Subject: Sun-Symbolic-Math Digest v1n10 Sun-Symbolic-Math Digest September 3, 1988 Volume 1: Number 10 Editor: Steve Christensen, steve@spock.ncsa.uiuc.edu, (217)244-0544 Today's Topics: Note on bugs in REDUCE's ALGINT package Mathematica Details Send contributions to: Sun-Symbolic-Math@spock.ncsa.uiuc.edu Send subscription add/delete requests to: Sun-Symbolic-Math-Request @spock.ncsa.uiuc.edu For BITNET: Sun-Symbolic-Math%spock.ncsa.uiuc.edu@uiucvmd.bitnet Sun-Symbolic-Math-Request%spock.ncsa.uiuc.edu@uiucvmd.bitnet Anonymous ftp to archive: ftp.ncsa.uiuc.edu (128.174.20.) cd to Directory /usr6/ftp/Symbolic See instructions in that directory. -------------------------------------------------------------------------- Date: Tue, 23 Aug 88 09:42:23 BST From: Computer Algebra Support Officer Subject: Note on bugs in REDUCE's ALGINT package Dear Dr Christensen, You may like to include the following short item in the next issue of the Sun Symbolic Math newsletter. It describes several bugs in the ALGINT algebraic integration package which is part of REDUCE version 3.3. The examples have been checked on several machines, including Sun workstations at the University of Aberdeen, so it seems that they represent bugs in ALGINT itself. Regards, Dr David Harper U.K. Universities Computer Algebra Support Officer ---------------------------- Item begins ------------------------------- Computer Algebra Support Project University of Liverpool Computer Laboratory Liverpool, U.K. Serious bugs in REDUCE Vn 3.3 ALGINT package --------------------------------------------- A number of serious bugs have been reported in the ALGINT algebraic integration package which is distributes with REDUCE version 3.3. Details are given below. All examples have been produced on the University of Liverpool IBM VM/CMS implementation of REDUCE Vn 3.3 and verified on the University of Nottingham VAX VMS implementation. 1. Reported by Dr Tracy Colgan and colleagues at Shell UK's Thornton Research Laboratories, Chester, U.K. When ALGINT is required to integrate certain functions of the form 1/SQRT(quadratic), a spurious 'constant of integration' is appended to the result (which is otherwise correct). The 'constant' includes LOG(-1) as a factor. This is a meaningless quantity in mathematical terms since LOG is undefined on the negative real axis. An example follows. This has also been reproduced on the Sun workstation implementation. REDUCE 3.3, 15-Jan-88 ... 1: off allfac; 2: on div; 3: p:=1/sqrt(a*x**2+b*x+c); 2 -1 P := SQRT(A*X + B*X + C) 4: int(p,x); 2 -1 SQRT(A)*LOG(2*SQRT(A)*SQRT(A*X + B*X + C) + 2*A*X + B)*A + -1 SQRT(A)*LOG(-1)*A 5: COMMENT now a specific example; p:=1/sqrt(x**2+x+1); 2 -1 P := SQRT(X + X + 1) 6: int(p,x); 2 LOG(2*SQRT(X + X + 1) + 2*X + 1) + LOG(-1) For comparison, the same integrals were evaluated using Maple Vn4.0 on the University of Liverpool VM/CMS system. The session log follows. |\^/| ._|\| |/|_. Watcom Products \ MAPLE / Version 4.0 --- April 1986 <____ ____> For on-line help, type help(); | > p:=1/sqrt(a*x**2+b*x+c); 1 p := --------------------- 2 1/2 (a x + b x + c) > int(p,x); 1/2 2 1/2 ln(2 a (a x + b x + c) + 2 a x + b) -------------------------------------------- 1/2 a > p:=1/sqrt(x**2+x+1); 1 p := ----------------- 2 1/2 (x + x + 1) > int(p,x); 2 1/2 ln(2 (x + x + 1) + 2 x + 1) 2. Reported by Dr John Pulham, Mathematics Department, University of Aberdeen, Scotland, U.K. When ALGINT is required to evaluate the integral of SQRT((1+X)/(1-X)) it fails with an error message. However it can integrate the general case, viz. SQRT((A+X)/(A-X)). REDUCE 3.3, 15-Jan-88 ... 1: p:=sqrt((1+x)/(1-x)); SQRT( - X - 1) P := ---------------- SQRT(X - 1) 2: int(p,x); *** Format error *** unable to go x:=x**2 (SQRT (PLUS X (MINUS 1))) ***** Failure to make integral at infinity 3: p:=sqrt((a+x)/(a-x)); SQRT(A + X) P := ------------- SQRT(A - X) 4: int(p,x); - (SQRT(A + X)*SQRT(A - X) - LOG(SQRT(A - X)*SQRT(A + X)*SQRT (-1) + X)*A*I) 3. Reported by Dr John Pulham, Department of Mathematics, University of Aberdeen, Scotland, U.K. This is a very puzzling bug and it seems to show that REDUCE/ALGINT cannot recognise two expressions as identical under some circumstances, even if their SYMBOLIC representations are demonstrably equal. It is best explained by the example. REDUCE 3.3, 15-Jan-88 ... 1: f:=1/sqrt(2*a*x+x**2); 1 F := ------------------ 2 SQRT(2*A*X + X ) 2: int(f,x); - (LOG(SQRT(2*A + X) - SQRT(X)) - LOG(SQRT(2*A + X) + SQRT(X) )) 3: g:=f; 1 G := ------------------ 2 SQRT(2*A*X + X ) 4: int(g,x); 1 INT(------------------,X) 2 SQRT(2*A*X + X ) 5: int(f,x); - (LOG(SQRT(2*A + X) - SQRT(X)) - LOG(SQRT(2*A + X) + SQRT(X) )) 6: symbolic aeval 'f; (!*SQ (1 (((EXPT (PLUS (TIMES 2 A X) (EXPT X 2)) (QUOTIENT 1 2)) . 1) . 1)) T) 7: symbolic aeval 'g; (!*SQ (1 (((EXPT (PLUS (TIMES 2 A X) (EXPT X 2)) (QUOTIENT 1 2)) . 1) . 1)) T) 8: symbolic equal(aeval 'f, aeval 'g); T 9: int(g,x); 1 INT(------------------,X) 2 SQRT(2*A*X + X ) David Harper (U.K. Universities Computer Algebra Support Officer) --------------------------------- Item ends ------------------------------- Date: Sept. 3, 1988 From: Steve Christensen Subject: Mathematica Details This is the full version of a note I sent to sci.math.symbolic. This includes pricing and other comments not in that message. ------------------------------------- From Stephen Wolfram: I've seen quite a bit of talk on the net about Mathematica, and I wanted to set a few things straight. 1. Mathematica for the Macintosh 1.1 Availability Mathematica for the Macintosh has been shipping (in quite large quantities) since the day it was announced: June 23. We seemed to have confused some people by not following what seems to be the industry standard of pre-announcing one's product. You can get Mathematica either directly from us, or from various dealers (such as ComputerWare in Palo Alto). Our prices are: $495 for the standard Macintosh version $795 for the Mac II version. Our number is: 1-800-441-MATH (for orders); 217-398-0700 (otherwise). So far as we know, Mathematica is not available through any discount mail-order houses. We have various special deals for universities. One deal involves a huge discount for large universities that bundle Mathematica with all the Macs that they resell. 1.2 Memory Mathematica needs a lot of memory to run well. We had originally thought that many of users would do rather simple things with Mathematica, so that 2 MB would be enough. Our users seem to be doing MUCH more sophisticated (and interesting) things than we had expected, and 2 MB isn't usually enough. With 4 or 5 MB, Mathematica will run really well. With 2.5 MB you can do a lot more than with 2 MB. It would be a lot better for all of us if memory were cheaper, or the Mac had virtual memory. (I'm happy to say that it looks as if the price by weight of 1 megabit SIMMs has now gone below the current price of gold.) 1.3 Documentation The main documentation for the kernel of Mathematica (the part that actually does the computations) is the book that I wrote, which is published by Addison-Wesley. The title is: "Mathematica: A System for Doing Mathematics by Computer". There is both a paperback ($29.95) and a hardback ($44.25) version. If you can't find these books in your local bookstore, call Addison-Wesley. (The person in charge of the Mathematica project at Addison-Wesley is Allan Wylde: 415-594-4444.) We're now shipping the hardback version of the book with the Macintosh software. (This has depleted supplies of the hardback from the first printing of the book, so right now, you may only be able to get the paperback from bookstores.) 1.4 Versions The current version of Mathematica for the Macintosh is 1.03. This version includes animation, and various other features not in 1.0. Unless you specifically call to request it, the first upgrade we will send you is Version 1.1. Version 1.1 will be ready to ship within a few weeks (the software is being tested; manufacturing is underway). This version includes a number of small fixes, together with some new features. Most notable among these is the ability to digitize mouse input -- if you click on a graph, you can have the coordinates of where you click fed into Mathematica. So long as you send in your registration card, you will get a free upgrade to 1.1 when it is ready. 2. Mathematica for Other Machines 2.1 Sun Workstations Mathematica will be available for Sun-3, Sun-4 and Sun 386i from Sun Microsystems. They assure us that it will be shipping within a month or so. Contact your local Sun sales representative for more information. The product manager for Mathematica at Sun is Andy MacRae (415-336-1047; amacrae@sun.com). If you're interested in seeing Mathematica be available on Sun-2's, please tell Andy MacRae. 2.2 IBM PC RT Mathematica will be available from IBM on the RT under AIX. Contact your local IBM sales representative for more information. The list price for Mathematica on the RT is $2000. The person responsible for Mathematica in the RT division of IBM is Vicky Markstein (512-823-4072). 2.3 Silicon Graphics Mathematica will be available from Silicon Graphics on Iris 4D workstations. The list price is $8000 (commercial); $4000 (educational). The interim contact person at Silicon Graphics is Lisa Paul (415-962-3361). Mathematica does some neat stuff on the Iris, using the Iris 3D graphics hardware. You can take 3D objects generated by Mathematica, and manipulate them in real time using external programs that come with Mathematica for the Iris. If you're interested in Mathematica for Iris Series 3000 machines, let Lisa Paul know. 2.4 Ardent and Stellar Versions of Mathematica are available from Ardent and Stellar for their machines. The list price is $8000 (commercial); $4000 (educational). The contact people are: Jim Newcombe at Ardent (408-732-0400) and Ian Reid at Stellar (617-964-1000). 2.5 NeXT Mathematica will be bundled on NeXT's machine, which we all hope will be out very soon. 2.6 Other Platforms We are actively working on ports of Mathematica to a number of other machines -- watch for an announcement around November. We'd be very interested feedback that anyone can give us on the desirability of having Mathematica on particular systems, e.g. Alliant Apple Mac A/UX Apollo Atari Mega AT&T UNIX PC (3B1) Commodore Amiga Convex Cray UNICOS DEC VAX: VMS or UNIX ETA Hewlett-Packard IBM mainframes (3090 etc.) IBM PC's: 386-based under MS-DOS; 286-based under MS-DOS; Under OS/2; Under Xenix; etc. Meiko Sony Tektronix. We are considering making a version of Mathematica for the AT&T UNIX PC available (probable price: $400). We will do this if there is enough interest. Please let us know if you're interested (end users, dealers, distributors, etc.) There is talk of setting up a consumer-oriented time sharing service that would let people use Mathematica on a supercomputer with over a gigabyte of memory. The idea is that you would set up a calculation on something like a Macintosh, but then, if you ran out of time or space, you could dial up the supercomputer and run the kernel remotely on that. Every version of Mathematica has the communication mechanisms necessary to do this built in. We're trying to gauge the level of interest in this service. Please let us have your comments. 3. Mathematica User Group etc. There are moves afoot to start a Mathematica User Group, which will maintain a library of Mathematica packages and notebooks, produce a newsletter, and run conferences. It will also coordinate with local user groups. The first president of the Mathematica User Group will be Steve Christensen of NCSA (217-244-0544; steve@ncsa.uiuc.edu). 4. Mathematica Developers I'm very happy to say that many people have contacted us about doing third-party development associated with Mathematica. We are now in the process of preparing an information kit for potential developers, that should be ready to send in 1-2 weeks. Please contact us if you would like one. 5. Mathematica Objects 5.1 T-Shirts We made some Mathematica T-shirts, which seem to have been selling even faster than the program. They cost $8 each; write or call us if you want one. 5.2 1989 Calendar We are intending to produce a 1989 Mathematica calender, with large color pictures generated by Mathematica. If you've produced some particularly nice-looking graphics with Mathematica, we'd very much like to consider it for the calendar. 6. Feedback, Please We'd really like to know what people are doing with Mathematica. One of the most satisfying things about writing programs is seeing people do imaginative and interesting things with them. If you are doing something exciting with Mathematica, do post a notice about it to a newsgroup, or send us mail about it. -- Stephen Wolfram. P.S. You can send mail to math@wri.com. ***********************************************************************