Mathematica Notes from Sci.Math.Symbolic, uiuc.mathematica and comp.sys.next Volume 3: March 16, 1989 - April 21, 1989 Editor: Steve Christensen Subjects: Mathematica and matrices Re: Unix "bc" to 45 digits Re: Unix "bc" to 45 digits Re: Unix "bc" to 45 digits 163 Re: Unix "bc" to 45 digits Re: Unix "bc" to 45 digits Re: Unix "bc" to 45 digits Re: Unix "bc" to 45 digits Re: Unix "bc" to 45 digits Laplace Transforms on Mathematica Re: Hardy-Ramanujan-Rademacher form mathematica arithmetic Re: Unix "bc" to 45 digits mathematica arithmetic functions in Mathematica Scratchpad II Re: Unix "bc" to 45 digits Mathematica for Apollos? Please? Gnumathematica distribution Re: Mathematica for Apollos? Please? Help with ** in Mathematica Re: Gnumathematica distribution Mathematica plots in complex plane Pattern matching in Mathematica Dynamics in Mathematica? Plot3D in Mathematica Re: Plot3D in Mathematica Re: Plot3D in Mathematica Images and Mathematica Computers & Mathematics 1989 Graphics Mathematica Mathematica Inertia of a matrix? LINPACK does ---------------------------------------------------------------------------- Date: Mar 16, 1989 From: gmk@wjh12.harvard.edu Subject: Mathematica and matrices 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 : Internet: gmk@wjh12.harvard.edu, BITnet: gmk@harvunxw, Phone: 617-495-2027 : Secretary: 617-495-8818; Government Data Center Assoc. Director: 617-495-5740 : Research Assistants and Data Center Staff: 617-495-4734, FAX: 617-495-0438 ---------------------------------------------------------------------------- Date: Mar 18, 1989 From: ags@s.cc.purdue.edu Subject: Re: Unix "bc" to 45 digits >In article <15383@obiwan.mips.COM>, mark@mips.COM (Mark G. Johnson) writes: >< >< Being an empiricist I tried out exp(PI*sqrt(163)) on good ole UNIX's >< arbitrary-precision programming language "bc": >< (program omitted for brevity) >< >< 262537412640768743.999999999999250072597198174072682220727495300 > ^ > | >Being an experimentalist, I ran Mark Johnson's program on bc on one >of our UNIX systems (this one). The results agree up to the digit >marked with the arrow. Using Mathematica on a Mac II, I evaluated N[E^(Pi Sqrt[163]),100] and got: 262537412640768743.99999999999925007259719818568887935385633733\ ^ 6990862707537410378210647910118607313 which differs at the marked position. Who is right? I also tried this with a buggy pre-release version of Mathematica on a NeXT. It printed an overflow message, followed by a completely nonsensical answer. Dave Seaman ags@j.cc.purdue.edu ----------------------------------------------------------------------------- Date: Mar 18, 1989 From: gjc@bu-cs.BU.EDU (George J. Carrette) Subject: Re: Unix "bc" to 45 digits DOE-Macsyma agrees with the result from Mathematica, so I would tend to think that the calculation done in "bc" was incorrectly formulated. sqrt(163) %pi Computing: %e With BC (Result from previous message) MM (Mathematica, from previous message) MC (DOE-Macsyma, run on a SUN-3) BC: 262537412640768743.999999999999250072597198174072682220727495300 MM: 262537412640768743.99999999999925007259719818568887935385633733 6990862707537410378210647910118607313 MC: 262537412640768743.99999999999925007259719818568887935385633733 6990862707537410378210647910118607313 ----------------------------------------------------------------------------- Date: Mar 18, 1989 From: mike@arizona.edu Subject: Re: Unix "bc" to 45 digits > DOE-Macsyma agrees with the result from Mathematica, so I would tend to > think that the calculation done in "bc" was incorrectly formulated. Perhaps it is time to point out again that bc is not a reliable arithmetic engine. I posted the following example of incorrect division a couple of years ago. I just tried it again (on VAX running BSD 4.3) and got a different, but still wrong, answer. Note: Shortly after I posted the following, a diff was posted that fixed a couple bugs in bc. It didn't fix them all; after applying that patch, the following example still failed. meg>> bc obase=16 ibase=16 a = 519E2FEA51A537AB0132DC6F3678E8539F1BEF64109473F752 b = A2F01268A40089 a 519E2FEA51A537AB0132DC6F3678E8539F1BEF64109473F752 b A2F01268A40089 c = a/b c 803BF0FC7753CC1552D0A09B286CAAEBE771 a-(b*c) F530645557A101E4C95E9095BD9 obase=A c 11170769584511689511742018590-12440481240754033 The variable c in the above transcript is obviously bogus; a mod b cannot be larger than b. And, when printed in base 10, it contains a minus-sign. BTW, the correct answer for c is 803BF0FC7753CC1552D0A0CE7125CE93A4C4 (base 16). Mike Coffin mike@arizona.edu Univ. of Ariz. Dept. of Comp. Sci. {allegra,cmcl2}!arizona!mike Tucson, AZ 85721 (602)621-2858 --------------------------------------------------------------------------- Date: Mar 18, 1989 From: wayne@pur-phy Subject: 163 ->< 262537412640768743.999999999999250072597198174072682220727495300 - ^ ->Being an experimentalist, I ran Mark Johnson's program on bc on one ->of our UNIX systems (this one). The results agree up to the ^ - -Using Mathematica on a Mac II, I evaluated - N[E^(Pi Sqrt[163]),100] -and got: - -262537412640768743.99999999999925007259719818568887935385633733\ - ^ -6990862707537410378210647910118607313 -Dave Seaman Here's SMP's value on a 750. It agrees with Mathematica, which really doesn't come as much of a surprise. 262537412640768743.99999999999925007259719818568887935385633733\ 69908627075374103782106479101186073130 I guess the thing to do is find someone with Macsyma or Maple to break the tie. I don't put too much value on the fact that Mathematica and SMP agree. wayne ----------------------------------------------------------------------------- Date: Mar 20, 1989 From: chrstnsn@uxe.cso.uiuc.edu Subject: Re: Unix "bc" to 45 digits With Mathematica 1.1 on a Sun-4/110 and on a Mac II I get: In[1]:= N[E^(Pi Sqrt[163]),100] Out[1]= 262537412640768743.99999999999925007259719818568887935385633733699086\ > 2707537410378210647910118607313 Using Maple 4.2 on a Sun-4/110 I get: > evalf(exp(Pi*sqrt(163))); .26253741264076874399999999999925007259719818568887935385633733699086270753741\ 03782106479101186073108 * 10 ^ 18 the two answers differ in the last two decimal places. Steve Christensen ----------------------------------------------------------------------------- Date: Mar 20, 1989 From: c0i+@andrew.cmu.edu Subject: Re: Unix "bc" to 45 digits *->< *262537412640768743.999999999999250072597198174072682220727495300 *- ^ *->Being an experimentalist, I ran Mark Johnson's program on bc on one *->of our UNIX systems (this one). The results agree up to the ^ *- *-Using Mathematica on a Mac II, I evaluated *- N[E^(Pi Sqrt[163]),100] *-and got: *- *-262537412640768743.99999999999925007259719818568887935385633733\ *- ^ *-6990862707537410378210647910118607313 *-Dave Seaman * * Here's SMP's value on a 750. It agrees with Mathematica, which really *doesn't come as much of a surprise. * * 262537412640768743.99999999999925007259719818568887935385633733\ * 69908627075374103782106479101186073130 * * I guess the thing to do is find someone with Macsyma or Maple to break *the tie. I don't put too much value on the fact that Mathematica and *SMP agree. I just ran the same thing on Maple, with 120 digits of precision: Maple agrees with Mathematica and SMP. I guess I believe it unless they all use the same wrong algorithm:-). Neil ----------------------------------------------------------------------------- Date: Mar 20, 1989 From: gjfee@watmum.waterloo.edu Subject: Re: Unix "bc" to 45 digits > Here's SMP's value on a 750. It agrees with Mathematica, which really > doesn't come as much of a surprise. > 262537412640768743.99999999999925007259719818568887935385633733\ > 69908627075374103782106479101186073130 > I guess the thing to do is find someone with Macsyma or Maple to break > the tie. I don't put too much value on the fact that Mathematica and > SMP agree. Here's maple's value: It agrees with SMP. > evalf(exp(Pi*sqrt(163)),120); .26253741264076874399999999999925007259719818568887935385633733699086270753741\ 0378210647910118607312951181346186064504194 * 10 ^ 18 ----------------------------------------------------------------------------- Date: Mar 21, 1989 From: cdl@mplvax.EDU Subject: Re: Unix "bc" to 45 digits In article <28820@bu-cs.BU.EDU> gjc@bu-cs.BU.EDU (George J. Carrette) writes: >DOE-Macsyma agrees with the result from Mathematica, so I would tend to >think that the calculation done in "bc" was incorrectly formulated. > > sqrt(163) %pi >Computing: %e I would tend to think that the note above was incorrectly formulated. :-) Apparently the structure of the computation is such that it needs about 20 guard digits. More modern math packages such as Macsyma and Mathematica seem to hide their guard digits from the user, while 'bc' doesn't. -- carl lowenstein marine physical lab u.c. san diego {decvax|ucbvax} !ucsd!mplvax!cdl cdl@mplvax.ucsd.edu --------------------------------------------------------------------------- Date: Mar 21, 1989 From: jimh@hpsad.HP.COM Subject: Re: Unix "bc" to 45 digits -Using Mathematica on a Mac II, I evaluated - N[E^(Pi Sqrt[163]),100] -262537412640768743.99999999999925007259719818568887935385633733\ -6990862707537410378210647910118607313 > Here's SMP's value on a 750. It agrees with Mathematica, which really >262537412640768743.99999999999925007259719818568887935385633733\ >69908627075374103782106479101186073130 I get: 262537412640768743.99999999999925007259719818568887935385633733\ 699086270753741037821064791011860731295118134618606450419308388 (Using Judson McClendon's `BIGCALC' extended precision calculator for MS/DOS, set to 500 digits of accuracy). Looks like three times says it's true. Jim Horn ----------------------------------------------------------------------------- Date: Mar 22, 1989 From: tca@ut-emx.UUCP Subject: Laplace Transforms on Mathematica 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 ----------------------------------------------------------------------------- Date: Mar 23, 1989 From: ags@s.cc.purdue.edu Subject: Re: Hardy-Ramanujan-Rademacher form >The Hardy_Ramanujan-Rademacher expansion of p(n) is a remarkable formula >which allows one to enumerate the partitions of an integer n (for example, >the partitions of 3 are (3), (2,2), and (1,1,1)). P(n) increases rapidly >with n (p(200) = 3972999029388). >However, I need to compute the value of p(n) but find >the formal presentation of the formulae in Andrews too daunting to implement; >does someone know of existing code to perform this computation, or an >explanation pitched at a slightly less sophisticated audience? The Mathematica function PartitionsP does the trick. Here is a sample session: Script started on Thu Mar 23 09:27:07 1989 seaman: math Mathematica NeXT 1.1 (September 7, 1988) by S. Wolfram, D. Grayson, R. Maeder, H. Cejtin, S. Omohundro, D. Ballman and J. Keiper Copyright 1988 Wolfram Research Inc. -- NeXT graphics initialized -- In[1]:= PartitionsP[200] Out[1]= 3972999029388 In[2]:= Dave Seaman ags@j.cc.purdue.edu ----------------------------------------------------------------------------- Date: Mar 23, 1989 From: mckay@concour.CS.Concordia.CA Subject: mathematica arithmetic Expanding then factoring (x+36)^3*(x-35)^3 works for 2 of the 4 choices of signs (here {+,-}) and not for the 2 others. This is on a MacIIX, shedding doubt on the correctnes of the arithmetic in Mathematica (or MacIIX hard- ware perhaps). /* End of text from uxe.cso.uiuc.edu:sci.math.symbolic */ /* Written 11:44 am Mar 21, 1989 by jimh@hpsad.HP.COM in uxe.cso.uiuc.edu:sci.math.symbolic */ -Using Mathematica on a Mac II, I evaluated - N[E^(Pi Sqrt[163]),100] -262537412640768743.99999999999925007259719818568887935385633733\ -6990862707537410378210647910118607313 > Here's SMP's value on a 750. It agrees with Mathematica, which really >262537412640768743.99999999999925007259719818568887935385633733\ >69908627075374103782106479101186073130 I get: 262537412640768743.99999999999925007259719818568887935385633733\ 699086270753741037821064791011860731295118134618606450419308388 (Using Judson McClendon's `BIGCALC' extended precision calculator for MS/DOS, set to 500 digits of accuracy). Looks like three times says it's true. Jim Horn ----------------------------------------------------------------------------- Date: Mar 23, 1989 From: mo@prisma Subject: Re: Unix "bc" to 45 digits I guess I'm not surprised the bc math library is tuned for extreme accuracy. ----------------------------------------------------------------------------- Date: Mar 23, 1989 From: mckay@concour.CS.Concordia.CA Subject: mathematica arithmetic Expanding then factoring (x+36)^3*(x-35)^3 works for 2 of the 4 choices of signs (here {+,-}) and not for the 2 others. This is on a MacIIX, shedding doubt on the correctnes of the arithmetic in Mathematica (or MacIIX hard- ware perhaps). ----------------------------------------------------------------------------- Date: Mar 27, 1989 From: alanw@django.berkeley.edu Subject: functions in Mathematica I would like to check possible solutions of the wave equation u_{tt}-u_{xx}=0, and eventually more complicated equations. Below is a log of mathematica session in which I tried to define the differential operator involved in this equation, and then to apply it to a simple trial function. Can someone explain to me why Mathematica won't evaluate the function in the last command (i.e. replace #1 by x and #2 by t)? Alan Weinstein -------------------------------------------------------------------------- SunMathematica (sun3.fpa) 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]:= box[f_]= Derivative[0,2][f]-Derivative[2,0][f] (0,2) (2,0) Out[1]= f - f In[2]:= wave[x_,t_]= Exp[I(a x + w t)] I (t w + a x) Out[2]= E In[3]:= box[wave] I (a #1 + w #2) 2 I (a #1 + w #2) 2 Out[3]= -(-(E a ) & ) + (-(E w ) & ) In[4]:= %[x,t] I (a #1 + w #2) 2 I (a #1 + w #2) 2 Out[4]= (-(-(E a ) & ) + (-(E w ) & ))[x, t] ----------------------------------------------------------------------------- Date: Mar 28, 1989 From: jma@litp.UUCP Subject: Scratchpad II I recently read the transaction of Philippe Flajolet (INRIA-Rocquencourt France) in which he compares Maple, Mathematica and Macsyma. So I realize the same benchmarks under the new computer algebra system Scratchpad II. I have used our IBM 4381 under VM/CMS. All tests run successfully, except a Taylor development (because this function is incorrect). I had to precise some types (to force evaluations) and write functions (to avoid loops at top-level not always accepted). Computations times are difficult to compare, first because computers are different. An estimation of the speed ratio between an IBM 4381 and a Sun 3/160 with examples in Aldes/SAC2 (compiled in Fortran) is near a factor 2 in favor the IBM. But this is only a simple estimation. Furthermore Scratchpad II is very different from the three other systems by its conception and its height. So I don't take in account : - the load time of the system (long) - the load time of the necessary librairies (very long ...) These times are not estimable, but cost only once. The indicated times are estimations, because they vary a lot from an execution to another. Two times are indicated : - the first is said 'interpreted' : we use Scratchpad like Maple or Macsyma, in writing our commands under the interpret (very slow ...) even for loops. - the second is said 'compiled' : we write previous commands in functions in an INPUT file. Then we read this INPUT file and call the right function. It is compiled. So the interpretation time of the commands are nearly null and the computation time is only the evaluation time. This is very clear for the B* tests with many loops. Note that we don't take into account the time spent in reading the INPUT file and compiling the function. First we must say that the 'compiled' times are to take with care, because this requires from the user a knowledge of the system and time to write the functions, even when the tests are in the spirit of an "algebraic calculator". But Scratchpad is not built and can't be used such a way. These times have only sense on the intrinsic efficiency of the kernel and of the algorithms. I can also give the total times to execute all the tests - interpreted version : about 550 seconds - compiled version : about 200 seconds These times take into account the garbage collections. At the end of this transaction, I join the INPUT file for the 'compiled' version. Joel Marchand L.I.T.P - Universite Paris VI - France e-mail : jma@frunip11.bitnet jma@litp.univ-p6-7.fr (uucp) ====================================================================== A1 : )set streams calculate 80 1/cos(t)$EFPS(t,RN) A2 : r : RN ; f:NNI := 8 r := 2**(1000*f)/3**(1000*f)*15**(1000*f)/10**(1000*f) A3 : digits 400 ; exp (pi()*sqrt(163)$NFLOAT) A4 : d := 1/(1+x**4) ; for i in 1..16 repeat d := pderiv(d,x) A5 : for i in 1..16 repeat d := integrate(d,x)::RF I MAPLE: 207.1 real 198.8 user 2.3 sys MATH: 770.4 real 677.7 user 5.5 sys MACSY: 1453.3 real 1429.8 user 3.2 sys SPAD(inter.): 127.9 real SPAD(comp.): 110.2 real ====================================================================== B1 : f := 1 ; s := 0 for i in 1..5000*f repeat if (i rem 2) = 0 then s := s + i + 1 else s := s - i s B2 : xfb:NFLOAT:= log(f*2000) /$NFLOAT log(( 1+sqrt(5) ) /$NFLOAT 2) nfb:I := xfb fb(n:I):I == if n <= 1 then 1 else 1 + fb(n-1) + fb(n-2) fb(nfb) B3 : id(n: I):I == n s := 0 ; for j in 1..500*f repeat s := s + id(j) ; s B3' : id(n: I):I == n s := 0 ; for j in 1..1000*f repeat s := s + id(j) ; s MAPLE: 14.8 real 13.5 user 0.7 sys MATH: 111.5 real 101.3 user 1.6 sys MACSY: 145.5 real 129.1 user 2.0 sys SAC2: 1.6 real 1.3 user 0.3 sys SPAD(inter.): 231.0 real SPAD(comp.): 0.50 real ====================================================================== digits 16 ; s:NFLOAT := 0 ; f := 1 C1 : for i in 1..100*f repeat s := s + sqrt(i) C2 : for i in 1..100*f repeat s := s + log(i) C3 : for i in 1..100*f repeat s := s + sin(i) digits 32 ; s:NFLOAT := 0 ; f := 1 C4 : for i in 1..100*f repeat s := s + sqrt(i) C5 : for i in 1..100*f repeat s := s + log(i) C6 : for i in 1..100*f repeat s := s + sin(i) MAPLE: 53.3 real 47.1 user 0.9 sys MATH: 24.7 real 18.5 user 0.9 sys MACSY: 287.0 real 261.6 user 2.5 sys SPAD(inter.): 74.0 real SPAD(comp.): 20.9 real ====================================================================== D1 : digits 50 ; s:NFLOAT := 1 ; for i in 1..12 repeat s := (s+2/s)/2 ; s**2 - 2 D2 : n := 500 ; s:NFLOAT := 0 ; for i in 1..n repeat s := s + 1/i ; s-log(n)$NFLOAT D3 : - error on a Taylor development of exp(cos(sqrt(1-x^4))) on 1/sqrt(2) at order 8 - D4 : m := 5 ; p:P I := 1 for j in 1.. m repeat for i in j+1..m repeat p := p*(x[i]- x[j]) q:=expand(p) ; factor(q) MAPLE: 27.1 real 21.9 user 0.9 sys MATH: 122.1 real 106.8 user 1.9 sys MACSY: 225.8 real 202.0 user 3.1 sys SPAD(inter.): 50.0 real (sans D3) SPAD(comp.): 5.6 real (sans D3) ====================================================================== Detailed timings for ... MAPLE MATH MACSY SPAD(inter/comp) A1: 35.1 122.7 268.2 39.6/33.7 <10^4dig> A2: 85.5 205.3 303.0 8.9/5.6 <400 dig> A3: 49.3 12.0 254.9 1.5/1.1 A4: 0.8 2.6 6.0 4.1/3.0 A5: 27.1 327.5 588.7 73.8/66.8 (5 gc) <5000Loop> B1: 7.87 28.0 96.2 138.9/0.25 <1973FCall> B2: 3.85 10.4 24.8 1.0/0.12 <500Mcall> B3: 0.75 58.4 7.5 36.2/0.06 <1000Mcall> B'3: 1.75 218.3 15.2 54.9/0.07 <16 dig> C1: 1.53 1.05 5.38 9.93/1.7 C2: 6.60 0.53 1.05 13.3/2.7 C3: 7.68 0.50 1.23 12.1/4.1 <32 dig> C4: 1.73 2.93 48.68 12.8/1.9 C5: 10.95 3.96 128.81 11.2/3.2 C6: 17.78 4.91 78.53 14.7/7.3 (1 gc) D1: 7.2 36.9 55.0 2.0/0.08 D2: 2.9 5.2 33.5 37.0/1.4 D3: 4.8 2.8 40.0 - erreur - D4: 6.9 35.0 50.0 11.0/4.1 ====================================================================== Compiled version : ****************** )set streams calculate 80 a1() == 1/cos(t)$EFPS(t,RN) a1() a2():RN == r : RN ; f:NNI := 8 ; 2**(1000*f)/3**(1000*f)*15**(1000*f)/10**(1000*f) a2() a3() == digits 400 exp (pi()*sqrt(163)$NFLOAT) a3() a4(d) == for i in 1..16 repeat d := pderiv(d,x) d dd := a4(1/(1+x**4)) a5(d: RF I):RF I == for i in 1..16 repeat d := integrate(d,x)::RF I d a5(dd) b1() == s := 0 for i in 1..5000 repeat if (i rem 2) = 0 then s := s + i + 1 else s := s - i s b1() xfb:NFLOAT:= log(2000) /$NFLOAT log(( 1+sqrt(5) ) /$NFLOAT 2) nfb:I := xfb b2(n:I):I == if n <= 1 then 1 else 1 + b2(n-1) + b2(n-2) b2(nfb) id(n:I):I == n b3(nb:I):I == s := 0 ; for j in 1..nb repeat s := s + id(j) s b3(500) b3(1000) c1():NFLOAT == s:NFLOAT := 0 ; for i in 1..100 repeat s := s + sqrt(i) s c2():NFLOAT == s:NFLOAT := 0 ; for i in 1..100 repeat s := s + log(i) s c3():NFLOAT == s:NFLOAT := 0 ; for i in 1..100 repeat s := s + sin(i) s digits 16 c1() c2() c3() digits 32 c1() c2() c3() d1() == s:NFLOAT := 1 ; for i in 1..12 repeat s := (s+2/s)/2 s**2 - 2 digits 50 d1() d2():NFLOAT == n := 500 ; s:NFLOAT := 0 ; for i in 1..n repeat s := s + 1/i s-log(n)$NFLOAT d2() d4() == m := 5 ; p:P I := 1 ; for j in 1.. m repeat for i in j+1..m repeat p := p*(x[i]- x[j]) q:=expand(p) ; factor(q) d4() ----------------------------------------------------------------------------- Date: Mar 29, 1989 From: boehm@flora.rice.edu Subject: Re: Unix "bc" to 45 digits If anybody still cares about exp(pi*sqrt(163)) or similar problems, we are distributing a calculator that does recursive real (essentially demand driven, arbitrary precision) arithmetic. It allows you to scroll sideways through answers, always ensuring +- 1 accuracy in the last displayed digit. A Sun 3 executable is available for anonymous ftp from the 3 files titan.rice.edu:~ftp/sun-source/calc.shar.0[123]. I believe that it can also be obtained by sending a mail message with the following text to archive-server@rice.edu: send sun-source calc.shar.01 send sun-source calc.shar.02 send sun-source calc.shar.03 The source is primarily written in Russell. A compiler with source for the calculator is available in titan.rice.edu:~ftp/public/russell.tar.Z (about 866 Kbytes). The 1001st to 1038th digits to the right of the decimal point of exp(pi*sqrt(163)) are 39810031577598025111445957741835964890. :-) Hans-J. Boehm boehm@rice.edu ----------------------------------------------------------------------------- Date: Mar 29, 1989 From: phcoates@uqvax.decnet.uq.oz Subject: Mathematica for Apollos? Please? Does anyone know whether Mathematica is available for Apollo 3500 or 10k machines? Is Steve Wolfram planning a port? Is *anybody* planning a port? Will the owners of these brand spanking new Apollo machines ever find peace? (we'll settle for a port of Mathematica) Thank you in advance for answers to any of these questions, or answers to any questions of deep religious significance. A.B.O.Coates ACSnet: coates@phvax.decnet.uq.oz Dept. of Physics The University of Queensland St. Lucia QLD 4067 Australia ----------------------------------------------------------------------------- Date: Apr 1, 1989 From: robison@m.cs.uiuc.edu Subject: Gnumathematica distribution Has anyone gotten Gnumathematica 1.0 to run under X-windows? The gnuemacs interface works fine, but it keeps dumping core under X. Here's the stack trace. __afprx(4027ec,ffffecb0,403b2c) __afprx+d1 _ppontx() _ppontx+11 _fromat() _fromat+17 _fill__Exp(40b914,1) _fill__Exp+3b _tlsx() _tlsx+af _X__driver() _X__driver+89 _main(1,ffffeeda,ffffe00d) _main+74 I'm running on a Sun/3 under Sun OS 4.0.1. ADR [Note the date on the above message before you take it seriously. -smc] ----------------------------------------------------------------------------- Date: Apr 1, 1989 From: ianh@merlin.bhpmrl.oz Subject: Re: Mathematica for Apollos? Please? From article <1366@uqvax.decnet.uq.oz>, by phcoates@uqvax.decnet.uq.oz: > Does anyone know whether Mathematica is available for Apollo 3500 or 10k > machines? Is Steve Wolfram planning a port? Is *anybody* planning a port? > Will the owners of these brand spanking new Apollo machines ever find peace? > (we'll settle for a port of Mathematica) > Yes, Apollo are about to release a version for their M68XXX based workstations. As far as the 10000 version goes, that is largely up to Apollo marketing and Wolfram getting a machine organized to do the port. I hope it is soon. I have a 4 processor DSP10000 that would luv to be chugging away using Mathematica :-) ian -- Ian Hoyle /\/\ Computer Systems Superintendent / / /\ BHP Melbourne Research Laboratories / / / \ 245 Wellington Rd, Mulgrave, 3170 / / / /\ \ AUSTRALIA \ \/ / / / \ / / / Phone : +61-03-560-7066 \/\/\/ ACSnet : ianh@merlin.bhpmrl.oz Internet: ianh%merlin.bhpmrl.oz@uunet.uu.net ----------------------------------------------------------------------------- Date: Apr 2, 1989 From: VOIROL@rcgl1.eng.ohio-state.edu Subject: Help with ** in Mathematica I am trying to work with elementary matrices in Mathematica (attempt to perform some computations with large very sparse matrices...) . So I defined the rule e/: c1_ e[i_,j_] ** c2_ e[k_,l_] = c1 c2 kronecker[j,k] e[i,l] But the program refuses to expand a product of monomials in the e objects into another one (e.g. (e[1,3]-2 e[2,2])**(4e[1,2]+e[2,1]) so I cannot even test my rule. What is going wrong ? I assume that ** is distributive wrt addition . I included the coefficients in the rule because I am not sure how ** behaves wrt standard multiplication. Has anybody already figured that out ? Thanks for your help Philippe Voirol , e-mail : voirol%rcgl1@eng.ohio-state.edu ---------------------------------------------------------------------------- Date: Apr 3, 1989 From: wsmith@m.cs.uiuc.edu Subject: Re: Gnumathematica distribution You must be forgetting to set the MATHFRONT environment variable. It should be set to the release of the GNU editor that you are using. WWS ----------------------------------------------------------------------------- Date: Apr 2, 1989 From: zaccone@rigel.bucknell.edu Subject: Mathematica plots in complex plane I am fairly new to Mathematica, so I apologize if this is a dumb question. I would like to produce a plot in the complex plane. Specifically, if h is complex, I would like to graph the following: Abs[1 + h + h^2/2] == 1 Can anyone tell me how to do this with Mathematica? Rick Zaccone zaccone@bknlvms.bitnet zaccone@rigel.bucknell.edu -- zaccone@bknlvms.bitnet zaccone@rigel.bucknell.edu ----------------------------------------------------------------------------- Date: Apr 4, 1989 From: ssroy@phoenix.Princeton.EDU Subject: Pattern matching in Mathematica I have a question about how Mathematica applies certain types of transformation rules. Suppose you have the transformation rule: q[a_]q[b_] -> d[a,b] and you apply it to a term with lots of other terms, say k[i] k[j] k[l] q[a] q[b] M[i,j,l,a,b] In what order does it test possible matches? Does it pick two terms, k[i] k[j] for example, test for a match, fail, pick two more terms, k[i] k[l], test for a match, fail, etc? This is obviously quadratic in time. Or does it search for a match for the first term q[a_] and find q[a] in linear time then search for a match for q[b_] and find q[b] in linear time? The reason I ask is that I'm working on a problem that generates a sum of hundreds to thousands of terms each with about 10 elements and I would like to be able to apply rules like the above in reasonable time. When I have applied them they have been so slow that I suspect that the former algorithm is in use. I realize that the linear algorithm is more difficult to generalize than the quadratic, but the time savings would be large for a large class of problems. Steve Roy ssr@courant.princeton.edu ----------------------------------------------------------------------------- Date: Apr 16, 1989 From: turk@Apple.COM Subject: Dynamics in Mathematica? Does anyone know of a Mathematica package that will do kinematics and formulate dynamic equations of motion for systems of rigid bodies? -- Ken Turkowski @ Apple Computer, Inc., Cupertino, CA UUCP: {sun,nsc}!apple!turk CSNET: turk@Apple.CSNET ARPA: turk%Apple@csnet-relay.ARPA --------------------------------------------------------------------------- Date: Apr 17, 1989 From: phcoates@uqvax.decnet.uq.oz Subject: Plot3D in Mathematica Has anyone managed to get the Mathematica routine 'Plot3D' to produce numbered axes? I seem to be able to change the axis parameters till I go blue in the face, but the program just seems to ignore the relevant parameters. The same applies to plot and axis titles. Can anyone help me? Is Steven Wolfram out there? Note that these problems are on a *ooh* Mac IIx, using the hardwired number-crunching version. Does this happen in other versions? Thanks in advance for any help you can give. Live long and prosper, Tony Coates. Tony Coates, ACSnet: coates@phvax.decnet.uq.oz Department of Physics, The University of Queensland, St. Lucia. Queensland. 4067. Australia. "The University wouldn't even think of having an opinion, so they're all mine." -------------------------------------------------------------------------------- Date: Apr 17, 1989 From: chari@nueces.UUCP Subject: Re: Plot3D in Mathematica In article <1405@uqvax.decnet.uq.oz>, phcoates@uqvax.decnet.uq.oz writes: > Has anyone managed to get the Mathematica routine 'Plot3D' to produce numbered > axes? I seem to be able to change the axis parameters till I go blue in the > face, but the program just seems to ignore the relevant parameters. The same Well, nobody who has a NeXT has Mathematica yet (at least not for about another week). But on the Mac and NeXT versions I have used as well as all others I suppose, you cannot do axes labeling on 3D graphics. I guess you are trying to use 'AxesLabel' and 'Axes' in conjuction with Plot3D'. Chris -- Chris Whatley | "fish.. plate... !bigtex!nueces!chari@cs.utexas.edu | plate of fish..." 1607 Nueces,Austin TX 78723 - 512/453-4238 | ---------------------------------------------------------------------------- Date: Apr 19, 1989 From: chrstnsn@uxc.cso.uiuc.edu Subject: Re: Plot3D in Mathematica I have Mathematica on my NeXT machine and it works fine (though I do recommend 16 megs of memory if you are going to do anything big). I have no trouble getting Plot3D to do axes labels, ticks, etc. If you will send the problem you are trying to do to me, I will see if it can be solved. If I can't do it, I have over 300 members of the Mathematica User Group mailing list who probably can. Wolfram's people read my mailing list. I suggest you send Mathematica questions to the sci.math.symbolic newsgroup instead of this one. More Mathematica people read that group's messages. Steve Christensen Senior Research Scientist NCSA, U. of Illinois steve@ncsa.uiuc.edu ----------------------------------------------------------------------------- Date: Apr 18, 1989 From: carlo@cvs.rochester.edu Subject: Images and Mathematica I am new to Mathematica, and I like it already. One thing I can't figure out how to do (and if it is possible to do it) is the following: I would like to plot some images as 3 dimensional surfaces. The images are a se- quence of pixels (1 byte per pixel) and I can read these pixel values in using: ReadList["file", Byte] but I don't think I can give this to ListPlot3D and get a 3D surface out of Mathematica (though I'd be happy to hear how if you think I can). What I would like to do then, is to pre-pend each byte read with its x- and y-coordinates, so that for a 10x10 point image I would end up with a list like: {{0, 0, 101}, {0, 1, 93}, {0, 2, 28}, .... , {0, 9, 199}, {1, 0, 73}, {1, 1, 193}, {1, 2, 255}, .... , {1, 9, 0}, {2, 0, 249}, {2, 1, 102}, {2, 2, 129}, .... , {2, 9, 212}, ..... {9, 0, 34}, {9, 1, 89}, {9, 2, 32}, .... , {9, 9, 59}} (the first 2 numbers in each point are its x- and y-coordinates, the 3rd its pixel value). Any ideas? Please post or e-mail, whichever is more convenient. Carlo. carlo@cvs.rochester.edu ----------------------------------------------------------------------------- Date: Apr 18, 1989 From: kaltofen@turing.cs.rpi.edu Subject: Computers & Mathematics 1989 Conference Announcement COMPUTERS & MATHEMATICS 1989 MIT, Cambridge, Massachusetts Tuesday, June 13 - Saturday, June 17, 1989 GENERAL INFORMATION Computers & Mathematics 1989 will be held June 13-17, 1989 at MIT, Cambridge, Massachusetts. This conference is the third in a series of international conferences focusing on the use of computers as a research tool in the mathematical sciences. The 5-day conference consists of 8 parts: o 22 invited talks o 8 three-hour tutorial minicourses o 36 contributed papers o 10 tutorials of symbolic mathematical systems o computer graphics & scientific visualization program o a wine-and-demo reception at The Computer Museum o computer art and music concert o exhibits of computer-based tools for research in the mathematical sciences Student/Regular registration is $40/$125 before May 12, 1989, $60/$150 thereafter. Registration fees cover all 8 parts except that students must pay an additional $22 to attend the reception. On-campus housing is available in MIT dormitories next to Kresge Hall along the Charles River at the cost of $33/day per person, including 2 meals, for a shared double, and $45/day for a single room including 2 meals. A Proceedings of Computers & Mathematics 1989, published by Springer-Verlag and containing the Contributed Papers for the conference, will be available at the conference. Payments for dormitory housing, Proceedings (discounted at $25.50), and minicourse notes must reach the Conference Secretary by June 2, 1989. For conference booklets and registration forms, please contact Heather Schmidt, Conference Secretary 62 Eastview, Pleasantville, NY 10570 Telephone: 914/769-2725, Fax: 914/945-2141 CSNET: cm89 at ibm.com, BITNET: cm89 at yktvmz KEYNOTE ADDRESS Sir Peter Swinnerton-Dyer (Cambridge) TUTORIAL MINICOURSES INTERACTIVE COMPUTER GRAPHICS AND DIFFERENTIAL GEOMETRY Thomas Banchoff (Brown) SYMBOLIC INTEGRATION IS ALGORITHMIC Manuel Bronstein, Barry Trager (IBM Research), James H. Davenport (Bath) AN INTRODUCTION TO COMPUTATIONAL GROUP THEORY Gregory Butler (Sydney), John Cannon (Sydney) COMPUTERS IN UNDERGRADUATE MATHEMATICS: MAKING IT HAPPEN J. S. Devitt (Saskatchewan), Michael Henle (Oberlin) THE REGRETTABLE FAILURE OF AUTOMATED ERROR ANALYSIS William M. Kahan (Berkeley) THE HP-28S AS A BRIDGE BETWEEN THEORY AND APPLICATIONS Yves Nievergelt (E. Washington) GROEBNER BASES: A FOUNDATION FOR COMMUTATIVE ALGEBRA Lorenzo Robbiano (Genoa) THE SCIENCE OF FRACTAL IMAGES Heinz-Otto Peitgen (Bremen), Richard F. Voss (IBM Research) INVITED TALKS -- Computers & Mathematics Education -- SOFTWARE FOR STUDENTS TO MAKE MATH: LESSONS FROM SECONDARY GEOMETRY & ALGEBRA Judah Schwartz (MIT/Harvard) UNDERGRADATE EXPLORATION INTO COMBINATORICS Dennis Stanton (Minnesota) -- Computers & Physics -- ARITHMETIC SERIES, EXPANSIONS, AND EXACT RESULTS IN STATISTICAL MECHANICS Rodney J. Baxter (Australian National Univ) THE BIRTH OF THE COSMOS Alan H. Guth (MIT) ROULETTE WHEELS AND QUANTUM FIELD THEORY Michael J. Creutz (Brookhaven) PLAYING GOD: BUILDING GALAXIES IN A COMPUTER Richard H. Miller (Chicago) -- Mathematics & Supercomputing -- COMPUTING IN THE PHOTONIC AGE Joseph W. Goodman (Stanford) HOW WE USE COMPUTER ALGEBRA FOR SUPERCALCULATIONS David V. and Gregory V. Chudnovsky (Columbia) SUPERCOMPUTING IN THE 1990'S: TERAFLOPS AND BEYOND Monty M. Denneau (IBM Research) -- Computers & New Directions in Mathematics -- RANDOM COMPUTATION AND DIFFERENTIAL EQUATIONS Alexandre Chorin (Berkeley) RAMANUJAN AND MAPLE: CLASSICAL ANALYSIS AND SYMBOLIC COMPUTATION Peter Borwein (Dalhousie) HOW I FIND FUNNY LOOKING FORMULAS R. William Gosper (Stanford) SCRATCHPAD AND THE THEORY OF PARTITIONS George Andrews (Penn State) -- Mathematics & Computer Graphics -- SUPERCOMPUTER GRAPHICS: CONVERGENCE OF ART AND MATHEMATICS Donna Cox (Illinois) NOVEL WAYS TO PAINT AND ANIMATE SURFACES EXTENDED IN FOUR OR MORE DIMENSIONS George K. Francis (Illinois) MATHEMATICS AND GRAPHICS OF FRACTALS Michael F. Barnsley (Georgia Tech) HOW TO MAKE PICTURES WITH A COMPUTER Alvy Ray Smith (PIXAR) THE MAKING OF MATHEMATICA Stephen Wolfram (Wolfram Research, Inc.) -- Computers & Combinatorics -- COMPUTATIONAL INSIGHTS INTO PROBLEMS OF COMBINATORICS AND NUMBER THEORY Andrew Odlyzko (AT&T Bell Labs) COMPUTERS AND FRIVOLITY J. H. Conway (Princeton) COMPUTERS AND THE SEARCH FOR ERROR-CORRECTING CODES N. J. A. Sloane (AT&T Bell Labs) HOW TO PROVE BILLIONS OF COMBINATORIAL IDENTITIES AT ONCE Herbert S. Wilf (Pennsylvania) SYSTEM TUTORIALS CAYLEY (Sydney) DERIVE (Soft Warehouse) GAP (Aachen) MACAULAY (Columbia/Cornell) MACSYMA (Symbolics, Inc.) MAPLE (Waterloo) MATHEMATICA (Wolfram Research) REDUCE (RAND Corporation) SCOLAR (USSR Academy of Sciences) SCRATCHPAD (IBM Research) SPECIAL EVENTS COMPUTER GRAPHICS & SCIENTIFIC VISUALIZATION Maxine Brown (Univ of Illinois, Chicago) COMPUTER ART AND MUSIC CONCERT Don Slepian, performing computer artist Carol Chiani, computer graphics producer CONTRIBUTED PAPERS A COMPLETION PROCEDURE FOR COMPUTING A CANONICAL BASIS FOR A k-SUBALGEBRA D. Kapur (SUNY, Albany), K. Madlener (Kaiserslautern) PRACTICAL DETERMINATION OF THE DIMENSION OF AN ALGEBRAIC VARIETY A. Galligo (Nice and INRIA/Sophia Antipolis), C. Traverso (Pisa) SUMMATION OF HARMONIC NUMBERS D. Y. Savio, E.A. Lamagna (Rhode Island), S.-M. Liu (Northwestern) CLASSICALITY OF TRIGONAL CURVES OF GENUS FIVE P. Viana (MIT and Pontificia Univ Catolica, Rio) ALGORITHM AND IMPLEMENTATION FOR COMPUTATION OF JORDAN FORM N. Strauss (Pontificia Univ Catolica, Rio) A COMPUTER GENERATED CENSUS OF CUSPED HYPERBOIC 3-MANIFOLDS M. V. Hildebrand (Harvard), J. Weeks (Ithaca, NY) FAST GROUP MEMBERSHIP USING A STRONG GENERATING TEST FOR PERMUTATION GROUPS G. Copperman, L. Finkelstein (Northeastern), P. W. Purdom Jr. (Indiana) SYMMETRIC MATRICES WITH ALTERNATING BLOCKS A. Hefez (Univ Fed do Esperito Santo, Vitoria, Brazil), A. Thorup (Copenhagen) COHOMOLOGY TO COMPUTE D. Leites (Stockholm), G. Post (Twente, The Netherlands) FINITE-BASIS THEOREMS AND A COMPUTATION-INTEGRATED APPROACH TO OBSTRUCTION SET ISOLATION M. R. Fellows (Idaho), N. G. Kinnersley, M. A. Langston (Washington State) USE OF SYMBOLIC METHODS IN ANALYSING AN INTEGRAL OPERATOR H. F. Trotter (Princeton) SIGNS OF ALGEBRAIC NUMBERS T. Sakkalis (New Mexico State Univ) EXAMPLE OF COMPUTER ENHANCED ANALYSIS P. J. Costa, R. H. Westlake (Raytheon, Wayland, MA) EFFICIENT REDUCTION OF QUADRATIC FORMS N. W. Rickert (Northern Illinois University) COMPUTER ALGEBRAIC METHODS FOR INVESTIGATING PLANE DIFFERENTIAL SYSTEMS OF CENTER AND FOCUS TYPE D. Wang (Academia Sinica, Beijing) A STORY ABOUT COMPUTING WITH ROOTS OF UNITY F. Bergeron (Universite du Quebec a Montreal) AN ALGORITHM FOR SYMBOLIC COMPUTATION OF HOPF BIFURCATION E. Freire, E. Gamero, E. Ponce (Univ Sevilla, Spain) EXACT ALGORITHMS FOR THE MATRIX-TRIANGULARIZATION SUBRESULTANT PRS METHOD A. G. Akritas (Univ of Kansas) APPLICATION OF THE REDUCE COMPUTER ALGEBRA SYSTEM TO STABILITY ANALYSIS OF DIFFERENCE SCHEMES V. Ganzha (Novosibirsk), R. Liska (Technical Univ of Prague) COMPUTATION OF FOURIER TRANSFORMS ON THE SYMMETRIC GROUP D. Rockmore (Harvard) INTEGRATION IN FINITE TERMS AND SIMPLIFICATION WITH DILOGARITHMS J. Baddoura (MIT) LOGIC AND COMPUTATION IN MATHPERT: AN EXPERT SYSTEM FOR LEARNING MATHEMATICS: M. J. Beeson (San Jose State) WHY INTEGRATION IS HARD H. J. Hoover (Alberta) REPRESENTATION OF INFERENCE IN COMPUTER ALGEBRA SYSTEMS WITH APPLICATIONS TO INTELLIGENT TUTORING T. A. Ager, R. A. Ravaglia (Stanford), S. Dooley (Berkeley) LIOUVILLIAN SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS WITH LIOUVILLIAN COEFFICIENTS M. F. Singer (North Carolina State) BUNNY NUMERICS: A NUMBER THEORY MICROWORLD C. Graci, J. Y. Narayan, R. Odendahl (SUNY, Oswego) RECIPES FOR CLASSES OF DEFINITE INTEGRALS INVOLVING EXPONENTIALS AND LOGARITHMS K. O. Geddes, T. C. Scott (Waterloo) ADVANCED MATHEMATICS FROM AN ELEMENTARY VIEWPOINT: CHAOS, FRACTAL GEOMETRY, AND NONLINEAR SYSTEMS W. Feurzeig, P. Horwitz, A. Boulanger (BBN Labs) ITERATED FUNCTION SYSTEMS AND THE INVERSE PROBLEM OF FRACTAL CONSTRUCTION USING MOMENTS E. R. Vrscay (Waterloo) SYMBOLIC DERIVATION OF EQUATIONS FOR MIXED FORMULATION IN FINITE ELEMENT ANALYSIS H.-Q. Tan (Univ of Akron) WORKING WITH RULED SURFACES IN SOLID MODELING J. K. Johnstone (Johns Hopkins) SEMANTICS IN ALGEBRAIC COMPUTATION D. L. Rector (Univ. of California at Irvine) USING MACSYMA TO CALCULATE THE EXTRINSIC GEOMETRY OF TUBES IN RIEMANNIAN MANIFOLDS H. S. Mills, M. H. Vernon (Lewis & Clark State College) SIMULTANEOUS COMPUTATIONS OF DIFFERENT CHARACTERISTICS D. Duval (Universite de Grenoble I) COMPUTER ALGEBRA IN THE THEORY OF ORDINARY DIFFERENTIAL EQUATIONS OF HALPHEN TYPE V.P. Gerdt, N. A. Kostov (Inst Nuclear Research, Dubna) SYMBOLIC COMPUTATION WITH SYMMETRIC POLYNOMIALS: AN EXTENSION TO MACSYMA A. Valibouze (LITP, Paris) CONFERENCE CHAIRS: David V. Chudnovsky (Columbia), Richard D. Jenks (IBM Research) ORGANIZING COMMITTEE: Richard Askey (Wisconsin), Anil Nerode (Cornell), Paul S. Wang (Kent State), Wolfgang Lassner (Liepzig), John McCarthy (Stanford), Gregory V. Chudnovsky (Columbia), Joel Moses (MIT) CONTRIBUTED PAPER COMMITTEE: Erich L. Kaltofen (Rensselaer), Chair; Johannes Buchmann (Saarbruecken), Herbert Edelsbrunner (Illinois), John Fitch (Univ of Bath, England), Keith Geddes (Waterloo), Daniel Lazard (Paris), Michael Overton (NYU), Fritz Schwarz (GMD Bonn), Neil Soiffer (Tektronix), Evelyn Tournier (Grenoble), Stephen M. Watt (IBM Research), Franz Winkler (Linz) TUTORIALS COMMITTEE: Patrizia Gianni (Pisa), Chair; Stanley Steinberg (New Mexico), Richard Zippel (Cornell), Larry A. Lambe (UNC) LOCAL ARRANGEMENTS: Ellen Golden (Symbolics, Inc.) ----------------------------------------------------------------------------- Date: Apr 21, 1989 From: campbell@jif.berkeley.edu Subject: Graphics I am trying to write some short programs in Mathematica which will be used to demonstrate the drawing of a tangent plane to a surface and the use of Lagrange multipliers. My problem is that Mathematica refuses to combine two objects of type SurfaceGraphics or two objects of type CountourGraphics. This would seem to be no more unreasonable or difficult than combining two objects of type Graphics, which is allowed. Can someone help me with a solution or simple workaround of some sort? - Robert Campbell - ----------------------------------------------------------------------------- Date: Apr 20, 1989 From: arnold@ux.cs.man.ac.uk Subject: Mathematica I've just got the Mathematica symbolic processing system, and I'd like to hear from anyone who has experience with it, or who might want to swap information, etc. Please contact me at FX%nnga.daresbury.ac.uk@NSS.Cs.Ucl.AC.UK or ...!ukc!daresbury!nnga!fx Thank you Dave Love ----------------------------------------------------------------------------- Date: Apr 21, 1989 From: fateman@renoir.Berkeley.EDU Subject: Mathematica In article <114@spam.ua.oz> you write: > > I am new to Mathematica, so clearly I have much to find out. I would > be grateful for any advice. I know the Integrate[..] facility is > `under development' (which I take it means `horribly buggy') but has > anyone noticed this kind of behaviour with definite integrals? .... > How reasonable is it to ask for a symbolic integrator to > perform definite integrals on such integrands in the most general > case? As you point out, it is possible to do much better than Mathematica does, and some systems do so. I have previously noted that Mathematica seems to point with pride to the fact that it does "generic" manipulation. This often gets it into hot water mathematically, so much so that some of my colleagues wonder whether any calculation that requires an extension to the domain of rational functions can be relied upon. x^n for n symbolic is no longer in that domain. And while for some values of n, the integral of x^n is x^(1+n)/(1+n), it is certainly not true for n=-1. There are many other examples of this kind of behavior. While there may be many errors that are attributable to outright bugs, they are likely to be stamped out, one by one, for as long as Mathematica is under active maintenance. I think the lesson of Macsyma, a system which pre-dates Mathematica by about 20 years (and can integrate x^n) is that stamping out "features" is much harder. ----------------------------------------------------------------------------- Date: Apr 21, 1989 From: desouza@math.berkeley.edu Subject: Inertia of a matrix ? LINPACK does Does anybody knows of any symbolic manipulator that can compute the inertia (# pos. eigenv. - # neg. eigenv.) of a matrix as a standard function ? It is such an central invariant that one should expect to find it very easily. I have looked in Vaxima, Cayley, muMath, Mathematica and could not find anything. What is even worst is that LINPACK has a routine called "ssidi.f" that supposedly does the job after you decompose the matrix with "ssifa.f", but when you feed them the matrix [ 6 5 4 ] [ 5 4 3 ] [ 4 3 2 ] it gives the WRONG answer (2,1,0) as opposed to the right one (1,1,1). Here (p,n,z) stands for p pos. eigenvalues, n negat. ones and z zeroes. Of course this is due to the inability of LINPACK to recognize if a particular aproximation to zero is zero or not, and should be wiped from there. Paulo de Souza Math. Dept. U. C. Berkeley desouza@math.berkeley.edu ---------------------------------------------------------------------------- ****************************************************************************