not optimized for speed and probably far from ideal. Has anybody come up with an efficient approach for non-linear parameter fitting in Mathematica or are these long execution times really the price one has to pay for convenience? Best regards! Stefan ================================================================= Dr. Stefan P. Mueller, Nuklearmedizin, Universitaetsklinikum, Hufelandstr. 55, D-4300 Essen 1, Federal Republic of Germany, e-mail: onm010@de0hrz1a on BITNET, FAX: <49> (201) 723-4694, phone: <49> (201) 723-2080 or 2081 or 2032 ================================================================= From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Oct 3 04:02:30 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA13141 (5.64+/IDA-1.3.4 for stevec); Wed, 3 Oct 90 04:02:28 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA23745; Wed, 3 Oct 90 03:58:29 CDT Received: by yoda.ncsa.uiuc.edu id AA11915 (5.64+/IDA-1.3.4 for ); Tue, 2 Oct 90 23:30:42 -0500 Received: by yoda.ncsa.uiuc.edu id AA11911 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 2 Oct 90 23:30:41 -0500 Message-Id: <9010030430.AA11911@yoda.ncsa.uiuc.edu> Date: Tue, 2 Oct 90 20:04:20 -0700 From: "Max G. Webb" To: mathgroup@yoda.ncsa.uiuc.edu Subject: Points problem Status: RO Help!!! The following code should draw some largish grey points and a few lines. When FAIL is asserted (as indicated by the ifdef - of course, you should also get rid of the #-lines inserted by the c preprocessor) the POINTS disappear!!?!! All the ifdef does is control the inclusion of the last two line commands (while keeping correct `,' separation) Why should these lines presence or absence control the display of the points? It is in a _different_list_!!?? ::::::cut here:::::: Show[Graphics3D[ { {PointSize[0.05], GrayLevel[0.5], Point[{-1.367511195263215, 0.001195340754223037, 0.003139555787092553}], Point[{-1.367512718901739, 0.001195342899414338, 0.001639740038943013}], Point[{1.36085379675106, 0.002607945574256309, 0.00372862923999308}], Point[{1.3608552544435, 0.00111807892934969, 0.003728634284214638}] }, { Line[{{0., 0., 0.}, {-0.003327336062, 0.0004133633611, 0.0008263234388}}], Line[{{-0.003327336062, 0.0004133633611, 0.0008263234388}, #ifdef FAIL {-0.1820927732, 0.0001372407256, 0.0002758916286}}], Line[{{-0.1854201093010261, 0.0005506040866933036, 0.001102215067405295}, {0., 0., 0.}}], Line[{{-0.1854201093010261, 0.0005506040866933036, 0.001102215067405295}, {-0.1820927751, 0.0001345637681, 0.0002715492562}}] #else FAIL {-0.1820927732, 0.0001372407256, 0.0002758916286}}] #endif FAIL } } ]] From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Oct 3 00:37:56 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA12650 (5.64+/IDA-1.3.4 for stevec); Wed, 3 Oct 90 00:37:53 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA26205; Wed, 3 Oct 90 00:35:52 CDT Received: by yoda.ncsa.uiuc.edu id AA11803 (5.64+/IDA-1.3.4 for ); Tue, 2 Oct 90 21:11:41 -0500 Received: by yoda.ncsa.uiuc.edu id AA11799 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 2 Oct 90 21:11:40 -0500 Message-Id: <9010030211.AA11799@yoda.ncsa.uiuc.edu> To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Fitting data with Mathematica Date: Mon, 01 Oct 90 08:35:06 PDT From: jacobson@cello.hpl.hp.com Status: RO MARZKE@ASUCP1.LA.ASU.EDU asks > If I want to fit data to an expression which I already know the > functional form of, but which contains adjustable parameters such as > the value of a magnetic field, initial angle of a nuclear spin with > respect to that field, etc., how do I use Mathematica to find > least-squares "best" values of these parameters to fit the data? In > other words, how do I use Mathematica to obtain non-linear, > parametric, least-squares fits to experimental data? The trick is to use FindMinimum. Develop your own function that expresses the goodness of fit. The sum of squares of differences is probably the thing to use. Then use FindMinimum. Here is an example I made a list of points in "datalist" that were pairs {x,3.456 E^(2.345 x)} for 300 random values of x. Now suppose we only knew that the form of the functions was f[x] = a + E^(b x) and we want to find a and b. "fitfunction" tells how good a given a and b fit the data. In step 11 I invoke FindMinimum telling it to start looking around a=3 and b=2. In[10]:= fitfunction[a_,b_] := Apply[Plus,Map[(#[[2]]-(a E^(b #[[1]])))^2&, datalist]] In[11]:= FindMinimum[fitfunction[a,b],{a,3},{b,2}] Out[11]= {0., {a -> 3.456, b -> 2.345}} The one catch is that I think FindMinimum will barf if it can't differentiate to get gradient functions. I haven't tried something that will test this, though. There are options to FindMinimum. Read its description carefully. Be careful of the WorkingPrecision option. It can be dangerous. -- David Jacobson From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Oct 3 01:22:27 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA12739 (5.64+/IDA-1.3.4 for stevec); Wed, 3 Oct 90 01:22:25 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA15895; Wed, 3 Oct 90 01:20:18 CDT Received: by yoda.ncsa.uiuc.edu id AA11793 (5.64+/IDA-1.3.4 for ); Tue, 2 Oct 90 21:11:29 -0500 Received: by yoda.ncsa.uiuc.edu id AA11789 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 2 Oct 90 21:11:28 -0500 Message-Id: <9010030211.AA11789@yoda.ncsa.uiuc.edu> Date: Mon, 1 Oct 90 09:25:09 EDT From: prs@cook.whoi.edu (Peter R. Shaw) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Spherical Harmonic summary Status: RO Thanks to everyone who responded to my query about evaluating the spherical harmonic function Ylm for theta=0 and phi=0. Given the way mathematica evaluates expressions, the most stable way to obtain this result is to use: SphericalHarmonicY[2,0,theta,phi] /. {theta->0, phi->0} (Several people pointed out variations of this command). John Schmidt writes that Wolfram acknowledges the error messages when asking for expressions like SphericalHarmonicY[2,0,0,0] be a bug, which may get fixed in a future release. Meanwhile, I have discovered that when I ask for the *plot*, say, using the command: Plot[{ SphericalHarmonicY[2,0,theta,phi] /.phi->0 }, {theta,0,Pi}] Mathematica barfs up a few complaints, and then goes on to draw the correct plot, presumably applying a limiting algorithm at theta->0. This also happens for the simpler command: Plot[SphericalHarmonicY[2,0,theta,0], {theta,0,Pi}] . By the way, what I'm using all this for is to make animations of Earth's free oscillations from an earthquake, for my class in Geophysics. If anybody wants to see the 1st Toroidal mode of oscillation, run this script, and then animate it (on the Macintosh): <{1,1,1}, PlotRange->{{-1,1},{-1,1},{-1,1}}, ViewPoint->{2.872, 1.166, 1.356}], {tphase,0,Pi,Pi/4}] --------------------------------------------- Peter R. Shaw pshaw@aqua.whoi.edu Woods Hole Oceanographic Institution --------------------------------------------- From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Oct 3 20:22:24 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA14307 (5.64+/IDA-1.3.4 for stevec); Wed, 3 Oct 90 20:22:22 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA28112; Wed, 3 Oct 90 20:20:33 CDT Received: by yoda.ncsa.uiuc.edu id AA14170 (5.64+/IDA-1.3.4 for ); Wed, 3 Oct 90 17:47:03 -0500 Received: by yoda.ncsa.uiuc.edu id AA14166 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Wed, 3 Oct 90 17:47:02 -0500 Message-Id: <9010032247.AA14166@yoda.ncsa.uiuc.edu> Date: Wed, 3 Oct 90 15:29:37 -0700 From: fateman@ucbarpa.Berkeley.EDU (Richard Fateman) Subject: Re: LISP/Mathematica Interface To: mathgroup@yoda.ncsa.uiuc.edu Status: RO There are several lisp systems that allow you to do virtually anything you could do "from C" from the lisp system. The so-called "foreign function call" feature is reasonably widespread. Although you are probably not referring to this kind of interface, I wrote a program in Common Lisp that has the ability to read what looks just like Mathematica input (version 1.2), and produce "FullForm" expressions in the usual Lisp prefix form. These can then be manipulated in Lisp. Thus you could (a) write a front end in Lisp to Mathematica (or for that matter, any other program) that "looked like" Mathematica. or (b) you could write a back end in Lisp that chewed on Mathematica syntax it was fed from a mathematica front end. or for that matter, by combining (a) and (b), you could eliminate the need for mathematica entirely by writing in Lisp, if you were so inclined. -- Richard Fateman From kirchner@cs.umn.edu Sat Oct 6 19:47:43 1990 Received: from cs.umn.edu by yoda.ncsa.uiuc.edu with SMTP id AA20570 (5.64+/IDA-1.3.4 for stevec); Sat, 6 Oct 90 19:47:39 -0500 Received: by cs.umn.edu (5.59/1.14) id AA00636; Sat, 6 Oct 90 19:48:07 CDT Date: Sat, 6 Oct 90 19:48:07 CDT From: "Roger B. Kirchner" Message-Id: <9010070048.AA00636@cs.umn.edu> To: kirchner@cs.umn.edu, stevec@yoda.ncsa.uiuc.edu Subject: Re: Problem with Function Status: RO Thanks you for letting me know. We should be getting 2.0 soon. Too bad, though, that the problem is in all earlier versions of Mathematica. The examples I would like to write -- with a function argument called with Function[...] won't be portable. (I hope you mean that 2.0 Mathematica is being supplied with 2.0 NeXT.) Roger From mathgroup-adm@yoda.ncsa.uiuc.edu Sat Oct 6 21:39:43 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA20700 (5.64+/IDA-1.3.4 for stevec); Sat, 6 Oct 90 21:39:26 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA17432; Sat, 6 Oct 90 21:37:23 CDT Received: by yoda.ncsa.uiuc.edu id AA20538 (5.64+/IDA-1.3.4 for ); Sat, 6 Oct 90 18:50:51 -0500 Received: by yoda.ncsa.uiuc.edu id AA20534 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Sat, 6 Oct 90 18:50:49 -0500 Message-Id: <9010062350.AA20534@yoda.ncsa.uiuc.edu> Date: Fri, 5 Oct 90 07:51:33 CDT From: "Roger B. Kirchner" To: mathgroup@yoda.ncsa.uiuc.edu Subject: Problem with Function Status: RO I am having the following problem on a NeXT. Is it specific to the NeXT or is it present in other versions of Mathematica? In[1]:= f = Function[x, x + x^2] 2 Out[1]= Function[x, x + x ] In[2]:= f'[2] Out[2]= 5 In[3]:= g = Function[x, x - x^2] 2 Out[3]= Function[x, x - x ] In[4]:= g'[2] 2 Out[4]= (Function[x, x - x ])'[2] Thanks. Roger Kirchner rkirchne@mathcs.carleton.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Sat Oct 6 23:00:06 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA20782 (5.64+/IDA-1.3.4 for stevec); Sat, 6 Oct 90 22:59:56 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA24550; Sat, 6 Oct 90 22:57:57 CDT Received: by yoda.ncsa.uiuc.edu id AA20543 (5.64+/IDA-1.3.4 for ); Sat, 6 Oct 90 18:50:57 -0500 Received: by yoda.ncsa.uiuc.edu id AA20539 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Sat, 6 Oct 90 18:50:56 -0500 Message-Id: <9010062350.AA20539@yoda.ncsa.uiuc.edu> Date: Fri, 5 Oct 90 17:38:02 -0400 (EDT) From: "Douglas F. DeJulio" To: mathgroup@yoda.ncsa.uiuc.edu (yoda.ncsa.uiuc.edu) Subject: MathTalk info? Status: RO Hello, I'm thinking of writing my own front-end to Mathematica, because I use a windowing system that's not widely used anywhere but at CMU. The only pointer I've found is a reference to a technical report called "The MathTalk Communication Protocol" by one D. Grayson. I haven't been able to find a copy of this. Was it published in a journal somewhere? Is it available online somewhere? Is a description of the protocol available from some other source? Is there a place from which I can order it? Any help would be appreciated. -- Doug DeJulio dd26@andrew.cmu.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Sun Oct 7 00:23:57 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA21605 (5.64+/IDA-1.3.4 for stevec); Sun, 7 Oct 90 00:23:42 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA27139; Sun, 7 Oct 90 00:21:52 CDT Received: by yoda.ncsa.uiuc.edu id AA20548 (5.64+/IDA-1.3.4 for ); Sat, 6 Oct 90 18:51:06 -0500 Received: by yoda.ncsa.uiuc.edu id AA20544 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Sat, 6 Oct 90 18:51:05 -0500 Message-Id: <9010062351.AA20544@yoda.ncsa.uiuc.edu> Date: Sat, 6 Oct 90 12:23:53 EDT From: myu@paul.rutgers.edu (Mike (Minjae) Yu) To: mathgroup-request@yoda.ncsa.uiuc.edu Subject: Question Status: RO Hi, Mathematica. I am a clumsy user of Mathematica. I am wondering about batch mode in Mathematica under UNiX. How can I do that? Please answer me as soon as possible. Thank you. Daiwoo Choi Dept. Statistics Hill ctr., Busch Campus Rutger Univ. Piscataway, NJ 08854 myu@paul.rutgers.edu P.S. Is there any information for Mathematica User's group? From mathgroup-adm@yoda.ncsa.uiuc.edu Sun Oct 7 01:09:35 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA21788 (5.64+/IDA-1.3.4 for stevec); Sun, 7 Oct 90 01:09:22 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA27848; Sun, 7 Oct 90 01:07:23 CDT Received: by yoda.ncsa.uiuc.edu id AA20553 (5.64+/IDA-1.3.4 for ); Sat, 6 Oct 90 18:51:15 -0500 Received: by yoda.ncsa.uiuc.edu id AA20549 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Sat, 6 Oct 90 18:51:14 -0500 Message-Id: <9010062351.AA20549@yoda.ncsa.uiuc.edu> Date: Sat, 6 Oct 90 11:04:15 -0700 From: fateman@ucbarpa.Berkeley.EDU (Richard Fateman) To: mathgroup@yoda.ncsa.uiuc.edu Subject: bugs with N ... Status: RO Telling fortunes by reading N-trails? Mathematica (sun3.68881) 1.2 (November 6, 1989) [With pre-loaded data] (* Change $Post to look at all three attributes on display *) In[1]:= p[x_]:= {x, Accuracy[x], Precision[x]} In[3]:= $Post=p ..... In[7]:= N[Sin[10^16],16,16] Out[7]= {0.779679945161067, 16, 16} In[9]:= N[Sin[10^16],20] (* increasing precision decreases "Accuracy" *) Out[9]= {0.78, 4, 4} In[10]:= N[Sin[10^16],50] Out[10]= {0.7796880066069787502355279540333621, 34, 34} In[11]:= a=10^50 In[13]:= N[Sin[a],16] Out[13]= {0.0937537918202386, 17, 16} (* this answer is not good to 17 places. it is wrong in all places, and even has the wrong sign. *) In[14]:= N[Sin[a],20] Format::imz: Warning: Number with negative accuracy being printed as 0. Out[14]= {0., -30, 0} (* I think this means that Mathematica cannot determine Sin[a] within a range of -10^30 to +10^30. Most people think that for real arguments the sine function is restricted to [-1,1] *) In[16]:= N[Sin[a],49] Out[16]= {0., -1, 0} .. In[19]:= N[Sin[a],52] Out[19]= {-0.8, 2, 2} In[20]:= N[Sin[a],60] Out[20]= {-0.789672493, 10, 10} In[21]:= b=N[a,60] Out[21]= {100000000000000000000000000000000000000000000000000., 10, 60} (* M'ma's policy of making this number "accurate" to 10 places leads to foolishness. Why the location of the decimal place is so important, is hard to understand. Are meters more accurate than millimeters? *) In[22]:= Sin[b] Out[22]= {-0.789672493, 10, 10} In[23]:= N[Sin[b],16] Out[23]= {-0.7896724934295026, 16, 16} In[24]:= N[Sin[b],18] Out[24]= {-0.789672493, 10, 10} ... In[27]:= N[Sin[b],100] Out[27]= {-0.789672493, 10, 10} .... Of course some of these anomalies are easily explained by knowing how Mathematica "works". That does not make them necessarily more comforting. -- Richard Fateman From mathgroup-adm@yoda.ncsa.uiuc.edu Sun Oct 7 02:04:57 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA21878 (5.64+/IDA-1.3.4 for stevec); Sun, 7 Oct 90 02:04:45 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA28696; Sun, 7 Oct 90 02:02:49 CDT Received: by yoda.ncsa.uiuc.edu id AA20533 (5.64+/IDA-1.3.4 for ); Sat, 6 Oct 90 18:50:45 -0500 Received: by yoda.ncsa.uiuc.edu id AA20529 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Sat, 6 Oct 90 18:50:43 -0500 Message-Id: <9010062350.AA20529@yoda.ncsa.uiuc.edu> Date: Thu, 4 Oct 90 00:49 EDT From: CAMERON@midd.cc.middlebury.edu Subject: Answer to "Points problem" To: mathgroup@yoda.ncsa.uiuc.edu Status: RO [[ Are members of MathGroup "MathGroupies" ? ]] [[ Should I say "elements of the MathGroup" ? ]] [[ Is it abelian? ]] maxwebb@vitus.cse.ogi.edu (Max G. Webb) asks why some code like Show[Graphics3D[ pointlist, shortlinelist ]]; displays the points in pointlist, but Show[Graphics3D[ pointlist, longlinelist ]]; produces a display in which the points are missing. He is falling afoul of a subtle feature of Mathematica graphics: automatic scaling. Consider the function boundingbox[x_] := Block[ {y=N[x]}, positions = Position[y,{_?NumberQ,_?NumberQ,_?NumberQ}]; coordinates = Apply[ (y[[##]])&, positions, {1} ]; {Min[#],Max[#]}& /@ Transpose[coordinates] ] This function takes a Graphics3D object (or list of 3D graphics primitives) and returns a list {{xmin,xmax},{ymin,ymax},{zmin,zmax}} indicating the ranges of x, y, and z coordinates in the object. The original posting's values for pointlist, shortlinelist, and longlinelist are reproduced for reference at the end of this note. With these values, we get boundingbox[pointlist] {{-1.367512718901739, 1.3608552544435}, {0.00111807892934969, 0.002607945574256309}, {0.001639740038943013, 0.003728634284214638}} boundingbox[shortlinelist] {{-0.1820927732, 0.}, {0., 0.0004133633611}, {0., 0.0008263234388}} boundingbox[longlinelist] {{-0.1854201093010261, 0.}, {0., 0.0005506040866933036}, {0., 0.001102215067405295}} Note that the smallest y coordinate among the points is greater than the largest y coordinate among the lines. Similarly for the z coordinates. The x range for the points encloses the x range for the lines, but is about fourteen times as big. Whenever Mathematica displays Graphics or Graphics3D objects, if PlotRange->Automatic is in effect (as it is by default if no explicit PlotRange is given) then Mathematica goes through a complicated (and, as far as I know, completely undocumented) sequence of calculations to decide what range of values to display along each coordinate axis. This computation includes, essentially, an analysis of the mean and variance of the coordinates in the graphics list, with graphics features whose coordinates are "outliers" being rejected. This is why, if you ask Mathematica to do Plot[ Tan[x], {x,0,2Pi} ] you get a reasonable plot, chopped off at reasonable y-coordinates. The points "near" +/- infinity are chopped off because they are too far from the mean y-coordinate (most points on that graph have y-coordinates near 0; only points with x-coordinates very near Pi/2 or 3Pi/2 have y-coordinates far from 0). Although I don't know the details of how Mathematica decides what to keep and what to reject, this example suggests that it gives more weight to Line objects than to Point objects, because adding a couple of Line's to the graphic radically changes the default scale. At any rate, if you do the following: Show[Graphics3D[{pointlist,shortlinelist}], PlotRange->{{-1.4,1.4},{0.,.003},{0.,.004}}, BoxRatios->{1,1,1} ]; and Show[Graphics3D[{pointlist,longlinelist}], PlotRange->{{-1.4,1.4},{0.,.003},{0.,.004}}, BoxRatios->{1,1,1} ]; then you override the automatic scaling, and you will get pictures that I believe are much closer to what the original poster wanted and expected to get. --Cameron Smith Mathematica programming consultant CAMERON@MIDD.BITNET --or-- cameron@midd.cc.middlebury.edu The original posting had pointlist = {PointSize[0.05], GrayLevel[0.5], Point[{-1.367511195263215, 0.001195340754223037, 0.003139555787092553}], Point[{-1.367512718901739, 0.001195342899414338, 0.001639740038943013}], Point[{1.36085379675106, 0.002607945574256309, 0.00372862923999308}], Point[{1.3608552544435, 0.00111807892934969, 0.003728634284214638}] }; and shortlinelist = { Line[{{0., 0., 0.}, {-0.003327336062, 0.0004133633611, 0.0008263234388}}], Line[{{-0.003327336062, 0.0004133633611, 0.0008263234388}, {-0.1820927732, 0.0001372407256, 0.0002758916286}}] }; and longlinelist = { Line[{{0., 0., 0.}, {-0.003327336062, 0.0004133633611, 0.0008263234388}}], Line[{{-0.003327336062, 0.0004133633611, 0.0008263234388}, {-0.1820927732, 0.0001372407256, 0.0002758916286}}], Line[{{-0.1854201093010261, 0.0005506040866933036, 0.001102215067405295}, {0., 0., 0.}}], Line[{{-0.1854201093010261, 0.0005506040866933036, 0.001102215067405295}, {-0.1820927751, 0.0001345637681, 0.0002715492562}}] }; From mathgroup-adm@yoda.ncsa.uiuc.edu Sat Oct 13 01:41:11 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA03736 (5.64+/IDA-1.3.4 for stevec); Sat, 13 Oct 90 01:41:09 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA10402; Sat, 13 Oct 90 01:39:12 CDT Received: by yoda.ncsa.uiuc.edu id AA02900 (5.64+/IDA-1.3.4 for ); Fri, 12 Oct 90 21:26:21 -0500 Received: by yoda.ncsa.uiuc.edu id AA02890 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 12 Oct 90 21:26:04 -0500 Message-Id: <9010130226.AA02890@yoda.ncsa.uiuc.edu> Date: Mon, 8 Oct 90 17:43:32 CDT From: carl@crazyman.med.ge.com (Carl Crawford) To: mathgroup@yoda.ncsa.uiuc.edu Subject: long comments Status: RO it appears that mathematica does not like blank lines in the middle of comments that stretch across a couple of lines. for example, the following code will generate an error: (* line1 line2 *) does anyone know why this happens? Carl R. Crawford, Ph.D. Voice: 414-521-6572 GE Medical Systems Fax: 414-521-6575 P.O. Box 414, W-875 Uucp: {sun!sunbird,uunet!crdgw1}!gemed!carl Milwaukee, WI 53201 Internet: carl@gemed.ge.com From mathgroup-adm@yoda.ncsa.uiuc.edu Sat Oct 13 05:15:23 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA04312 (5.64+/IDA-1.3.4 for stevec); Sat, 13 Oct 90 05:15:20 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA15231; Sat, 13 Oct 90 05:13:24 CDT Received: by yoda.ncsa.uiuc.edu id AA03791 (5.64+/IDA-1.3.4 for ); Sat, 13 Oct 90 01:58:12 -0500 Received: by yoda.ncsa.uiuc.edu id AA03787 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Sat, 13 Oct 90 01:58:11 -0500 Message-Id: <9010130658.AA03787@yoda.ncsa.uiuc.edu> Date: Wed, 10 Oct 90 13:11 CST From: MEZZINO@cl.uh.edu Subject: Gear method To: mathgroup@yoda.ncsa.uiuc.edu Status: RO Has anyone written a Mathematica package which implements the Gear method for integrating stiff systems of differential equations? Mike Mezzino, Chairman Department of Mathematics University of Houston - Clear Lake 2700 Bay Area Blvd. Houston, TX 77058 mezzino@cl.uh.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Sat Oct 13 04:26:46 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA04180 (5.64+/IDA-1.3.4 for stevec); Sat, 13 Oct 90 04:26:44 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA14526; Sat, 13 Oct 90 04:24:47 CDT Received: by yoda.ncsa.uiuc.edu id AA02878 (5.64+/IDA-1.3.4 for ); Fri, 12 Oct 90 21:25:32 -0500 Received: by yoda.ncsa.uiuc.edu id AA02874 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 12 Oct 90 21:25:30 -0500 Message-Id: <9010130225.AA02874@yoda.ncsa.uiuc.edu> Date: Sat, 6 Oct 90 21:13:22 pdt From: David Jacobson To: mathgroup@yoda.ncsa.uiuc.edu Subject: Parameter passing "feature" Status: RO When a function has the HoldAll (or HoldFirst or HoldRest) attributes, there are possible name conflicts between symbols in actual parameters (arguments) and local variable declared in blocks (and I presume iterators, but I didn't check). See the following example In[1]:= SetAttributes[baz,HoldAll] In[2]:= baz[x_] := {Block[{z=3},x],x} In[3]:= baz[1] Out[3]= {1, 1} In[4]:= z=1 Out[4]= 1 In[5]:= baz[z] Out[5]= {3, 1} I'm not sure this is a bug, but I thought it was something some of you would like to know about. -- David Jacobson >From carl@crazyman.med.ge.com Mon Oct 8 18:04:33 1990 Received: from CRDGW1.GE.COM by yoda.ncsa.uiuc.edu with SMTP id AA23597 (5.64+/IDA-1.3.4 for stevec); Mon, 8 Oct 90 18:04:25 -0500 Received: by crdgw1.ge.com (5.57/GE 1.73) id AA24610; Mon, 8 Oct 90 19:00:16 EDT Received: from crazyman. by med.ge.com (3.2/SMI-3.2/bgb 8/30/89) id AA10422; Mon, 8 Oct 90 17:43:26 CDT Received: by crazyman. (4.0/SMI-4.0) id AA00998; Mon, 8 Oct 90 17:43:32 CDT Date: Mon, 8 Oct 90 17:43:32 CDT From: carl@crazyman.med.ge.com (Carl Crawford) Message-Id: <9010082243.AA00998@crazyman.> To: mathgroup-adm@yoda.ncsa.uiuc.edu Subject: long comments Status: RO it appears that mathematica does not like blank lines in the middle of comments that stretch across a couple of lines. for example, the following code will generate an error: (* line1 line2 *) does anyone know why this happens? Carl R. Crawford, Ph.D. Voice: 414-521-6572 GE Medical Systems Fax: 414-521-6575 P.O. Box 414, W-875 Uucp: {sun!sunbird,uunet!crdgw1}!gemed!carl Milwaukee, WI 53201 Internet: carl@gemed.ge.com From mathgroup-adm@yoda.ncsa.uiuc.edu Sat Oct 13 03:56:35 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA04085 (5.64+/IDA-1.3.4 for stevec); Sat, 13 Oct 90 03:56:34 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA14038; Sat, 13 Oct 90 03:54:37 CDT Received: by yoda.ncsa.uiuc.edu id AA02904 (5.64+/IDA-1.3.4 for ); Fri, 12 Oct 90 21:26:28 -0500 Received: by yoda.ncsa.uiuc.edu id AA02887 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 12 Oct 90 21:25:56 -0500 Message-Id: <9010130225.AA02887@yoda.ncsa.uiuc.edu> From: macg@SLCS.SLB.COM (Bill Macgregor) Date: Wed, 10 Oct 90 14:44:39 CDT To: mathgroup@yoda.ncsa.uiuc.edu Subject: Flat esoterica Status: RO Two examples below of apparently inconsistent behavior wrt. the Flat attribute. Can anyone explain it? - Bill MacGregor ------------------ In[1]:= SetAttributes[f, Flat] In[2]:= f[x_] := x In[3]:= On[] In[4]:= f[1] f::trace: f[1] --> f[1]. f::trace: f[1] --> f[1]. f::trace: f[1] --> f[1]. f::trace: f[1] --> f[1]. f::trace: f[1] --> f[1]. f::trace: f[1] --> f[1]. f::trace: f[1] --> f[1]. ^C Interrupt: continue (or c) to continue show (or s) to show current operation (and then continue) trace (or t) to show all operations abort (or a) to abort current calculation exit (or quit) to exit program ? abort -interrupted- Out[4]= $Interrupted In[5]:= Clear[f] Clear::trace: Clear[f] --> Null. In[6]:= f[x__] := Identity[x] SetDelayed::trace: f[x__] := Identity[x] --> Null. In[7]:= f[1] f::trace: f[1] --> Identity[1]. Identity::trace: Identity[1] --> 1. Out[7]= 1 From mathgroup-adm@yoda.ncsa.uiuc.edu Sat Oct 13 03:23:14 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA03991 (5.64+/IDA-1.3.4 for stevec); Sat, 13 Oct 90 03:23:13 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA13612; Sat, 13 Oct 90 03:21:06 CDT Received: by yoda.ncsa.uiuc.edu id AA02883 (5.64+/IDA-1.3.4 for ); Fri, 12 Oct 90 21:25:39 -0500 Received: by yoda.ncsa.uiuc.edu id AA02879 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 12 Oct 90 21:25:38 -0500 Message-Id: <9010130225.AA02879@yoda.ncsa.uiuc.edu> Date: Wed, 10 Oct 90 11:50:19 CDT From: "Roger B. Kirchner" To: mathgroup@yoda.ncsa.uiuc.edu Subject: On the Function problem Status: RO Several people have pointed out that the problem with Function is a bug in Derivative[1] which doesn't know how to handle Subtract in the version of Function which uses variables. The bug seems to be in all current versions of Mathematica. A couple of people have observed that the problem does not exist with the version of Function which uses slots. This is just as good for my purposes because I want to deemphasize variable names in function definitions. In[1]:= f = Function[x, x^2 - x] 2 Out[1]= Function[x, x - x] In[2]:= f'[x] 2 Out[2]= (Function[x, x - x])'[x] In[3]:= g = Function[#^2 - #] 2 Out[3]= #1 - #1 & In[4]:= g'[x] Out[4]= -1 + 2 x Roger Kirchner rkirchne@mathcs.carleton.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Sat Oct 13 02:37:16 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA03894 (5.64+/IDA-1.3.4 for stevec); Sat, 13 Oct 90 02:37:15 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA11240; Sat, 13 Oct 90 02:35:17 CDT Received: by yoda.ncsa.uiuc.edu id AA02902 (5.64+/IDA-1.3.4 for ); Fri, 12 Oct 90 21:26:26 -0500 Received: by yoda.ncsa.uiuc.edu id AA02893 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 12 Oct 90 21:26:11 -0500 Message-Id: <9010130226.AA02893@yoda.ncsa.uiuc.edu> Date: Mon, 8 Oct 90 14:16:06 PDT From: decide!bobk@uunet.UU.NET (Bob Korsan) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Problem with Function (there isn't any...) Status: RO If you further define In[1]:= h=Function[x,x + -x^2] Out[1]:= Function[x, x- x^2] In[2]:= h'[2] Out[2]:= -3 The trick is that Subtract is not associative and hence In[3]:= D[Funcion[x, x-x^2],x] (1,0) 2 (0,1) 2 Out[3]:= Function[x, Subtract [x, x ] + Subtract [x, x ] 2 x] All in all, this is the reason why languages like APL have a different symbol which is used for negation and for subtraction. They are different concepts. Peace Bob Korsan From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Oct 16 01:54:18 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA08554 (5.64+/IDA-1.3.4 for stevec); Tue, 16 Oct 90 01:54:16 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA21587; Tue, 16 Oct 90 01:52:22 CDT Received: by yoda.ncsa.uiuc.edu id AA07790 (5.64+/IDA-1.3.4 for ); Mon, 15 Oct 90 23:57:27 -0500 Received: by yoda.ncsa.uiuc.edu id AA07786 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Mon, 15 Oct 90 23:57:26 -0500 Message-Id: <9010160457.AA07786@yoda.ncsa.uiuc.edu> From: macg@SLCS.SLB.COM (Bill Macgregor) Date: Mon, 15 Oct 90 11:18:57 CDT To: mathgroup@yoda.ncsa.uiuc.edu Subject: Parameter passing "feature" Status: RO [in reply to a previous message from David Jacobson. -smc] David - I don't think this problem is restricted to the case where the function is HoldFirst or HoldAll--I think it's a general problem. In fact, when I showed this problem around the office, the Lisp people said "Mathematica has the funarg problem; tell them to get with the times." This is a hoary problem for the Lisp community. The problem, as I understand it, is that Block variables aren't really new symbols; they're the dynamically enclosing variable with the values push'd at block entry and pop'd at exit. This is an invitation to disaster in cases like - f[x_] := Block[{y}, y = 2 x] where f[y] produces an infinite loop. In fact, to be completely safe, you must insure that function block variables used as lhs's of Set are distinct from all symbols in their corresponding rhs's, which may involve the function arguments in arbitrary ways. At first glance this is a major violation of information hiding--the function's callers must avoid using the function's local variables in actual arguments! The Mma book claims that this behavior is sometimes desirable (don't think I believe it). It further states (correctly) that the problem is made less severe when f is defined in a package, and is therefore defined context different from the one in which it normally used. For example, if f is defined in package FPackage, but called from context Global on Global`y, the effect is f[Global`y] -> Block[{FPackage`y}, FPackage`y = 2 Global`y] and everything is OK because the two y's are really different symbols. Name substitution still seems, to me at least, to be a serious design mistake in this case. It's too dangerous. Lisp abandoned it. Forcing all Block variables to be truly unique symbols would seem a much better choice. - Bill MacGregor From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Oct 16 03:13:44 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA08640 (5.64+/IDA-1.3.4 for stevec); Tue, 16 Oct 90 03:13:42 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA22897; Tue, 16 Oct 90 03:11:40 CDT Received: by yoda.ncsa.uiuc.edu id AA07775 (5.64+/IDA-1.3.4 for ); Mon, 15 Oct 90 23:57:04 -0500 Received: by yoda.ncsa.uiuc.edu id AA07771 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Mon, 15 Oct 90 23:57:02 -0500 Message-Id: <9010160457.AA07771@yoda.ncsa.uiuc.edu> Date: Sat, 13 Oct 90 04:41:06 CDT From: cook@dragonfly.wri.COM To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Flat esoterica Status: RO The attribute Flat has the following effect on pattern matching: In[67]:= SetAttributes[f,Flat] In[68]:= f[foo]:=bar In[69]:= f[glub, flub, foo, snoo] Out[69]= f[glub, flub, bar, snoo] As you can see, it uses the fact that f is Flat as permission to interpret f[glub, flub, foo, snoo] as f[glub, flub, f[foo], snoo]. A definition like f[x_]:=x will lead to an infinite loop when used, since f's Flatness tells Mathematica to first look at f[x] as f[f[x]]. Flatness of f f[x_]:=something f[x] -------------------> f[f[x]] ----------------------> f[something] ^ / | / -------------------------------------------------- Basically, if f is Flat, then you should be very careful when defining rules for f of a single argument, since every argument of f can be thought of as having its own little f enveloping it. From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Oct 16 04:08:48 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA08725 (5.64+/IDA-1.3.4 for stevec); Tue, 16 Oct 90 04:08:43 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA25269; Tue, 16 Oct 90 04:06:46 CDT Received: by yoda.ncsa.uiuc.edu id AA07780 (5.64+/IDA-1.3.4 for ); Mon, 15 Oct 90 23:57:12 -0500 Received: by yoda.ncsa.uiuc.edu id AA07776 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Mon, 15 Oct 90 23:57:11 -0500 Message-Id: <9010160457.AA07776@yoda.ncsa.uiuc.edu> Date: Sun, 14 Oct 90 15:02 EDT From: CAMERON@midd.cc.middlebury.edu Subject: Parameter passing "feature" is correct! To: mathgroup@yoda.ncsa.uiuc.edu Status: RO David Jacobson writes: > When a function has the HoldAll (or HoldFirst or HoldRest) attributes, > there are possible name conflicts between symbols in actual parameters > (arguments) and local variable declared in blocks... Quite true. Mathematica's evaluation strategy is (at least 80% of the time) pure textual substitution and term-rewriting. In the example below, "foo[z]" causes the pattern variable "x" to match the "z" (which is not rewritten because of the "HoldAll" attribute). The MEANING of the ":=" is that whatever is matched by the pattern variables on the left-hand side is substituted for those variables on the right-hand side. Thus "foo[z]" is rewritten to "{Block[{z=3},z],z}". After that rewriting happens, "foo" (and its "HoldAll" attribute) are no longer part of the expression, so further rewriting can now happen. The first element of the list has "z" inside a Block in which "z" has the value 3, so that "z" rewrites to 3 (this rewriting is what it MEANS in Mathematica for "z" to "have the value 3"). The second element is not inside a block, so the "z" there gets rewritten according to the global rules, which give "z" the value 1. > I'm not sure this is a bug, ... It's not. I suppose you could claim that it's a "design misfeature", but Mathematica IS DOING what it's documented to do. This is why there are "Contexts" in the language. Compare the behavior of "foo" to that of "bar" below. Once again the "z" in "bar[z]" is not rewritten immediately because of a "HoldAll" attribute. But this time "bar[z]" gets rewritten to "{Block[{Private`z=3},{z,Private`z}],{z,Private`z}}". Now a "z" in the context "Private`" is NOT the same symbol as a "z" in the (default) context "Global`", so the rule on "Private`z" inside the Block does not affect the "z" that was passed in as the argument to "bar". The result is that of the two distinct "z"'s inside the Block, the first one gets rewritten according to the rules for "Global`z", so it becomes a 1, while the second gets rewritten according to the rules for "Private`z", so it becomes a 3. The two "z"'s in the second sublist are in the scope of the global rules only, not inside a Block, so the first one ("Global`z") gets rewritten to 1 as before, but the second one ("Private`z") does not get rewritten at all, because the global rule base contains no rules for the symbol "Private`z". Of course, the usual way of putting symbols into a different context than "Global`" is not to write the fully-qualified names with explicit context prefixes, but to use "Begin[]" or "BeginPackage[]" to tell the parser to use a different context as default until the corresponding "End[]" or "EndPackage[]". The parser interprets symbol names not explicitly qualified by a context prefix as belonging to the context named by the current value of "$Context", which is affected by "Begin[]", "BeginPackage[]", "End[]", and "EndPackage[]". In[1]:= SetAttributes[foo, HoldAll] In[2]:= foo[x_] := { Block[{z=3},x], x } In[3]:= foo[1] Out[3]= {1, 1} In[4]:= z=1; foo[z] Out[4]= {3, 1} In[5]:= SetAttributes[bar, HoldAll] In[6]:= bar[x_] := { Block[{Private`z=3}, {x,Private`z} ], {x,Private`z} } In[7]:= z Out[7]= 1 In[8]:= bar[z] Out[8]= {{1, 3}, {1, Private`z}} In[9]:= bar[1] Out[9]= {{1, 3}, {1, Private`z}} I hope this explanation causes more understanding than confusion! --Cameron Smith Mathematica programming consultant CAMERON@MIDD.BITNET --or-- cameron@midd.cc.middlebury.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Oct 16 04:16:29 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA08745 (5.64+/IDA-1.3.4 for stevec); Tue, 16 Oct 90 04:16:25 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA25345; Tue, 16 Oct 90 04:14:31 CDT Received: by yoda.ncsa.uiuc.edu id AA07785 (5.64+/IDA-1.3.4 for ); Mon, 15 Oct 90 23:57:19 -0500 Received: by yoda.ncsa.uiuc.edu id AA07781 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Mon, 15 Oct 90 23:57:18 -0500 Message-Id: <9010160457.AA07781@yoda.ncsa.uiuc.edu> Date: Sun, 14 Oct 90 14:32:41 -0400 From: fink@acf5.NYU.EDU (Howard Fink) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Mathematica Conference attendance Status: RO I'd like to go, and wonder if anyone in San Francisco is attending and would like to make some money putting me up for a few days. Jan 11-15, 1991. Please reply to: fink@acf5.nyu.edu Thanks! From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Oct 17 23:49:10 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA12442 (5.64+/IDA-1.3.4 for stevec); Wed, 17 Oct 90 23:49:07 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA20431; Wed, 17 Oct 90 23:47:11 CDT Received: by yoda.ncsa.uiuc.edu id AA12253 (5.64+/IDA-1.3.4 for ); Wed, 17 Oct 90 20:44:10 -0500 Received: by yoda.ncsa.uiuc.edu id AA12249 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Wed, 17 Oct 90 20:44:08 -0500 Message-Id: <9010180144.AA12249@yoda.ncsa.uiuc.edu> Date: Tue, 16 Oct 90 09:53:10 -0400 (EDT) From: Michael Albert To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Flat esoterica Status: RO As noted, rules for flat functions on one variable lead to problems as Mathematica finds that it can continually use them by nsting the function. Is there any way around this? The examples I have in mind particularly are functions like union and intersection (where f[x_] := x is a very desirable simplification!) Michael Albert Dept. of Mathematics Carnegie Mellon University From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Oct 18 00:49:34 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA13154 (5.64+/IDA-1.3.4 for stevec); Thu, 18 Oct 90 00:49:32 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA22660; Thu, 18 Oct 90 00:47:30 CDT Received: by yoda.ncsa.uiuc.edu id AA12259 (5.64+/IDA-1.3.4 for ); Wed, 17 Oct 90 20:45:45 -0500 Received: by yoda.ncsa.uiuc.edu id AA12255 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Wed, 17 Oct 90 20:45:43 -0500 Message-Id: <9010180145.AA12255@yoda.ncsa.uiuc.edu> Date: Wed, 17 Oct 90 16:11:12 CDT From: pea@dragonfly.wri.com To: mathgroup@yoda.ncsa.uiuc.edu Subject: Mathematica Conference Status: RO ---------------o0o--------------- 1991 MATHEMATICA CONFERENCE January 12-15, 1990 San Francisco, California ---------------o0o--------------- LOCATION Hyatt Regency Hotel, Embarcadero Center, San Francisco, California TIMES Sessions and Exhibits: 2 pm Saturday, January 12 -- 2 pm Tuesday, January 15 On-Site Registration begins at 12 noon on Saturday, January 12 RELATED CONFERENCES IN SAN FRANCISCO o MACWORLD Expo, January 10-13 o American Mathematical Society Meeting, January 16-19 FEATURES o Invited Lectures o Application Highlights Show o Forums/Panels o Mathematica Clinics o Workshops o Programming Competition o Special Interest Groups TUTORIALS Elementary: o Introduction to Mathematica o Introduction to Mathematica Programming o Numeric Computation o Algebraic Computation o Text Manipulation o Using Notebooks o New Features Update Intermediate: o Graphics Programming o Data Analysis o Calling Programs from Mathematica o Mathematica Programming Style o Producing Graphics for Publication o Mathematica Educational Labs o Creating Mathematica Courseware Advanced: o Advanced Programming o MathLink o Mathematica Implementation o Designing Mathematica Packages o Networking o Advanced New Features o Mathematica System Administration Other topics to be announced. EXHIBITS o Hardware systems o Compatible software o Books/Publications o Mathematica services o Training/Consulting OTHER CONTRIBUTED MATERIAL o Short Talks o Computer-aided Poster Presentations o Teaching Laboratory Sessions o Graphics Gallery FEES Before December 14, 1990: Regular: $275 Educational: $175 Student: $50 After December 14, 1990: Regular: $325 Educational: $225 Student: $75 INFORMATION/REGISTRATION: 1991 Mathematica Conference P.O. Box 3848 Champaign, IL 61826-3848 217-398-0700 fax: 217-398-0747 email: conf@wri.com Deadline for conference submissions November 15, 1990 ABOUT MATHEMATICA Mathematica is an integrated technical computing environment, which performs numeric, symbolic and graphical computations, and embodies a high-level programming language. Developed by Wolfram Research, Inc. Mathematica is available on Macintosh, MS-DOS 386, workstations and larger computers. The 1991 Mathematica Conference is intended for all current and prospective users of Mathematica. Sponsored in part by Wolfram Research, Inc. and Addison-Wesley Publishing Company From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Oct 23 02:50:14 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA20803 (5.64+/IDA-1.3.4 for stevec); Tue, 23 Oct 90 02:50:12 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA00692; Tue, 23 Oct 90 02:48:21 CDT Received: by yoda.ncsa.uiuc.edu id AA20727 (5.64+/IDA-1.3.4 for ); Tue, 23 Oct 90 01:29:44 -0500 Received: by yoda.ncsa.uiuc.edu id AA20723 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 23 Oct 90 01:29:43 -0500 Message-Id: <9010230629.AA20723@yoda.ncsa.uiuc.edu> Date: Thu, 18 Oct 90 18:44:11 CDT From: cook@dragonfly.wri.com To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Flat esoterica Status: RO The way to get around problems when defining f[x_]=something for flat functions f is to set the attribute OneIdentity: In[1]:= SetAttributes[f,{Flat,OneIdentity}] In[2]:= f[x_]:=x In[3]:= f[f[a]] Out[3]= a The OneIdentity attribute tells Mathematica that it should not waste its time wrapping single items in an f[]. cook@dragonfly.wri.com From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Oct 23 05:40:36 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA21200 (5.64+/IDA-1.3.4 for stevec); Tue, 23 Oct 90 05:40:34 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA04884; Tue, 23 Oct 90 05:38:44 CDT Received: by yoda.ncsa.uiuc.edu id AA20722 (5.64+/IDA-1.3.4 for ); Tue, 23 Oct 90 01:29:40 -0500 Received: by yoda.ncsa.uiuc.edu id AA20718 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 23 Oct 90 01:29:37 -0500 Message-Id: <9010230629.AA20718@yoda.ncsa.uiuc.edu> Date: Thu, 18 Oct 90 17:27:22 EDT From: Olin Sibert To: mathgroup@yoda.ncsa.uiuc.edu Subject: Logical expressions in Mathematica Status: RO I'd like to use Mathematica for simplifying and evaluating large logical expressions, the same way that arithmetic expressions can be manipulated. In some casual experimenting and manual reading, I didn't see any obvious way to do this, but I'm no Mathematica expert. It seems like it ought to be possible to use the pattern matching facilities for simplification, but I thought I'd ask and see whether someone more knowledgeable than I has already done so. Is there an existing package that will do this, or do I need to learn how to write my own? Is there something other than Mathematica that I should use instead? It'd be especially helpful to have something that could consider operations like XOR as primitive (i.e., worth reducing to) in addition to AND, OR, and NOT. Thanks. Olin Sibert |Internet: Sibert@Oxford.COM Oxford Systems, Inc. |UUCP: uunet!oxford!sibert From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Oct 23 03:44:36 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA20893 (5.64+/IDA-1.3.4 for stevec); Tue, 23 Oct 90 03:44:34 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA03232; Tue, 23 Oct 90 03:42:44 CDT Received: by yoda.ncsa.uiuc.edu id AA20732 (5.64+/IDA-1.3.4 for ); Tue, 23 Oct 90 01:29:53 -0500 Received: by yoda.ncsa.uiuc.edu id AA20728 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 23 Oct 90 01:29:51 -0500 Message-Id: <9010230629.AA20728@yoda.ncsa.uiuc.edu> Date: Fri, 19 Oct 90 09:38:09 +0200 From: pjanhune@finsun.csc.fi To: mathgroup@yoda.ncsa.uiuc.edu Subject: Fit[] Status: RO To Bob Marzke and other Fit[] people... Nonlinear fitting is now possible in Mathematica. I wrote a package named NonlinearFit.m which is available from the anonymous ftp server. It uses the Levenberg-Marquardt iterative method. The file NLFitTest.m contains testing with Gaussian functions. There are no limitations to the fitted model or to the dimensionality of the data. You can send bug reports, hopes, criticism, comparisons with other methods etc. to: Pekka Janhunen Finnish Meteorological Institute Geophysics Dept. email: pjanhune@finsun.csc.fi From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Oct 23 04:41:10 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA21004 (5.64+/IDA-1.3.4 for stevec); Tue, 23 Oct 90 04:41:08 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA04102; Tue, 23 Oct 90 04:39:18 CDT Received: by yoda.ncsa.uiuc.edu id AA20742 (5.64+/IDA-1.3.4 for ); Tue, 23 Oct 90 01:30:11 -0500 Received: by yoda.ncsa.uiuc.edu id AA20738 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 23 Oct 90 01:30:09 -0500 Message-Id: <9010230630.AA20738@yoda.ncsa.uiuc.edu> From: jdelany@sargas.ACS.CalPoly.EDU (Jim Delany) Subject: math coprocessors To: mathgroup@yoda.ncsa.uiuc.edu Date: Sat, 20 Oct 90 11:30:23 PDT Status: RO Richard Fateman's note on the pitfalls of relying on the Motorola floating point coprocessor prompts me to share the example I like to use: Mathematica (sun3.68881) 1.2 (November 6, 1989) [With pre-loaded data] ... In[1]:= x = 2^100; In[2]:= N[ Sin[x] ] Out[2]= 0.973158 In[3]:= N[ Sin[x], 40 ] Out[3]= -0.872183605 The difference between the hardware and software values is almost 2. Does anyone have a sharper example? Jim Delany ( jdelany@cosmos.acs.calpoly.edu ) Math Department, Cal Poly, San Luis Obispo CA 93407 From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Oct 23 04:54:35 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA21023 (5.64+/IDA-1.3.4 for stevec); Tue, 23 Oct 90 04:54:33 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA04289; Tue, 23 Oct 90 04:52:43 CDT Received: by yoda.ncsa.uiuc.edu id AA20737 (5.64+/IDA-1.3.4 for ); Tue, 23 Oct 90 01:30:02 -0500 Received: by yoda.ncsa.uiuc.edu id AA20733 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 23 Oct 90 01:30:01 -0500 Message-Id: <9010230630.AA20733@yoda.ncsa.uiuc.edu> Date: Fri, 19 Oct 90 09:25:56 -0400 (EDT) From: Michael Albert To: mathgroup@yoda.ncsa.uiuc.edu Subject: Still puzzled about Flat Status: RO I had tried using OneIdentity, but this still seems to cause problems, as the following session indicates. In[1] := Clear[Int] Attributes[Int] = {Flat, OneIdentity, Orderless, Listable} ?Int Out[1] = Int Attributes[Int] = {Flat, Listable, OneIdentity, Orderless} In[2]:= Clear[x,y] Int[x,y] Out[2] = Int[x, y] In[3]:= Int[x_] := x In[4]:= Int[a] Out{4}= a In[4]:= Int[a,b] General::recursion: Recursion depth of 256 exceeded. Hold[Int[a,b]] Out[4]= Hold[Int[a,b]] Obviously it is trrying to do something very clever, and simplify a function with two arguments, when the only rule it knows applies only in the case of a single argument ... unfortunately, it doesn't seem to get anywhere! From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Oct 23 22:08:21 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA22602 (5.64+/IDA-1.3.4 for stevec); Tue, 23 Oct 90 22:08:19 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA23843; Tue, 23 Oct 90 22:06:28 CDT Received: by yoda.ncsa.uiuc.edu id AA22454 (5.64+/IDA-1.3.4 for ); Tue, 23 Oct 90 19:50:19 -0500 Received: by yoda.ncsa.uiuc.edu id AA22450 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 23 Oct 90 19:50:18 -0500 Message-Id: <9010240050.AA22450@yoda.ncsa.uiuc.edu> Date: Mon, 22 Oct 90 15:53:20 TST From: DALFE@trboun.bitnet (Nuzhet Dalfes) Subject: Ecology... To: mathgroup@yoda.ncsa.uiuc.edu Status: RO Hi! I am interested to find out about the use of Mathematica in ecological research and/or education. I would appreciate any pointer to packages, articles, notebooks etc. Nuzhet Dalfes Bogazici University 80815 Bebek Istanbul TURKEY From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Oct 23 22:43:25 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA22729 (5.64+/IDA-1.3.4 for stevec); Tue, 23 Oct 90 22:43:23 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA24393; Tue, 23 Oct 90 22:41:34 CDT Received: by yoda.ncsa.uiuc.edu id AA22459 (5.64+/IDA-1.3.4 for ); Tue, 23 Oct 90 19:50:26 -0500 Received: by yoda.ncsa.uiuc.edu id AA22455 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 23 Oct 90 19:50:25 -0500 Message-Id: <9010240050.AA22455@yoda.ncsa.uiuc.edu> Date: Tue, 23 Oct 90 08:17:10 -0700 From: fateman@ucbarpa.Berkeley.EDU (Richard Fateman) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: math coprocessors Status: RO The problem is not with the math coprocessor, but the software used by mathematica in computing range reduction. To reduce the range of 2^100 you need about 120 bits of Pi. If Mathematica is supposed to provide a seamless "mathematical" computational environment, it should not give wrong answers and allege that they have high Accuracy and Precision. From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Oct 23 23:42:42 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA22939 (5.64+/IDA-1.3.4 for stevec); Tue, 23 Oct 90 23:42:40 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA06464; Tue, 23 Oct 90 23:40:41 CDT Received: by yoda.ncsa.uiuc.edu id AA22469 (5.64+/IDA-1.3.4 for ); Tue, 23 Oct 90 19:50:44 -0500 Received: by yoda.ncsa.uiuc.edu id AA22465 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 23 Oct 90 19:50:42 -0500 Message-Id: <9010240050.AA22465@yoda.ncsa.uiuc.edu> Date: Tue, 23 Oct 90 11:13:54 CDT From: gabriel@athens.ees.anl.gov (John Gabriel) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Logical expressions in Mathematica Status: RO There are a number of traps in simplification of large logical expressions by any symbolic algebra package. Of these, the biggest is that the "obvious" elementary operators do not give rise to a Church-Rosser set of reduction rules. I think I'm right in saying that AND and XOR give Church Rosser rewriting rules if used alone - i.e. first turn everything into AND and XOR and only then begin to simplify. The rewriting algorithms in Boyer & Moore's theorem prover are the outcome of many years of work, and perhaps you should mail a question to boyer@cli.com before venturing too far into the jungle on your own. For more information on rewriting, Church-Rosser, and canonical forms - if a reduction is not canonical then it's not very useful - see Alan Bundy's book on Computer Modelling of Mathematics or a similar title, mine's at home so I can't quote chapter and verse. Also, you have a Net doppelganger wos@mcs.anl.gov. People who have worked with him have done a good deal on this, and he could probably point you at somebody. Brian Smith, now at the Dept. of CS at U. of New Mexico Albuquerque is also a good source of advice. John Gabriel (gabriel@ees.anl.gov) From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Oct 24 00:42:36 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA23691 (5.64+/IDA-1.3.4 for stevec); Wed, 24 Oct 90 00:42:34 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA20365; Wed, 24 Oct 90 00:40:43 CDT Received: by yoda.ncsa.uiuc.edu id AA22464 (5.64+/IDA-1.3.4 for ); Tue, 23 Oct 90 19:50:35 -0500 Received: by yoda.ncsa.uiuc.edu id AA22460 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 23 Oct 90 19:50:34 -0500 Message-Id: <9010240050.AA22460@yoda.ncsa.uiuc.edu> Date: Tue, 23 Oct 90 11:00:02 CDT From: gabriel@athens.ees.anl.gov (John Gabriel) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: math coprocessors Status: RO I may be speaking from a position of ignorance here, because my knowledge is several years out of date, but the computation of y=sin(x) contains deep pitfalls even for values of x as small as small as 62.83. The point is that for x outside [0..pi/4), multiples of pi/4 must be subtracted from x. For x values close to n*(pi/4) this must be done with consummate skill if work is being done in double precision, or a good deal of significance will be lost. Cody & Waite (A Handbook for the Elementary Functions) discuss the issue at length. So computation of sin(x) for large arguments is always fraught with danger. For a given machine precision, there is typically a value of x beyond which computation of sin(x) will inevitably have significant error, and for some algorithms even x in the region of a few hundreds gives trouble (the worst I ever saw gave noticeable error round about x=30). More recent cases involving functions other than sin(x), investigated by a colleague in the context of FORTRAN exonerated an INTEL floating point co-processor, and laid the blame squarely on a compiler writer in one case, and perhaps on the operating system in another (I don't really know about the second case). So, I suppose the point of all this is that you should not necessarily blame the floating point chip. But perhaps Mathematica takes all the appropriate precautions about argument reduction and has the proper approximation to pi to allow the usual 2 step argument reduction to work OK. On the other hand, if pi is simply held to working precision (no matter how long that may be) argument reduction holds traps for the unwary. But I would be surprised if any IEEE standard chip gave good answers for 2^100. Good answers for 2^70 however, are not obviously ruled out except by a much more careful examination than I have given to the question. John Gabriel (gabriel@ees.anl.gov) From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Oct 24 10:03:18 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA24198 (5.64+/IDA-1.3.4 for stevec); Wed, 24 Oct 90 10:03:16 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA16108; Wed, 24 Oct 90 10:01:24 CDT Received: by yoda.ncsa.uiuc.edu id AA23896 (5.64+/IDA-1.3.4 for ); Wed, 24 Oct 90 08:04:11 -0500 Received: by yoda.ncsa.uiuc.edu id AA23892 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Wed, 24 Oct 90 08:04:09 -0500 Message-Id: <9010241304.AA23892@yoda.ncsa.uiuc.edu> Date: Wed, 24 Oct 90 09:31:13 +0200 From: pjanhune@finsun.csc.fi To: mathgroup@yoda.ncsa.uiuc.edu Subject: NonLinearFit.m Status: RO As a reminder... MATHGROUP ANONYMOUS FTP SERVER ------------------------------ The mathgroup anonymous ftp server address is 128.174.20.50. (i.e. to get there, write "ftp 128.174.20.50", give login as "anonymous" and send your real login name as password. Then you need the commands cd,dir,help,quit,get.) My packages NonlinearFit.m and NLFitTest.m are found in Symbolic/New. Some older postings of mine are also there; you can also find them at Symbolic/Mathematica/Packages/JANHUNEN. Everyone has write/read permissions to the directory Symbolic/New. [All of the packages mentioned above are in Symbolic/Mathematica/Packages/JANHUNEN now. Please report problems getting these packages. -- smc] If the ftp connection is not possible on your system, mail me and I can mail to packages to you. From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Oct 26 23:45:33 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA28862 (5.64+/IDA-1.3.4 for stevec); Fri, 26 Oct 90 23:45:31 -0500 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA04203; Fri, 26 Oct 90 23:43:45 CDT Received: by yoda.ncsa.uiuc.edu id AA28766 (5.64+/IDA-1.3.4 for ); Fri, 26 Oct 90 22:12:02 -0500 Received: by yoda.ncsa.uiuc.edu id AA28762 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 26 Oct 90 22:12:01 -0500 Message-Id: <9010270312.AA28762@yoda.ncsa.uiuc.edu> Date: Fri, 26 Oct 90 17:30:07 ITA From: Riccardo Rigon Subject: Ignorance To: Mathematica special Interest Group Status: RO Dear mathgroupers, I have a function defined like this: MatrixB[x_List]:=Block[{tt={x},z,i,n,zoo}, n=x[[1]]/2; zoo=x; z=Table[0,{i,Length[x]}];z[[2]]++; For[i=1,i<=n-x[[2]],i++,tt=AppendTo[tt,zoo=zoo+z]];tt ] It is probably a bad example of Mathematica programming, but anyway it does what I want: taking as input a vector it builds an appropriate matrix. Now it would be interesting if it accepted as input a list of vectors, giving as result the matrix of the matrices resulting from the analisys of each element of the input. How must I modified my code? Thank you in advance for your help. Riccardo Rigon (an absolute beginner) RIGON@iveuncc.bitnet From mathgroup-adm@yoda.ncsa.uiuc.edu Mon Oct 29 02:29:30 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA01784 (5.64+/IDA-1.3.4 for stevec); Mon, 29 Oct 90 02:29:29 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA08939; Mon, 29 Oct 90 02:27:46 CST Received: by yoda.ncsa.uiuc.edu id AA01056 (5.64+/IDA-1.3.4 for ); Sun, 28 Oct 90 23:05:26 -0600 Received: by yoda.ncsa.uiuc.edu id AA01052 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Sun, 28 Oct 90 23:05:25 -0600 Message-Id: <9010290505.AA01052@yoda.ncsa.uiuc.edu> Date: 28 Oct 90 13:40:47 From: Paul Abbott Subject: Logical Expressions To: mathgroup@yoda.ncsa.uiuc.edu Status: RO Subject: Time:1:58 PM OFFICE MEMO Logical Expressions Date:10/28/90 The following code from Dana Scott will works well with Logical expressions. It relies on AlgebraicRules (which in turn uses Groebner bases). Format[Rep[x:_,_,_]] := x Rep[x_, g_, p_] + Rep[y_, g_, p_] ^:= Rep[Mod[x+y /.g, p], g, p] Rep[x_, g_, p_] + y_ ^:= Rep[Mod[x+y /.g, p], g, p] Rep[x_, g_, p_] * Rep[y_, g_, p_] ^:= Rep[Mod[x*y /.g, p], g, p] Rep[x_, g_, p_] * y_ ^:= Rep[Mod[x*y /.g, p], g, p] Rep[x_, g_, p_] ^ y_ ^:= Rep[Mod[x^y /.g, p], g, p] (* Rules for Boolean algebra *) gbool = AlgebraicRules[{p^2 == p,q^2 == q,r^2 == r,s^2 == s, t^2 == t,u^2 == u,v^2 == v,w^2 == w}, {w,v,u,t,s,r,q,p}]; e = Rep[1,gbool,2]; (* The logical functions *) and[x_,y_] := e x y; or[x_,y_] := e x + y + x y; imp[x_,y_] := e + x + x y; iff[x_,y_] := e + x + y; (* Examples *) p ~imp~ q ~imp~ q ~iff~ (p ~or~ q) (* Mathematica verifies that "p implies q all implies q" is equivalent to the inclusive disjunction of p and q. This is done by translating everything into Boolean polynomials and this reduces to 1. *) (* An example of an invalid formula *) p ~iff~ (p ~or~ q) ~iff~ (p ~and~ q) (* No matter what truth value we give to p, this formula is false. *) From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Nov 1 08:49:22 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA07559 (5.64+/IDA-1.3.4 for stevec); Thu, 1 Nov 90 08:49:19 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA20870; Thu, 1 Nov 90 08:48:06 CST Received: by yoda.ncsa.uiuc.edu id AA07450 (5.64+/IDA-1.3.4 for ); Thu, 1 Nov 90 02:33:31 -0600 Received: by yoda.ncsa.uiuc.edu id AA07446 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Thu, 1 Nov 90 02:33:28 -0600 Message-Id: <9011010833.AA07446@yoda.ncsa.uiuc.edu> Date: Wed, 31 Oct 90 10:32:40 -0500 From: murison@cfacx2.harvard.edu (Marc Murison) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Mathematica on a PC Status: RO Hello, I am trying to get in touch with users of Mathematica on an IBM PC compatible. Our group just had a bad experience with another product, and we'd like some first-hand accounts before we take another financial plunge. Could you put me in touch with PC Mathematica users, or send my e-mail/FAX/phone info to them? Thanks very much, Marc A. Murison Smithsonian Astrophysical Observatory 60 Garden Street, Mail Stop 63 Cambridge, MA 02138 Phone: (617) 495-7079 FAX: (617) 495-7326 SPAN: cfarg3::murison bitnet: murison%cfacx2@cfa.bitnet or pepmmu@cfaamp.bitnet From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Nov 1 09:44:06 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA07631 (5.64+/IDA-1.3.4 for stevec); Thu, 1 Nov 90 09:43:59 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA22083; Thu, 1 Nov 90 09:42:48 CST Received: by yoda.ncsa.uiuc.edu id AA07445 (5.64+/IDA-1.3.4 for ); Thu, 1 Nov 90 02:33:21 -0600 Received: by yoda.ncsa.uiuc.edu id AA07441 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Thu, 1 Nov 90 02:33:19 -0600 Message-Id: <9011010833.AA07441@yoda.ncsa.uiuc.edu> Date: 31 Oct 90 13:41 +0100 From: Robert Staerk To: Subject: Integrate? Status: RO Mathematica gives a wrong answer to the following integral: 2 Pi / | 1/2 | (2 - 2 cos(x)) dx | / 0 Is this a known bug? idefix> math Mathematica (sun4) 1.2 (August 22, 1989) [With pre-loaded data] by S. Wolfram, D. Grayson, R. Maeder, H. Cejtin, S. Omohundro, D. Ballman and J. Keiper with I. Rivin and D. Withoff Copyright 1988,1989 Wolfram Research Inc. -- Terminal graphics initialized -- In[1]:= Integrate[ Sqrt[2 - 2 Cos[x]], {x, 0, 2 Pi}] Out[1]= 0 In[2]:= NIntegrate[ Sqrt[2 - 2 Cos[x]], {x, 0, 2 Pi}] Out[2]= 8. In[3]:= Quit idefix> maple |\^/| MAPLE V ._|\| |/|_. Copyright (c) 1981-1990 by the University of Waterloo. \ MAPLE / All rights reserved. MAPLE is a registered trademark of <____ ____> Waterloo Maple Software. | Type ? for help. > int( sqrt(2 - 2 * cos(x)), x=0...2*Pi ); 8 > done bytes used=1447572, alloc=917336, time=8.116 idefix> ------------------------------------------------------------------------- Robert Staerk (St\"ark) | Laenggassstrasse 51 | Phone: +41 31 65 85 58 Institut fuer Informatik | CH-3012 Bern | Fax: +41 31 65 39 65 und angewandte Mathematik | Switzerland | ------------------------------------------------------------------------- From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Nov 2 22:15:08 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA10539 (5.64+/IDA-1.3.4 for stevec); Fri, 2 Nov 90 22:15:06 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA00866; Fri, 2 Nov 90 22:13:40 CST Received: by yoda.ncsa.uiuc.edu id AA10427 (5.64+/IDA-1.3.4 for ); Fri, 2 Nov 90 19:39:47 -0600 Received: by yoda.ncsa.uiuc.edu id AA10423 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 2 Nov 90 19:39:45 -0600 Message-Id: <9011030139.AA10423@yoda.ncsa.uiuc.edu> Date: Thu, 1 Nov 90 13:52:13 -0500 From: Jack To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Integrate? Status: RO Macsyma also gives the same incorrect result 0 for this integral (version 416.48 for Sparc Computers). That really surprised me. jack@brahms.udel.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Nov 2 22:45:52 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA10577 (5.64+/IDA-1.3.4 for stevec); Fri, 2 Nov 90 22:45:50 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA01251; Fri, 2 Nov 90 22:44:24 CST Received: by yoda.ncsa.uiuc.edu id AA10422 (5.64+/IDA-1.3.4 for ); Fri, 2 Nov 90 19:39:40 -0600 Received: by yoda.ncsa.uiuc.edu id AA10418 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 2 Nov 90 19:39:39 -0600 Message-Id: <9011030139.AA10418@yoda.ncsa.uiuc.edu> Date: Thu, 1 Nov 90 11:32:07 -0500 From: sg04%harvey@gte.com (Steven Gutfreund) To: mathgroup@yoda.ncsa.uiuc.edu Subject: surface-fit Status: RO Does anyone have a surface fit routine for mathematica? I need to obtain a surface based on a regular x-y grid of points from a data set of points that are scattered on the x-y plane (but fairly smooth in the z dimension). -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= Yechezkal Shimon Gutfreund sgutfreund@gte.com GTE Laboratories, Waltham MA harvard!bunny!sgutfreund -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Nov 2 23:47:08 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA10742 (5.64+/IDA-1.3.4 for stevec); Fri, 2 Nov 90 23:47:06 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA02255; Fri, 2 Nov 90 23:45:27 CST Received: by yoda.ncsa.uiuc.edu id AA10417 (5.64+/IDA-1.3.4 for ); Fri, 2 Nov 90 19:39:22 -0600 Received: by yoda.ncsa.uiuc.edu id AA10413 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 2 Nov 90 19:39:20 -0600 Message-Id: <9011030139.AA10413@yoda.ncsa.uiuc.edu> Date: Wed, 31 Oct 90 10:32:40 -0500 From: murison@cfacx2.harvard.edu (Marc Murison) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Mathematica on a PC Status: RO Hello, I am trying to get in touch with users of Mathematica on an IBM PC compatible. Our group just had a bad experience with another product, and we'd like some first-hand accounts before we take another financial plunge. Could you put me in touch with PC Mathematica users, or send my e-mail/FAX/phone info to them? Thanks very much, Marc A. Murison Smithsonian Astrophysical Observatory 60 Garden Street, Mail Stop 63 Cambridge, MA 02138 Phone: (617) 495-7079 FAX: (617) 495-7326 SPAN: cfarg3::murison bitnet: murison%cfacx2@cfa.bitnet or pepmmu@cfaamp.bitnet From mathgroup-adm@yoda.ncsa.uiuc.edu Sat Nov 3 00:30:08 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA11505 (5.64+/IDA-1.3.4 for stevec); Sat, 3 Nov 90 00:30:06 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA04210; Sat, 3 Nov 90 00:28:06 CST Received: by yoda.ncsa.uiuc.edu id AA10432 (5.64+/IDA-1.3.4 for ); Fri, 2 Nov 90 19:39:55 -0600 Received: by yoda.ncsa.uiuc.edu id AA10428 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 2 Nov 90 19:39:54 -0600 Message-Id: <9011030139.AA10428@yoda.ncsa.uiuc.edu> To: mathgroup@yoda.ncsa.uiuc.edu Subject: getting Limit[] to evaluate Date: Thu, 01 Nov 90 15:00:00 PST From: jacobson@cello.hpl.hp.com Status: RO I wanted to compute the following definite integral, where b > 0 In[1]:= Integrate[x (1-x)^b,{x,0,1}] Limit::nlm: Could not find definite limit. 1 + b 2 + b 1 1 (1 - x) (1 - x) Out[1]= ----- - ----- + Limit[-(------------) + ------------, x -> 1] 1 + b 2 + b 1 + b 2 + b The problem is that it doesn't know that b is not -1 or -2. In this particular case, I can see "by inspection" that the Limit[...] term evaluates to zero, but how can I get Mathematica to do this itself? -- David Jacobson From mathgroup-adm@yoda.ncsa.uiuc.edu Sat Nov 3 01:07:17 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA11594 (5.64+/IDA-1.3.4 for stevec); Sat, 3 Nov 90 01:07:06 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA04830; Sat, 3 Nov 90 01:05:40 CST Received: by yoda.ncsa.uiuc.edu id AA10437 (5.64+/IDA-1.3.4 for ); Fri, 2 Nov 90 19:40:02 -0600 Received: by yoda.ncsa.uiuc.edu id AA10433 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 2 Nov 90 19:40:01 -0600 Message-Id: <9011030140.AA10433@yoda.ncsa.uiuc.edu> From: ccetinka@symcom.math.uiuc.edu (Cetin Cetinkaya) Subject: rootfind problem... Date: Fri, 2 Nov 90 02:00:03 GMT To: mathgroup@yoda.ncsa.uiuc.edu Status: RO Hi; Could anybody tell me what I am doing wrong in the following Mathematica session: In[22]:= f[x_]:=NIntegrate[Sin[s],{s,0,x}] In[23]:= FindRoot[f[y]==0,{y,-1}] NIntegrate::lim: Numerical integration limits {s, 0, y} are not invalid. NIntegrate::lim: Numerical integration limits {s, 0, s} are not invalid. NIntegrate::vars: Integration range specification #2 is not of the form {x, xmin, xmax}. FindRoot::jnotnum: Partial derivative of function 1 w.r.t. variable 1 is not numerical at (0.,1.) {-1.}={0., 0., NIntegrate [Sin[s], {s, 0., -1.}]} . Try giving two starting values for each variable. Out[23]= FindRoot[NIntegrate[Sin[s], {s, 0, y}] == 0, {y, -1}] In[24]:= f[3] Out[24]= 1.98999 Thank You, C.Cetinkaya From mathgroup-adm@yoda.ncsa.uiuc.edu Sat Nov 3 01:49:48 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA11778 (5.64+/IDA-1.3.4 for stevec); Sat, 3 Nov 90 01:49:46 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA05475; Sat, 3 Nov 90 01:48:19 CST Received: by yoda.ncsa.uiuc.edu id AA10447 (5.64+/IDA-1.3.4 for ); Fri, 2 Nov 90 19:43:37 -0600 Received: by yoda.ncsa.uiuc.edu id AA10443 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 2 Nov 90 19:43:36 -0600 Message-Id: <9011030143.AA10443@yoda.ncsa.uiuc.edu> Date: Fri, 2 Nov 90 13:52:39 EST From: pkane@Kodak.COM (Paul Kane) To: mma@isr01.kodak.com Subject: two dimensional NIntegrate Status: RO Here is a question for the mathgroup : I am an advanced amateur with respect to Mathematica. Lately I have been trying to do some integrals involving first order Bessel functions. I am interested in integrands that look like this : (BesselJ[1,(a Sqrt[x^2 + y^2])] / (a Sqrt[x^2 + y^2]) ) g[x], where g[x] is some (one-dimensional) smooth, well-behaved function. I wish to perform a two dimensional numerical integration on this, over a reasonably large domain. If g[x] had polar symmetry, I could reduce this to a one dimensional integration and use NIntegrate over one dimension - I have done this and it works just fine, and finishes within 60 seconds. But now if the integrand no longer has polar symmetry, I am forced to do a 2D integration in rectangular coordinates. The problem is that it takes **forever**, even over one quadrant in xy space. We're talking hours - in fact, I've never had the patience to wait longer than 160 minutes, so I don't know if it ever converges on an answer, let alone the right answer. I have played with the NIntegrate parameters (AccuracyGoal, etc.), but to no avail. My suspicion is that the program is going nuts trying to track the rapidly oscillating Bessel function at larger values of the argument. (This is a classic problem in numerical Hankel transforms, also). My next move was going to be to try some asymptotic approximations for BesselJ[1, ], but before I do that, what do you folks think? Has anyone out there done this before? Thanks in advance for any help ... you can mail to pkane@Kodak.COM and I will post a summary of the answers, if any come in! Paul J. Kane Eastman Kodak Co. Photographic Research Labs Rochester,NY 14650-1717 (716)-477-1895 (pkane@Kodak.COM) From mathgroup-adm@yoda.ncsa.uiuc.edu Sat Nov 3 00:59:58 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA11564 (5.64+/IDA-1.3.4 for stevec); Sat, 3 Nov 90 00:59:53 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA04687; Sat, 3 Nov 90 00:58:24 CST Received: by yoda.ncsa.uiuc.edu id AA10442 (5.64+/IDA-1.3.4 for ); Fri, 2 Nov 90 19:40:12 -0600 Received: by yoda.ncsa.uiuc.edu id AA10438 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 2 Nov 90 19:40:10 -0600 Message-Id: <9011030140.AA10438@yoda.ncsa.uiuc.edu> Date: Fri, 2 Nov 90 18:21:48 +0100 From: Harald Hanche-Olsen To: Subject: Integrate? Status: RO Robert Staerk writes ... Mathematica gives a wrong answer to the following integral: 2 Pi / | 1/2 | (2 - 2 cos(x)) dx | / 0 Is this a known bug? In[1]:= Integrate[ Sqrt[2 - 2 Cos[x]], {x, 0, 2 Pi}] Out[1]= 0 This is apparently caused by Mathematicas attempts at being clever about things like complex square roots, branch cuts and the like. Yes, it is known. And some people think Mathematica is brain-dead because of it. Myself, I haven't decided yet. I keep alternating between Mathematica and Maple, just like you seem to do... - Harald Hanche-Olsen Division of Mathematical Sciences The Norwegian Institute of Technology N-7034 Trondheim, NORWAY From mathgroup-adm@yoda.ncsa.uiuc.edu Sat Nov 3 21:16:01 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA12321 (5.64+/IDA-1.3.4 for stevec); Sat, 3 Nov 90 21:15:59 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA15204; Sat, 3 Nov 90 21:14:27 CST Received: by yoda.ncsa.uiuc.edu id AA12150 (5.64+/IDA-1.3.4 for ); Sat, 3 Nov 90 17:51:59 -0600 Received: by yoda.ncsa.uiuc.edu id AA12146 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Sat, 3 Nov 90 17:51:58 -0600 Message-Id: <9011032351.AA12146@yoda.ncsa.uiuc.edu> Date: Fri, 2 Nov 1990 18:14 PST From: "Mr. Mathematica Man" Subject: One-sided limits To: mathgroup@yoda.ncsa.uiuc.edu Status: RO How can someone find a ONE-SIDED limit? For example, finding the limit as x->0+ and as x->0-. The zero case can be fudged by substituting (1/x) for every occurrence of x and then using directional +/- Infinity. How can one do this for the non-zero case? Thanks, Lyle Wright Mathematica Developer Harvey Mudd College Claremont, CA 91711 lwright@hmcvax.claremont.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Sat Nov 3 21:40:21 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA12367 (5.64+/IDA-1.3.4 for stevec); Sat, 3 Nov 90 21:40:19 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA17552; Sat, 3 Nov 90 21:38:56 CST Received: by yoda.ncsa.uiuc.edu id AA12155 (5.64+/IDA-1.3.4 for ); Sat, 3 Nov 90 17:52:08 -0600 Received: by yoda.ncsa.uiuc.edu id AA12151 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Sat, 3 Nov 90 17:52:07 -0600 Message-Id: <9011032352.AA12151@yoda.ncsa.uiuc.edu> Date: Sat, 3 Nov 90 12:26 +0800 From: "Mike Reid, Physics, Hong Kong University" Subject: RE : Integrate? To: mathgroup@yoda.ncsa.uiuc.edu Status: RO Well, if we are going to quote Macsyma, I note that REDUCE doesn't integrate the expression at all (it's rare that REDUCE is wrong in my experience, but in many cases like this not being wrong is not quite helpful enough). If you do the indefinite integral with Mathematica you'll find that it is singular at Pi(!?) but has the value -4 at the end-points, so is consistent with the definite integral (no surprise there). Is this a clue? Mike Reid. mfreid@hkucc.bitnet From mathgroup-adm@yoda.ncsa.uiuc.edu Sat Nov 3 22:48:23 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA12489 (5.64+/IDA-1.3.4 for stevec); Sat, 3 Nov 90 22:48:20 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA18466; Sat, 3 Nov 90 22:46:55 CST Received: by yoda.ncsa.uiuc.edu id AA12145 (5.64+/IDA-1.3.4 for ); Sat, 3 Nov 90 17:51:53 -0600 Received: by yoda.ncsa.uiuc.edu id AA12141 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Sat, 3 Nov 90 17:51:52 -0600 Message-Id: <9011032351.AA12141@yoda.ncsa.uiuc.edu> Date: Fri, 2 Nov 1990 18:10 PST From: "Mr. Mathematica Man" Subject: Limit[Sum[...,{n,1,Infinity}], n->Infinity] To: mathgroup@yoda.ncsa.uiuc.edu Status: RO Here is my dilemma. I am trying to model things like Reimann sums and other techniques for approximating the area underneath a curve. Here is a sample scenario. | | |----|----|----|----|----|----|----|----| 0 1 2 We have some interval (in this case, [0,2]) that we are concerned with. It is divided into n sections. Say we are interested in the function f(x) = x^3. So we want to find the area under the graph of x^3 from x=0 to 2. If we subdivide the interval [0,2] into n equal subintervals, then dx = 2/n and xi = 0 + i(2/n) = 2i/n Therefore, Sum[f(xi)dx,{i,1,n}] = Sum[(xi)^3 dx, {i,1,n}] = Sum[(2i/n)^3 (2/n), {i,1,n}] = 16/(n^4) Sum[i^3,{i,1,n}] *** The problem is that Mathematica cannot proceed from this last step. It also doesn't seem like it can factor out irrelevant terms. Mathematica gives me the following: Sum[(16 i^3)/(n^4),{i,1,n}] *** The BIGGER problem is that we are unable to get a limit of this sum as n goes to infinity. If you attempt to do it, Mathematica will give you several screens full of garbage. Induction tells us that it is ((n^2)(n+1)^2)/4. Consequently our limit is 4. Is there some way to handle limits of infinite sums? Is there some way to use a lookup table for special cases? What is Mathematica actually doing when it is computing the limit and/or sums? What about numerically approximating? Any help would be greatly appreciated since so many things are represented as a limit of an infinite sum. Thanks, Lyle Wright Mathematica Developer Harvey Mudd College Claremont, CA 91711 lwright@hmcvax.claremont.edu From mathgroup-adm@yoda.ncsa.uiuc.edu Mon Nov 5 14:47:23 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA15662 (5.64+/IDA-1.3.4 for stevec); Mon, 5 Nov 90 14:47:18 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA00201; Mon, 5 Nov 90 14:45:52 CST Received: by yoda.ncsa.uiuc.edu id AA15022 (5.64+/IDA-1.3.4 for ); Mon, 5 Nov 90 10:34:16 -0600 Received: by yoda.ncsa.uiuc.edu id AA15018 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Mon, 5 Nov 90 10:34:14 -0600 Message-Id: <9011051634.AA15018@yoda.ncsa.uiuc.edu> Date: Mon, 05 Nov 90 11:42:06 ITA From: Riccardo Rigon Subject: binary trees (and Map ?) To: Mathematica special Interest Group Status: RO Dear mathgroupers, is to build all the binary trees with a given number of leaves, n. The total number of internal arcs is n-1 as can be proven by induction. The thing can be solved recursively, being a binary tree with n leaves the union of a left tree with n-i leaves and a right tree with i leaves. For my purposes every binary tree with n leaves can be parametrized by a sequence of 2n-1 letters, for instance of n-1 `i` for internal arcs,and n `l` for the leaves as follow: we start at the root and follow the tree left-hand puttingin the sequence an i when we meet an internal arc or an l in the case of leaves. When we meet for the second time the same arc we do not add anything. The math code suitable for the operation could be: Tree[n_]:=Block[{i,ka},ka=Table[Flatten[{i,Tree[n-i],Tree[i]}],{i,n}];ka] Tree[1]:=l The problem is that when n=4 the result gives two elements ( a matrix ) and the body of the Table statement do not work. My solution should involve the use if the Map function and the first step would be the merging of two sequenceces like these: {{1,2,3},{4,5,6}} and {{a,b,c},{d,e,f}} in: {{1,2,3,a,b,c},{1,2,3,d,e,f},{4,5,6,a,b,c},{4,5,6,d,e,f}}. My solution to this problem is to use a double Map statement: first[x_,y_List]:=Map[Join[x,#],y] (* x is a simple array *) second[xx_,yy_]:=Map[first[#,yy],xx] which is not a very good (if any) solution. Subsequent step should be the change of the body in the approriate way. Does somebody would so kind to help me, for the first (tree`s) problem and/or for the second (merging matrix)? Thank you in advance. Riccardo Rigon bitnet: Rigon@iveuncc internet: Rigon@iveuncc.unive.it From mathgroup-adm@yoda.ncsa.uiuc.edu Mon Nov 5 13:50:44 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA15460 (5.64+/IDA-1.3.4 for stevec); Mon, 5 Nov 90 13:50:42 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA28281; Mon, 5 Nov 90 13:49:17 CST Received: by yoda.ncsa.uiuc.edu id AA15033 (5.64+/IDA-1.3.4 for ); Mon, 5 Nov 90 10:34:32 -0600 Received: by yoda.ncsa.uiuc.edu id AA15029 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Mon, 5 Nov 90 10:34:30 -0600 Message-Id: <9011051634.AA15029@yoda.ncsa.uiuc.edu> Date: Mon, 5 Nov 90 09:13 EST From: Steve Buyske Subject: Product rule and Cross[] To: mathgroup@yoda.ncsa.uiuc.edu Status: RO I must be stupid, but I can't figure out how to provide a pattern to Mathematica so that, given D[Cross[u[t],v[t]],t] it will give Cross[u[t], v'[t]] - Cross[v[t], u'[t]] instead of (0,1) (1,0) v'[t] Cross [u[t], v[t]] + u'[t] Cross [u[t], v[t]] Now I can write a pattern that would work for this particular case, of course, but it fails with something like D[w[t] . Cross[u[t], v[t]],t] because it gets to my pattern to late in the process. Can anyone out there help me? Steve Buyske uucp : rutgers!lehi3b15!lafcol!buyskes Mathematics Department Bitnet : BUYSKES@LAFAYETT Lafayette College Easton, PA 18042 From mathgroup-adm@yoda.ncsa.uiuc.edu Mon Nov 5 13:04:12 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA15279 (5.64+/IDA-1.3.4 for stevec); Mon, 5 Nov 90 13:04:10 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA26293; Mon, 5 Nov 90 13:02:42 CST Received: by yoda.ncsa.uiuc.edu id AA15012 (5.64+/IDA-1.3.4 for ); Mon, 5 Nov 90 10:34:03 -0600 Received: by yoda.ncsa.uiuc.edu id AA15008 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Mon, 5 Nov 90 10:33:59 -0600 Message-Id: <9011051633.AA15008@yoda.ncsa.uiuc.edu> Date: Sun, 4 Nov 90 20:53:14 GMT From: duncan@smogland.janet.ucla.edu (Phil Duncan) To: mathgroup@yoda.ncsa.uiuc.edu Subject: mathematica question Status: RO I am new to the world of Mathematica. I hope this is an appropriate question for this mail alias. I am looking into the possibility of using Mathematica for an application that combines graph manipulation and linear programming. It appears that linear programming routines do not come standard with Mathematica. Does anyone know of a package for linear programming, Simplex or otherwise? Please send replies to duncan@janet.ucla.edu or !(uunet,ucbvax,rutgers)!seas.ucla.edu!duncan All suggestions will be greatly appreciated. Phil Duncan From mathgroup-adm@yoda.ncsa.uiuc.edu Mon Nov 5 12:05:08 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA15138 (5.64+/IDA-1.3.4 for stevec); Mon, 5 Nov 90 12:05:03 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA24669; Mon, 5 Nov 90 12:03:39 CST Received: by yoda.ncsa.uiuc.edu id AA15027 (5.64+/IDA-1.3.4 for ); Mon, 5 Nov 90 10:34:24 -0600 Received: by yoda.ncsa.uiuc.edu id AA15023 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Mon, 5 Nov 90 10:34:22 -0600 Message-Id: <9011051634.AA15023@yoda.ncsa.uiuc.edu> Date: Mon, 5 Nov 90 14:18:40 +0100 From: wsgbfs@win.tue.nl (F. Simons) To: mathgroup-adm@yoda.ncsa.uiuc.edu Subject: mathematica bug Status: RO For about a year I am reading the Mathematica messages on usenet, and since some months I have also subscribed to the Mathematica newsgroup. Particularly this newsgroup very much attributes to my knowledge of Mathematica, so I very much appreciate the work you are doing for this newsgroup. At the end of September I sent you a message about a bug in Mathematica, which I have not seen being mentioned so far. This message was meant as a contribution to the Mathematica newsgroup, but as far as I could see it was not distributed there. I send you this message once again (separately), in the hope that it might be interesting for the readers of the newsgroup. If I am using an incorrect e-mail address, please can you inform me on the correct address? Thank you very much in advance, Fred Simons Eindhoven University of Technology Department of Mathematics and Computing Science P.O.Box 513 NL - 5600 MB Eindhoven wsgbfs@win.tue.nl  From mathgroup-adm@yoda.ncsa.uiuc.edu Mon Nov 5 15:24:42 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA15852 (5.64+/IDA-1.3.4 for stevec); Mon, 5 Nov 90 15:24:40 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA01628; Mon, 5 Nov 90 15:23:11 CST Received: by yoda.ncsa.uiuc.edu id AA15039 (5.64+/IDA-1.3.4 for ); Mon, 5 Nov 90 10:34:49 -0600 Received: by yoda.ncsa.uiuc.edu id AA15034 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Mon, 5 Nov 90 10:34:47 -0600 Message-Id: <9011051634.AA15034@yoda.ncsa.uiuc.edu> Date: Mon, 5 Nov 90 11:09:51 EST From: shenkin@avogadro.barnard.columbia.edu (Peter S. Shenkin) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Problems with graphics using Mathematica on a Personal Iris Status: RO I've just installed Mathematica, which I purchased from SGI with my 4D-25TG. Using the default GL graphics window, ("-- GL graphics installed --"), a window is put up when I try to "Plot[ Sin[x], {x,0,10}]", but the window contains gibberish; it's clearly trying to plot something, but there are ascii characters (plot labels) scattered here an there over the screen, a few line segments that are trying to be the plot, etc. "ps -ef" from a shell reveals that indeed glps is running. If I override use of GL by "<<4Sight.m", then I get good results, but of course then I'm not using GL. "< Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA16229; Tue, 6 Nov 90 20:09:41 CST Received: by yoda.ncsa.uiuc.edu id AA17776 (5.64+/IDA-1.3.4 for ); Tue, 6 Nov 90 17:04:37 -0600 Received: by yoda.ncsa.uiuc.edu id AA17772 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 6 Nov 90 17:04:36 -0600 Message-Id: <9011062304.AA17772@yoda.ncsa.uiuc.edu> Date: 5 Nov 90 23:42:00 EDT From: "WILLIAM M. GOLDING" Subject: Integrate? To: "mathgroup" Status: RO In a previous posting concerning this integration flaw in Mathematica which Robert Staerk recently brought up, Integrate[Sqrt[2-2 Cos[x]],{x,0,2 Pi}] =?= 0 Jeffrey Golden mentions an integral which he has just been able to get Macsyma to do correctly. The integral he mentions is Integrate[Sqrt[x + 1/x -2],{x,0,1}] = 4/3 . Jeff says that Macsyma used to give the result as -4/3, which by the way is what Mathematica gives. I just wanted to point out the similarity between these two integrals. If in the second integral x is replaced by e^(i x) the first integral is almost obtained except for a phase factor and for the integration contour which I don't quite know how to interpret at the moment. Anyways I just thought I'd mention the connection since Jeff implied that the second form has been corrected in Macsyma. Mike Golding Email golding@ccf.nrl.navy.mil From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Nov 6 19:25:06 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA17997 (5.64+/IDA-1.3.4 for stevec); Tue, 6 Nov 90 19:25:04 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA15595; Tue, 6 Nov 90 19:23:43 CST Received: by yoda.ncsa.uiuc.edu id AA17781 (5.64+/IDA-1.3.4 for ); Tue, 6 Nov 90 17:06:36 -0600 Received: by yoda.ncsa.uiuc.edu id AA17777 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 6 Nov 90 17:06:35 -0600 Message-Id: <9011062306.AA17777@yoda.ncsa.uiuc.edu> From: Steve Maybank Date: Tue, 6 Nov 90 08:38:20 GMT To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Integrate Status: RO re. the result In[1] := Integrate[Sqrt[2-2 Cos[x]], {x, 0, 2 Pi}] Out[1] := 0 the problem seems to be with the square root. In the range 0 to Pi the plus sign is taken, but in the range Pi to 2 Pi the minus sign is taken. From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Nov 6 21:17:48 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA18202 (5.64+/IDA-1.3.4 for stevec); Tue, 6 Nov 90 21:17:45 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA17274; Tue, 6 Nov 90 21:16:22 CST Received: by yoda.ncsa.uiuc.edu id AA17786 (5.64+/IDA-1.3.4 for ); Tue, 6 Nov 90 17:06:45 -0600 Received: by yoda.ncsa.uiuc.edu id AA17782 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 6 Nov 90 17:06:44 -0600 Message-Id: <9011062306.AA17782@yoda.ncsa.uiuc.edu> Date: Tue, 6 Nov 90 10:33:34 +0100 From: wsgbfs@win.tue.nl (F. Simons) To: mathgroup-adm@yoda.ncsa.uiuc.edu Subject: mathematica bug Status: RO While preparing a demonstration with Mathematica, I discovered a bug in version 1.2 that did not occur in version 1.1. I wrote to WRI twice, but did not get any reaction. The bug has to do with SeriesData. Multiplication works fine, but the power function produces results of too low degree, as shown by the following example. Mathematica (MS-DOS 386/7) 1.2 (September 27, 1989) [With pre-lo- aded data] by S. Wolfram, D. Grayson, R. Maeder, H. Cejtin, S. Omohundro, D. Ballman and J. Keiper with I. Rivin, D. Withoff and T. Sherlock Copyright 1988,1989 Wolfram Research Inc. In[1]:= a = x^2 + x^3 + O[x]^4 2 3 4 Out[1]= x + x + O[x] In[2]:= a^3 4 Out[2]= O[x] In[3]:= a*a*a 6 7 8 Out[3]= x + 3 x + O[x] The following definitions in the file debug.m help: Unprotect[ SeriesData ] SeriesData /: Power[ SeriesData[ a_, b_, c_, d_, e_, f_ ], n_Integer?Positive ] := Times[ Power[ SeriesData[ a, b, c, d, e, f ], n-1 ], SeriesData[ a, b, c, d, e, f ] ] /; OddQ[ n ] && (n > 1) SeriesData /: Power[ SeriesData[ a_, b_, c_, d_, e_, f_ ], n_Integer?Positive ] := Times[ Power[ SeriesData[ a, b, c, d, e, f ], n/2 ], Power[ SeriesData[ a, b, c, d, e, f ], n/2 ] ] /; EvenQ[ n] Loading this file results in two error messages, probably due to the fact that SeriesData is not a Mathematica function. But it fixes the bug: In[4]:= < Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA18052; Tue, 6 Nov 90 22:10:30 CST Received: by yoda.ncsa.uiuc.edu id AA17771 (5.64+/IDA-1.3.4 for ); Tue, 6 Nov 90 17:04:28 -0600 Received: by yoda.ncsa.uiuc.edu id AA17767 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 6 Nov 90 17:04:26 -0600 Message-Id: <9011062304.AA17767@yoda.ncsa.uiuc.edu> Date: 5 Nov 90 16:07:00 EDT From: "WILLIAM M. GOLDING" Subject: Integrate? To: "mathgroup" Status: RO We've seen that Mathematica gives incorrectly a result of zero for this one particular integral, Integrate[Sqrt[2-2 Cos[x]],{x,0,2 Pi}] . Because the Sqrt function has a branch cut along the negative real axis, and it seems likely that Mathematica would try to do the trigonometric integral in the complex plane thereby encountering the cut at x or "theta" equal to Pi, I translated the integrand from x = Pi to x = 0 and integrated from -Pi to Pi thinking that this might make it easier for mma to deal with the cut. That is I tried the integral Integrate[Sqrt[2+2 Cos[x]],{x,-Pi, Pi}] . This integral is also returned incorrectly as zero. The second integrand is obtained from the first by letting x go to x - Pi. Next it seemed reasonable to look at the two integrals over the same region of integration. That is Integrate[Sqrt[2-2 Cos[x]],{x,0, Pi}] => 4 Integrate[Sqrt[2+2 Cos[x]],{x,0, Pi}] => - 4 The two integrals should be identical. The only difference between the two integrands is that the first is monotonically increasing and the second is monotonically decreasing. Is this the cause of the sign error? It seems that mma is taking perfectly good symmetric functions and making them antisymmetric by multiplying by +1 if going uphill and multiplying by -1 if going downhill. There is another integral which shows a similar behaviour , Integrate[ Sqrt[ Sec[x]-1 ],{x,0, Pi/2}] => 1.76275 Integrate[ Sqrt[ Sec[x]-1 ],{x,- Pi/2,0}] => - 1.76275 That is we get a positive result on the uphill side and a negative result on the downhill side. In each of these integrals, if you use the second order series expansion of the trigonometric function in place of the trig function, this sign flipping phenomenon appears to go away and for a small range chosen symmetrically about the symmetry axis the integrate function returns a correct non-zero result. This seems to imply that mma will likely have trouble of the of the above sort with integrands of the form Sqrt[ Function[ any trig function ]] where Function is non-negative in the range of integration and where the integration is taken through a complete period of the trig functions involved. I would like to hear of any functions in the above form that mma can handle correctly, and also if anyone can explain why Mathematica should have problems with integrals of the above form. Thanks Mike Golding Email golding@ccf.nrl.navy.mil From mathgroup-adm@yoda.ncsa.uiuc.edu Wed Nov 7 00:07:13 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA19225 (5.64+/IDA-1.3.4 for stevec); Wed, 7 Nov 90 00:07:11 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA10950; Wed, 7 Nov 90 00:05:23 CST Received: by yoda.ncsa.uiuc.edu id AA18240 (5.64+/IDA-1.3.4 for ); Tue, 6 Nov 90 21:22:18 -0600 Received: by yoda.ncsa.uiuc.edu id AA18236 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 6 Nov 90 21:22:17 -0600 Message-Id: <9011070322.AA18236@yoda.ncsa.uiuc.edu> Date: 6 Nov 90 22:00:00 EST From: "WILLIAM M. GOLDING" Subject: Integrate? To: "mathgroup" Status: RO In a previous posting concerning this integration flaw in Mathematica which Robert Staerk recently brought up, Integrate[Sqrt[2-2 Cos[x]],{x,0,2 Pi}] =?= 0 Jeffrey Golden mentions an integral which he has just been able to get Macsyma to do correctly. The integral he mentions is Integrate[Sqrt[x + 1/x -2],{x,0,1}] = 4/3 . Jeff says that Macsyma used to give the result as -4/3, which by the way is what Mathematica gives. I just wanted to point out the similarity between these two integrals. If in the second integral x is replaced by E^(I x) the first integral is almost obtained except for a phase factor and for the integration contour which I don't quite know how to interpret at the moment. Anyways I just thought I'd mention the connection since Jeff implied that the second form has been corrected in Macsyma. Mike Golding Email golding@ccf.nrl.navy.mil From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Nov 9 01:56:26 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA23266 (5.64+/IDA-1.3.4 for stevec); Fri, 9 Nov 90 01:56:24 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA09717; Fri, 9 Nov 90 01:54:58 CST Received: by yoda.ncsa.uiuc.edu id AA22513 (5.64+/IDA-1.3.4 for ); Thu, 8 Nov 90 22:50:24 -0600 Received: by yoda.ncsa.uiuc.edu id AA22509 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Thu, 8 Nov 90 22:50:23 -0600 Message-Id: <9011090450.AA22509@yoda.ncsa.uiuc.edu> From: "Keith R. Slavin" To: mathgroup@yoda.ncsa.uiuc.edu Subject: Input accuracy Date: Wed, 07 Nov 90 12:45:18 PST Status: RO I have recently been trying to get mathematica to accept an input of GIVEN accuracy, ie: Foo[1.3,25] implies 1.300000000000000000000000, ie: 25 digit precision according to the Precision[] function, otherwise the OUTPUT accuracy suffers due to the 'machine accuracy' assumed for '1.3'. The only way I have found to do this is to use Rationalize[1.3,10^-25], and use 13/10 in my calculations to arbitrary precision, but Rationalize[] assumes an input of machine accuracy too, so Rationalize[0.9999999999999999999,10^-25] gives 1 which is not adequate for 25-digit processing! Any ideas? Thanks, Keith Slavin, Tektronix, Beaverton,Or. (503) 627-4907 keith@videovax.tv.tek.com From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Nov 9 03:08:39 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA23354 (5.64+/IDA-1.3.4 for stevec); Fri, 9 Nov 90 03:08:37 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA10901; Fri, 9 Nov 90 03:07:06 CST Received: by yoda.ncsa.uiuc.edu id AA22528 (5.64+/IDA-1.3.4 for ); Thu, 8 Nov 90 22:50:45 -0600 Received: by yoda.ncsa.uiuc.edu id AA22524 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Thu, 8 Nov 90 22:50:43 -0600 Message-Id: <9011090450.AA22524@yoda.ncsa.uiuc.edu> Date: Thu, 08 Nov 90 17:30:17 ITA From: Riccardo Rigon Subject: Retry on tree and Map To: Mathematica special Interest Group Status: RO I apologize if you have just received this mail, but it seems it was not completely delivered. Further I did some errors which I have now corrected. Dear mathgroupers, my problem is to build all the binary trees with a given number of leaves, n. The thing then can be solved recursively, being a binary tree with n leaves the union of a left tree with n-i leaves and a right tree with i leaves. In every binary tree with n leaves, the total number of internal arcs is n-1 as it can be proven by induction. Hence every binary tree with n leaves can be parametrized by a sequence of 2n-1 letters, for instance of n-1 `i` for internal arcs,and n `l` for the leaves as follow: we start at the root and follow the tree left-hand putting in the sequence an i when we meet an internal arc or an l in the case of leaves. ( draw the tree and follow it beginning from the left of the root and turn when you meet the beginning of a leaf. In this way the total distance covered equals two times the total lenght of the tree. Every arc is in fact followed two times: on the left and on the left ) When we meet for the second time the same arc we do not add anything. The Mathematica code suitable for the operation could be: Tree[n_]:=Block[{i,ka},ka=Table[Flatten[{i,Tree[n-i],Tree[i]}],{i,n}];ka] Tree[1]:=i The problem is that when n=4 the result gives two elements ( a matrix ) and the body of the Table statement do not work as one would. My solution should involve the use if the Map function and the first step would be the merging of two sequenceces like these: {{1,2,3},{4,5,6}} and {{a,b,c},{d,e,f}} in: {{1,2,3,a,b,c},{1,2,3,d,e,f},{4,5,6,a,b,c},{4,5,6,d,e,f}}. My solution to this `Map` problem is to use a double Map statement: first[x_,y_List]:=Map[Join[x,#]&,y] (* x is a simple array *) second[xx_,yy_]:=Flatten[Map[first[#,yy]&,xx] which is not a very good solution. (How one can do this in one single statement ?) Subsequent steps should be the change of the body in the approriate way. Thew solution should sound like this: .... aa=Tree[n-i];bb=Tree[i]; sol[aa_,bb_]:= Block[{apple,melon}, melon=Insert[aa,i,1]; apple=second[melon,bb] ] but because I am first looking for the solution of the first problem I have not tried it till now (Does the recursion still work?) Does someone would so kind to help me ? Thank you in advance. Riccardo Rigon bitnet: Rigon@iveuncc internet: Rigon@iveuncc.unive.it P.S. Probably my questions are tedious and/or obvious, but I am a beginner with not people with whom discuss.Thank you again. From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Nov 9 04:44:35 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA23472 (5.64+/IDA-1.3.4 for stevec); Fri, 9 Nov 90 04:44:33 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA12343; Fri, 9 Nov 90 04:43:10 CST Received: by yoda.ncsa.uiuc.edu id AA22523 (5.64+/IDA-1.3.4 for ); Thu, 8 Nov 90 22:50:37 -0600 Received: by yoda.ncsa.uiuc.edu id AA22519 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Thu, 8 Nov 90 22:50:36 -0600 Message-Id: <9011090450.AA22519@yoda.ncsa.uiuc.edu> Date: 7 Nov 90 21:48:00 EDT From: "WILLIAM M. GOLDING" Subject: Integrate ??? To: "mathgroup" Status: RO Hi there, Sorry, to keep bringing up this integrate point but its been nagging at me. I agree with everyone that mathematica is doing the definite integral by doing the indefinite integral and evaluating at 0 and 2 Pi. The problem is that it's doing the indefinite integral incorrectly. It's not totally incorrect, the integral is legit for the range 0 to Pi but negative of the right answer for the range Pi to 2 Pi. I don't know how important this is in the whole scheme of things but it sure makes me aware that one has to take with a few grains of salt the results obtained from a symbolics package. Obviously the integral could be done over the two ranges separately and pieced together, but when the program comes back and tells you its got the answer I want to be able to believe it. Anyways here is the original problem an how I think it should be solved. Integrate[Sqrt[2-2 Cos[x]],{x,0,2 Pi}] simplify the integrand 2-2 Cos[x] = 2 - Exp[I x] - Exp[-I x] = - [ Exp[I x/2]- Exp[-I x/2] ]^2 = - 4 I^2 Sin[x/2]^2 = 4 Sin[x/2]^2 We want the square root of this last expression so we get Sqrt[ 2-2 Cos[x] ] = Sqrt[ 4 Sin[x/2]^2 ] = Abs [ 2 Sin[x/2] ] In general, we have to include the absolute value sign here because we might not know the range of the integration variable. That is assuming x to be real, and there is no reason in this case not to assume x to be real, we have taken the positve sqrt of number which is definitely >= 0, and we require the result to be on the positive branch of our square root function. For example, suppose x = 3 Pi then if we exclude the absolute value sign we get Sqrt[ 4 Sin[3 Pi/2]^2] = 2 Sin[3 Pi/2] = 2 (-1) = - 2 but the Sqrt function must be >= 0 if we're going to stay on the positive branch, so the absolute value sign is necessary in the general case. Actually, with the integrand in this form and limiting x to the range 0 to 2 Pi as for our special case the Abs is not needed since 2 Sin[x/2] = 2 Abs[ Sin[x/2] ] 0 <= x <= 2 Pi . Thus we should be able to calculate the indefinte integral from Integrate[ Sqrt[2-2 Cos[x]] ,x] = Integral[ 2 Sin[x/2] ,x] = -4 Cos[x/2] only for 0<= x <= 2 Pi . To find the definite integral as in the original problem we get Integrate[Sqrt[2-2 Cos[x]],{x,0,2 Pi}] = | 2 Pi = ( -4 Cos[x/2] )| | 0 = -4 ( Cos[Pi] - Cos[0] ) = -4 ( -1 - 1 ) = 8 And this is the correct result at last. The result that Mathematica gives for the indefinite integral is In[1]:= Integrate [Sqrt[ 2-2 Cos[x]] , x ] -4 Out[1]= ----------------------- 2 Sin[x] Sqrt[1 + -------------] 2 (1 + Cos[x]) By using a little algebra and trigonometry you can show that this last result is the same as ours in the range 0 to Pi , and the negative of ours in the range pi to 2 Pi . That is The indefinite integral that mathematica produces is equivalent to -4 Cos[x/2] 0 <= x <= Pi (Identical to our result except our range is 0 to 2 Pi) 4 Cos[x/2] Pi <= x <= 2 Pi So we evaluate this at 0 and get -4 then we evaluate at 2 Pi and get -4 take the difference and the result is zero which is what mathematica has been getting. Notice that this function is continuous at x=Pi, but has discontinuous slope at x = Pi. Is it unreasonable for the integral of a continuous function to have discontinuous slope within the integration range. And if so might this be used as a clue to expect an error in the integration algorithm. The thing that bothers me about all this is that it is possible to get an integral that covers the whole integration range and seems reasonable, without mathematica once mentioning that there might be a problem with what we are doing. Here is an example of the neglect of the range applicability that I thought interesting. In[2]:= Sqrt[Sin[x]^2] Out[2]= Sin[x] Seems like a reasonable result but what about In[3]:= Integrate[Sqrt[Sin[x]^2] , x ] Out[3]= -Cos[x] In[4]:= Quit In[1]:= Sqrt[Sin[x]^2] Out[1]= Sin[x] Seems like a reasonable result but what about x = 3 Pi/2 In[2]:= Integrate[Sqrt[Sin[x]^2] , x] Out[2]= -Cos[x] It decided that Sin[x] was what I really wanted to integrate In[3]:= Integrate[Sqrt[Sin[x]^2],{x,0,Pi}] Out[3]= 2 This is right !!! In[4]:= Integrate[Sqrt[Sin[x]^2],{x,Pi,2 Pi}] Out[4]= -2 This is wrong !! In[5]:= Integrate[Sqrt[Sin[x]^2],{x,0,2 Pi}] Out[5]= 0 This is wrong ! In[6]:= I Quit From mathgroup-adm@yoda.ncsa.uiuc.edu Fri Nov 9 01:19:31 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA23234 (5.64+/IDA-1.3.4 for stevec); Fri, 9 Nov 90 01:19:29 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA09089; Fri, 9 Nov 90 01:18:03 CST Received: by yoda.ncsa.uiuc.edu id AA22518 (5.64+/IDA-1.3.4 for ); Thu, 8 Nov 90 22:50:31 -0600 Received: by yoda.ncsa.uiuc.edu id AA22514 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Thu, 8 Nov 90 22:50:29 -0600 Message-Id: <9011090450.AA22514@yoda.ncsa.uiuc.edu> From: "Keith R. Slavin" To: mathgroup@yoda.ncsa.uiuc.edu Subject: Bernoulli numbers. Date: Wed, 07 Nov 90 14:49:43 PST Status: RO I noticed (by way of erroneous results) that although NBernoulliB[n,m] is faster than N[BernoulliB[n],m], it is WRONG for n=0 (it gives 0.5 instead of 1). Users beware! Keith Slavin Tektronix TV division, (503) 627 4907 keith@videovax.tv.tek.com From mathgroup-adm@yoda.ncsa.uiuc.edu Sat Nov 10 01:49:30 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA25438 (5.64+/IDA-1.3.4 for stevec); Sat, 10 Nov 90 01:49:28 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA02535; Sat, 10 Nov 90 01:48:10 CST Received: by yoda.ncsa.uiuc.edu id AA24630 (5.64+/IDA-1.3.4 for ); Fri, 9 Nov 90 23:14:42 -0600 Received: by yoda.ncsa.uiuc.edu id AA24626 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 9 Nov 90 23:14:40 -0600 Message-Id: <9011100514.AA24626@yoda.ncsa.uiuc.edu> Date: Fri, 09 Nov 90 01:29:18 From: randy@sparc.ncpa.olemiss.edu (Randy Zagar) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Problems converting clipboard to Illustrator format Status: RO Have a slight problem I would like to ask about. I just made a 10201 point DensityGraphics object that I would like to put into Adobe Illustrator 88. I'm using Mathematica v1.2 on a Mac-2 with a color screen and Illustrator 88 v1.6. I selected the cell with the graphics, copied it, and did the "Convert Clipboard" menu item. Illustrator couldn't sucessfully read an EPSF document created by Mathematica. When I created a v1.1 Illustrator file all I got was the axes bounding the plot. None of the data appeared in the Illustrator window. My question is this: Am I having a stone-age version conflict, or am I close enough to the cutting edge to have found a _real_ bug ? Has anyone had success getting Mathematica graphics into Illustrator 88 ? Please reply by direct E-mail as I'm not yet on this list. Thanks ahead of time, Randy Zagar National Center for Physical Acoustics Phone: (601)-232-5614 Colisium Drive FAX: (601)-232-7494 University of Mississippi University, MS 38677 p.s. Is there an archive site for this group ? From mathgroup-adm@yoda.ncsa.uiuc.edu Sat Nov 10 01:06:46 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA25384 (5.64+/IDA-1.3.4 for stevec); Sat, 10 Nov 90 01:06:44 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA01918; Sat, 10 Nov 90 01:05:26 CST Received: by yoda.ncsa.uiuc.edu id AA24640 (5.64+/IDA-1.3.4 for ); Fri, 9 Nov 90 23:16:05 -0600 Received: by yoda.ncsa.uiuc.edu id AA24636 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 9 Nov 90 23:16:04 -0600 Message-Id: <9011100516.AA24636@yoda.ncsa.uiuc.edu> Date: Fri, 9 Nov 90 05:55:30 PST From: jdelany@sargas.ACS.CalPoly.EDU (Jim Delany) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Integrate??? Status: RO Dear Mr. Golding Sqrt is a real weak point in Mathematica. Any computation using it is in doubt. Apparently WRI has a corporate policy that Sqrt[x^2] is x. It reminds me of the story of the state legislature the passed a law decreeing that pi equals three. In[1]:= Sqrt[ x^2 ] === x Out[1]= True In[2]:= Simplify[ Sqrt[8] - 2^(3/2) ] 3/2 Out[2]= 2 Sqrt[2] - 2 Jim Delany ( jdelany@nike.calpoly.edu ) Math Department Cal Poly, San Luis Obispo CA 93407 From mathgroup-adm@yoda.ncsa.uiuc.edu Sat Nov 10 03:24:07 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA25595 (5.64+/IDA-1.3.4 for stevec); Sat, 10 Nov 90 03:24:05 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA04019; Sat, 10 Nov 90 03:22:42 CST Received: by yoda.ncsa.uiuc.edu id AA24635 (5.64+/IDA-1.3.4 for ); Fri, 9 Nov 90 23:14:48 -0600 Received: by yoda.ncsa.uiuc.edu id AA24631 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 9 Nov 90 23:14:47 -0600 Message-Id: <9011100514.AA24631@yoda.ncsa.uiuc.edu> Date: Fri, 9 Nov 90 08:20:50 EST From: pkane@Kodak.COM (Paul Kane) To: mathgroup@yoda.ncsa.uiuc.edu Subject: 2D NIntegrate Status: RO Hello again, I didn't get many replies to my 2D NIntegrate dilemma, but I did get a couple that I thought others would find interesting. The problem, in case you've deleted it from your memories, was that a two dimensional numerical integration, involving Bessel functions, was taking a prohibitively long time to execute. Paul Abbott of wri suggested : > One suggestion (which I have not tried in the 2 dimensional case) is that the > option Method->DoubleExponential may help for rapidly oscillating functions > > DoubleExponential is a choice for the option Method > of NIntegrate. Method -> DoubleExponential causes > a doubly exponentially convergent algorithm to be > used. This was interesting to me since this option is not in the Mathematica book or the Reference Guide Updates (1.2) that I have. mma seemed to know about the option, although unfortunately it did not have any impact on the results. A colleague of mine at Kodak offered this : > I was going to suggest that you simply generate a 2-D array of the bessel function, J1(x)/x and a vector representing the other function and simply > > Apply[Plus, matrix . vector]; > where matrix has the J1(x)/x values and vector has the other function. In a nut shell, this is what I do for hankel transforms. (NOTE the . means DOT PRODUCT) In fact, I have done this in the past (at his suggestion) and it does run in an acceptable length of time. Of course, one must be careful about integrands that have singularities. Although this is not a very satisfying solution to the NIntegrate problem, it does get the job done, and usually I am dealing with well-behaved functions. Still another suggestion was to write a C or FORTRAN program. A good idea, since specialized code in C or FORTRAN will probably run faster in any case. But it would be nice to have mma do the job, since it would spare me the time involved to write my own code. After all, that's why I bought mma in the first place, among other reasons. Thanks to all who responded. Paul J. Kane Eastman Kodak Co. Photographic Research Labs Rochester,NY 14650-1717 (716)-477-1895 (pkane@Kodak.COM) From mathgroup-adm@yoda.ncsa.uiuc.edu Sat Nov 10 02:52:14 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA25540 (5.64+/IDA-1.3.4 for stevec); Sat, 10 Nov 90 02:52:11 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA03375; Sat, 10 Nov 90 02:50:54 CST Received: by yoda.ncsa.uiuc.edu id AA24645 (5.64+/IDA-1.3.4 for ); Fri, 9 Nov 90 23:16:14 -0600 Received: by yoda.ncsa.uiuc.edu id AA24641 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Fri, 9 Nov 90 23:16:13 -0600 Message-Id: <9011100516.AA24641@yoda.ncsa.uiuc.edu> To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Input accuracy Date: Fri, 09 Nov 90 09:10:49 PST From: jacobson@cello.hpl.hp.com Status: RO Keith Slavin, writes: > I have recently been trying to get mathematica to accept an input of GIVEN > accuracy, ie: Foo[1.3,25] implies 1.300000000000000000000000, ie: 25 digit > precision according to the Precision[] function, otherwise the > OUTPUT accuracy suffers due to the 'machine accuracy' assumed for > '1.3'. > ... > Any ideas? Yes, this does it. (I've called it PNum instead of Foo.) The first definition accepts a string input, so you would write: PNum["1.3",25]. For easier input when rationalize would work, I added the second definition, which takes a number and calls Rationalize. The third is just there so it works on integers as well. PNum[st_String, n_] := \ SetPrecision[ToExpression[StringJoin[st, Apply[StringJoin, Table["0", {Max[n, Precision[1.] + 5]}]]]], n] PNum[x_Real, n_] := \ SetPrecision[N[Rationalize[x], Max[n, Precision[1.] + 5]], n] PNum[x_Integer, n_] := SetPrecision[N[x, Max[n, Precision[1.] + 5]], n] Big floats are extremely dangerous in Mathematica. Caveat Emptor! (There are many iterative calculations that ratchet down the precision by 1 each iteration, and Mathematica uses the precision to determine the number of bits in the representation. So when you are done you have a totally meaningless result. Mathematica also has some bugs that let the precision get too big, so don't trust what you get. If you can live with their accuracy/precision, machine numbers are much safer.) -- David Jacobson From mathgroup-adm@yoda.ncsa.uiuc.edu Mon Nov 12 21:12:33 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA29346 (5.64+/IDA-1.3.4 for stevec); Mon, 12 Nov 90 21:12:31 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA17388; Mon, 12 Nov 90 21:11:16 CST Received: by yoda.ncsa.uiuc.edu id AA29160 (5.64+/IDA-1.3.4 for ); Mon, 12 Nov 90 18:40:21 -0600 Received: by yoda.ncsa.uiuc.edu id AA29156 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Mon, 12 Nov 90 18:40:20 -0600 Message-Id: <9011130040.AA29156@yoda.ncsa.uiuc.edu> Date: Mon, 12 Nov 90 09:20:41 +0200 From: pjanhune@finsun.csc.fi Subject: Definite Integrals etc. To: mathgroup@yoda.ncsa.uiuc.edu Status: RO About Integrate[ Sqrt[2 - 2 Cos[x]], {x, 0, 2 Pi}]: If you load the package Calculus/DefiniteIntegrate.m before integrating, you at least get a lot of error messages (and the wrong answer 0). I've found the package DefiniteIntegrate.m useful, because it warns you if something is likely to be going wrong. About NIntegrate: Paul J. Kane has had problems with two-dimensional NIntegrate. His example contained Bessel functions. But there seems to be problems even with very simple polynomial functions as the following example shows: In[1]:= NIntegrate[x^2+y^2,{x,-1,1},{y,-1,1}] (* this is fine *) Out[1]= 2.66667 In[2]:= NIntegrate[x^4+y^2,{x,-1,1},{y,-1,1}] (* problems! *) NIntegrate::conv: Numerical integral failed to reach specified accuracy after 7 recursive subdivisions near -1. for variable number 1. NIntegrate::conv: Numerical integral failed to reach specified accuracy after 7 recursive subdivisions near -0.999999 for variable number 1. NIntegrate::conv: Numerical integral failed to reach specified accuracy after 7 recursive subdivisions near -0.999985 for variable number 1. General::stop: Further output of NIntegrate::conv will be suppressed during this calculation. ^C Interrupt: continue (or c) to continue show (or s) to show current operation (and then continue) trace (or t) to show all operations abort (or a) to abort current calculation exit (or quit) to exit program ? a Out[2]= $Interrupted In[3]:= Integrate[x^4+y^2,{x,-1,1},{y,-1,1}] (* I interrupted after about 30 seconds on a Sun-4. Both integrals, of course, exits and can be calculated exactly: *) 32 Out[3]= -- 15 In[4]:= Integrate[x^2+y^2,{x,-1,1},{y,-1,1}] 8 Out[4]= - 3 I think there is a real bug in the two-dimensional NIntegrate. One-dimensional NIntegrate works so well that this kind of behavior cannot be otherwise understood. From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Nov 13 16:54:46 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA02081 (5.64+/IDA-1.3.4 for stevec); Tue, 13 Nov 90 16:54:43 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA13497; Tue, 13 Nov 90 16:55:28 CST Received: by yoda.ncsa.uiuc.edu id AA01376 (5.64+/IDA-1.3.4 for ); Tue, 13 Nov 90 15:05:37 -0600 Received: by yoda.ncsa.uiuc.edu id AA01372 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 13 Nov 90 15:05:35 -0600 Message-Id: <9011132105.AA01372@yoda.ncsa.uiuc.edu> Date: Fri, 9 Nov 90 13:45:29 PST From: van-bc!mdivax1!kenward (Gary Kenward) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Problem with Complement? Status: RO Why does the Complement function reverse lists under some circumstances? In[37]:= Complement[{Null,1,2,3,4,5}, {Null}] Out[37]= {1, 2, 3, 4, 5} In[38]:= Complement[{Null,1,1/2,1/3,1/4,1/5}, {Null}] 1 1 1 1 Out[38]= {-, -, -, -, 1} 5 4 3 2 van-bc!mdivax1!kenward (Gary Kenward) From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Nov 13 17:42:54 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA02380 (5.64+/IDA-1.3.4 for stevec); Tue, 13 Nov 90 17:42:51 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA14239; Tue, 13 Nov 90 17:43:38 CST Received: by yoda.ncsa.uiuc.edu id AA01371 (5.64+/IDA-1.3.4 for ); Tue, 13 Nov 90 15:05:28 -0600 Received: by yoda.ncsa.uiuc.edu id AA01367 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 13 Nov 90 15:05:26 -0600 Message-Id: <9011132105.AA01367@yoda.ncsa.uiuc.edu> From: "Keith R. Slavin" To: mathgroup@yoda.ncsa.uiuc.edu Subject: NIntegrate Date: Tue, 13 Nov 90 08:54:40 PST Status: RO To help with numerical integration of expressions like: NIntegrate[x^4+y^2,{x,-1,1},{y,-1,1}] try increasing the MaxRecursion depth to allow it to go down more subdivision depths to reach its required accuracy goal. eg: use: NIntegrate[x^4+y^2,{x,-1,1},{y,-1,1},MaxRecursion->10] This works just fine. Keith Slavin Tektronix Inc, Beaverton Or, (503) 627 4907 From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Nov 13 18:55:23 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA02525 (5.64+/IDA-1.3.4 for stevec); Tue, 13 Nov 90 18:55:21 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA15314; Tue, 13 Nov 90 18:56:09 CST Received: by yoda.ncsa.uiuc.edu id AA01361 (5.64+/IDA-1.3.4 for ); Tue, 13 Nov 90 15:05:14 -0600 Received: by yoda.ncsa.uiuc.edu id AA01357 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 13 Nov 90 15:05:12 -0600 Message-Id: <9011132105.AA01357@yoda.ncsa.uiuc.edu> Date: Tue, 13 Nov 90 09:25:34 EST From: Jim_Wendel@ub.cc.umich.edu To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: logical expressions Status: RO This is about Paul Abbott's note of 10/28, logical expressions. The second example, supposedly of an invalid formula, is incorrect, in the sense that the formula evaluates to q for every p, not to false; this is readily checked by doing a truth-table by hand. Furthermore, what is the role of the quantity e=Rep[1,gbool,2}? It evaluates to 1, so why not just use 1, or nothing at all in multiplicative environments, e.g. and[x_,y_]:=x y, rather than e x y? From mathgroup-adm@yoda.ncsa.uiuc.edu Tue Nov 13 19:37:59 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA02637 (5.64+/IDA-1.3.4 for stevec); Tue, 13 Nov 90 19:37:57 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA15849; Tue, 13 Nov 90 19:38:44 CST Received: by yoda.ncsa.uiuc.edu id AA01366 (5.64+/IDA-1.3.4 for ); Tue, 13 Nov 90 15:05:20 -0600 Received: by yoda.ncsa.uiuc.edu id AA01362 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Tue, 13 Nov 90 15:05:18 -0600 Message-Id: <9011132105.AA01362@yoda.ncsa.uiuc.edu> Date: Mon, 12 Nov 90 22:56:30 +0100 From: Markus Lautenbacher Subject: User defined aliases To: mathgroup@yoda.ncsa.uiuc.edu Status: RO Hi mathgroup readers, perhaps some of you can give me a little advice on the following problem: I have defined a function `OperatorProduct' which I want to transform via pattern matching in something else on the right hand side of several transformation rules, e.g. OperatorProduct[a_,b_] := f[a,b] (What is actually on the right hand side doesn't matter for the problem I describe here.) Now, `OperatorProduct' is a quite descriptive but also long name and I wanted to have something shorter. Since `Alias[]' tells you that `*' is just an alias for `Times' I tried `<>::=OperatorProduct' (I used `<>' is still unused) in order to allow for typing just `a <> b' instead of `OperatorProduct[a,b]'. However, Mathematica refused to accept this alias. Trying several versions like `<>::=~OperatorProduct~" and likewise forms didn't work either. Somehow Mathematica seems to resolve `<>' to the mathematical `less' and `greater' relations instead of a new combined symbol `<>'. What worked was `op::=OperatorProduct' with a usage like e.g. `a ~op~ b' but that is not excatly what I wanted. Does anybody know whether aliases like `*' are hard wired in Mathematica or is there a simple way to get my `<>' to work. The important point is that I want to define a new kind of valid _input_ format for the user defined function `OperatorProduct'. If it just were for formatting the output of `OperatorProduct' the `Infix' function (p. 278 MathBook) would of course do the job. Thanks in advance, MARKUS +=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+ # MARKUS E. LAUTENBACHER, # # office: Technical University Munich, Physics Department # # Theoretical Physics T31, WD-8046 Garching, FRG # # phone: 0049/89/3209-2398 # # INTERNET: lauten@ds0.cip.physik.tu-muenchen.de # # private: Gohrenstr. 4/319, WD-8000 Muenchen 19, FRG # #-------------------------------------------------------------------------# # SIR ERNEST RUTHERFORD: `Science is physics, and the rest is # # stamp collecting' # # Surely Rutherford (1871-1937) knew nothing about computers! ;-) # +=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+ From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Nov 15 21:28:29 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA03284 (5.64+/IDA-1.3.4 for stevec); Thu, 15 Nov 90 21:28:26 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA24409; Thu, 15 Nov 90 21:29:15 CST Received: by yoda.ncsa.uiuc.edu id AA03188 (5.64+/IDA-1.3.4 for ); Thu, 15 Nov 90 20:09:27 -0600 Received: by yoda.ncsa.uiuc.edu id AA03184 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Thu, 15 Nov 90 20:09:26 -0600 Message-Id: <9011160209.AA03184@yoda.ncsa.uiuc.edu> Date: Thu, 15 Nov 90 16:35:22 -0500 From: sg04%harvey@gte.com (Steven Gutfreund) To: mathgroup@yoda.ncsa.uiuc.edu Subject: Follow-up request Status: RO Has anyone written any B-Spline code for mathematica? In particular I am looking for Uniform or non-Uniform (NURB) patches for surface data. -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= Yechezkal Shimon Gutfreund sgutfreund@gte.com GTE Laboratories, Waltham MA harvard!bunny!sgutfreund -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= From mathgroup-adm@yoda.ncsa.uiuc.edu Thu Nov 15 22:28:39 1990 Received: from newton.ncsa.uiuc.edu by yoda.ncsa.uiuc.edu with SMTP id AA03342 (5.64+/IDA-1.3.4 for stevec); Thu, 15 Nov 90 22:28:37 -0600 Return-Path: Received: from yoda.ncsa.uiuc.edu by newton.ncsa.uiuc.edu (4.1/NCSA-4.1) id AA25227; Thu, 15 Nov 90 22:29:28 CST Received: by yoda.ncsa.uiuc.edu id AA03168 (5.64+/IDA-1.3.4 for ); Thu, 15 Nov 90 20:08:48 -0600 Received: by yoda.ncsa.uiuc.edu id AA03164 (5.64+/IDA-1.3.4 for /usr/lib/sendmail -odq -oi -fmathgroup-adm@yoda.ncsa.uiuc.edu mathgroup-out); Thu, 15 Nov 90 20:08:46 -0600 Message-Id: <9011160208.AA03164@yoda.ncsa.uiuc.edu> To: mathgroup@yoda.ncsa.uiuc.edu Subject: Re: Problem with Complement? Date: Tue, 13 Nov 90 14:03:45 PST From: jacobson@cello.hpl.hp.com Status: RO > Why does the Complement function reverse lists under some circumstances? It sorts lists into a canonical order (aka "standard order"). See the description of Complement on page 607 and the description of Order on page 660. "Canonical order has several properties. Smaller numbers of a particular type come first. Symbols are ordered lexicographically according to the textual names. Strings are ordered lexicographically. Shorted expressions come first." -- David Jacobson