[Top][All Lists]
[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
[Axiom-mail] Re: Axiom, Rosetta and Quantian
|
From: |
Dirk Eddelbuettel |
|
Subject: |
[Axiom-mail] Re: Axiom, Rosetta and Quantian |
|
Date: |
Fri, 12 Mar 2004 13:09:27 -0600 |
|
User-agent: |
Mutt/1.3.28i |
Tim,
On Fri, Mar 12, 2004 at 01:50:23PM -0500, root wrote:
> Dirk,
>
> Great, I'm downloading the 0.4.9.5 iso now.
>
> Yeah, Axiom is large. I've tried to package multiple math systems on a
> single CD and eventually ran out of space. The Rosetta CD normally
> contains about 10 systems (which vary depending on the conference).
> But I'd like to find a way that all of the math package maintainers could
>
> (a) have a coordinated outlet for their work and
> (b) cooperate with each other to make the various systems compatible.
Both sound like excellent goals.
> The Rosetta CD was originally intended to cover the first item but it
> requires more work than one person can do and the cooperation of the
> various maintainers.
Yep.
> The second item I've discussed many times in many places. The only
> (current) result I've got is an attempt to develop a Computer Algebra
> Test Suite (CATS). Many systems have ad-hoc test suites and the
> expertise to develop tests in any area is quite limited. The idea is
> to merge tests from the various systems (similar to the NIST work) so
> we get expanded coverage by exploiting common work. CATS is intended
> to be the Rosetta-like effort for common testing. I have a CATS
> Gnu-arch branch available with the current effort but it is not yet
> far along (it just started in August).
>
> Cooperation has not been a big priority for commercial systems which
> have tended to dominate the math scene. There is a very limited pool
> of people who are "computational mathematicians" and their efforts
> have been spread widely and thinly so far.
I can see that. I'd be glad to help in my limited social-scientist ways :)
> I think that we might give some thought to constructing a "scientific
> workbench" kind of distribution from the kitchen sink version. Michel
Absolutely. I started with Quantian because so many pieces were already in
place: Debian with its vast pool of packages, including many math / science /
quant. ones; Knoppix with its incredible cdrom-based system; openMosix; ...
> Lavaud did a really nice front-end for his version of Rosetta that
> made it possible to start individual packages from a list.
As a launcher? Or as in 'will be added to the iso'.
> Re: Rosetta doc
>
> The Rosetta document I maintain has "synonyms" for commands from
> Axiom, Derive, GAP, Gmp, DoCon, Macsyma, Magnus, Maxima, Maple,
> Mathematcia, MuPAD, Octave, Pari, Reduce, Scilab, Sumit, and Yacas.
A good number of these are already in Quantian.
> Some of them are commercial but the idea is to allow someone
> experienced in one system to gain a quick overview of a second
> system. It's a fairly short document and I've appended it.
>
> Re: Tony Rossini. Do you have an email address?
Already in the CC list :)
Cheers, Dirk
>
> Tim
>
>
>
> ===================================================================
>
> On Fri, Mar 12, 2004 at 12:53:00PM -0500, root wrote:
> > Dirk,
> >
> > I've just tripped across your Quantian site.
> > (http://dirk.eddelbuettel.com/quantian.html)
> >
> > I see that you have a CD tailored to numerical and quantitative analysis.
> > I'd like to work with you on two fronts.
> >
> > FIrst, I'm the lead developer of Axiom, a large, free and open source
> > computer algebra system. I'd like to work with you to add it to the
> > Quantian CD if you feel it might be useful to your target audience.
>
> Sure, I just checked and see that it is already packaged for Debian, and
> even maintained by Camm, who is one of the number crunching whiz kids around
> Debian.
>
> But it also a huuuge package. If you look at the detailed package lists on
> my Quantian sites, you see that there are few packages as large as that. I
> cannot currently fit axiom on the cdrom edition of Quantian as those 700mb
> (compressed) are taken up. That said, I should definitiely add it to the
> next 'kitchen sink' release (of isos > 700mb that can be booted from hd by
> lilo and friends, and will morph into bootable dvds, one day).
>
> That said, there is also at least some interest into reverse-engineering
> what Morphix does in terms of a core and several modules. There is enough
> interest from different, non-overlapping user groups with non-overlapping
> interests to warrant this. Unfortunately, I doubt i'll have time to look
> into this.
>
> > Second, I distribute a Rosetta CD at conferences I attend. I have dozens
> > of free and open source algebra packages that I've collected and I
> > select a subset of them, based on the nature of the conference, to
> > create a CD. Perhaps some of them are of interest to you. In particular,
> > I have a file called "Rosetta" that has tables which tell you how to
> > write a command in a dozen different systems (e.g how to make a matrix
> > in Axiom, Mathematica, Maple, etc).
>
> Absolutely, that would be useful. Mind you, Debian cares less about
> Mathematica and Maple as we can't distribute them. But to the extent that
> users may have learned the ropes on those system, such cheat sheets are very
> useful. From the Octave and R projects, I know that people work on and off
> on these w.r.t. Matlab and S-Plus compatibility.
>
> > Michel Lavaud distributes a similar Rosetta CD for Windows.
>
> Tony Rossini at U of Washington has (had?) something with a stats / latex
> focus that is (was?) sponsored by ASA (stats folks), if memory serves.
>
> > Let me know if you have any interest.
>
> Sure do, let's talk some more.
>
> Thanks, Dirk
>
>
>
> ==========================================================================
>
> \documentclass{book}
> \normalsize\baselineskip=12pt
> \parskip=0pt
> \parindent=10pt
> \tolerance=5000
> \pretolerance=5000
> \frenchspacing
> \hangindent=10pt
> \skip\footins=18pt
> \global\textwidth 31pc \global\textheight 47pc
> \headsep 12pt
> \oddsidemargin 0pt
> \evensidemargin 0pt
> %
> \renewcommand{\textfraction}{.1}
> \renewcommand{\floatpagefraction}{.75}
> %
> \def\chaptername{}
> %
> address@hidden
> address@hidden@address@hidden
> address@hidden@address@hidden
> address@hidden@address@hidden@oddfoot}
> address@hidden@address@hidden
> address@hidden@address@hidden
> address@hidden@address@hidden@oddfoot}
> address@hidden
> %
> \def\sysdetails{\parbox{\textwidth}{%
> Based on material originally published in {\sl Computer Algebra Systems: A
> Practical Guide\/} edited by Michael J.\ Wester, John Wiley \& Sons,
> Chichester, United Kingdom, ISBN 0-471-98353-5, xvi+436 pages, 1999.}}
> %
> \pagestyle{plain}
>
> \begin{document}
> %
> % \nth{n} produces 1^{st}, 2^{nd}, 3^{rd}, 4^{th}, etc.
> %
> \def\nth#1{$#1^{\rm \ifcase#1 th\or st\or nd\or rd\else th\fi}$}
> %
> % Abbreviations
> %
> \newcommand{\Axiom}{{\sf Axiom}}
> \newcommand{\Derive}{{\sf Derive}}
> \newcommand{\DoCon}{{\sf DoCon}}
> \newcommand{\GAP}{{\sf GAP}}
> \newcommand{\Gmp}{{\sf Gmp}}
> \newcommand{\Macsyma}{{\sf Macsyma}}
> \newcommand{\Magnus}{{\sf Magnus}}
> \newcommand{\Maxima}{{\sf Maxima}}
> \newcommand{\Maple}{{\sf Maple}}
> \newcommand{\Mathematica}{{\sf Mathematica}}
> \newcommand{\MuPAD}{{\sf MuPAD}}
> \newcommand{\Octave}{{\sf Octave}}
> \newcommand{\Pari}{{\sf Pari}}
> \newcommand{\Reduce}{{\sf Reduce}}
> \newcommand{\Scilab}{{\sf Scilab}}
> \newcommand{\Sumit}{{\sf Sumit}}
> \newcommand{\Yacas}{{\sf Yacas}}
>
> \chapter{Rosetta Translations}
>
> \section{Introduction}
>
> The following is a collection of synonyms for various operations in
> the computer algebra systems \Axiom, \Derive, \GAP, \Gmp, \DoCon,
> \Macsyma, \Magnus, \Maxima, \Maple, \Mathematica, \MuPAD, \Octave,
> \Pari, \Reduce, \Scilab, \Sumit\ and \Yacas. This collection does not
> attempt to be comprehensive, but hopefully it will be useful in giving
> an indication of how to translate between the syntaxes used by the
> different systems in many common situations. Note that a blank entry
> means either (a) that there may be an exact translation of a
> particular operation for the indicated system, but we don't know what
> it is or (b) there is no exact translation but it may still be
> possible to work around this lack with a related functionality.
>
> While commercial systems are not provided on this CD the intent of the
> Rosetta effort is to make it possible for experienced Computer Algebra
> users to experiment with other systems. Thus the commands for
> commercial systems are included to allow users of those systems to
> translate.
>
> Some of these systems are special purpose and do not support a lot of
> the functionality of the more general purpose systems. Where they do
> support an interpreter the commands are provided.
>
> Originally written by Michael Wester.
> Modified for Rosetta by Timothy Daly, Alexander Hulpke (GAP).
>
> \section{System availability}
>
> \begin{tabular}{l|lll}
> System & \rm{License} & \rm{Status (May 2002)} & \rm{Web Location} \\
> \hline
> \Axiom & BSD & available & http://www.aldor.org \\
> \Axiom & open source & pending &
> http://home.earthlink.net/~jgg964/axiom.html \\
> \Derive & commercial & available & http://www.mathware.com \\
> \DoCon & open source & available & http://www.haskell.org/docon \\
> \GAP & GPL & Rosetta & http://www.gap-system.org/~gap \\
> \Gmp & GPL & Rosetta & http://www.swox.com/gmp \\
> \Macsyma & commercial & dead & unavailable \\
> \Magnus & GPL & Rosetta & http://zebra.sci.ccny.cuny.edu/web
> \\
> \Maxima & GPL & Rosetta &
> http://www.ma.utexas.edu/maxima.html\\
> \Maple & commercial & available & http://www.maplesoft.com \\
> \Mathematica & commercial & available & http://www.wolfram.com \\
> \MuPAD & commercial & available & http://www.mupad.de \\
> \Octave & GPL & Rosetta & http://www.octave.org \\
> \Pari & GPL & Rosetta & http://www.parigp-home.de \\
> \Reduce & commercial & available & http://www.zib.de/Symbolik/reduce \\
> \Scilab & Scilab & available & http://www-rocq.inria.fr/scilab \\
> \Sumit & & available &
> http://www-sop.inria.fr/cafe/soft-f.html \\
> \Yacas & GPL & available & http://yacas.sourceforge.net \\
> \end{tabular} \\[10pt]
> \\
> \begin{tabular}{l|ll}
> System & \rm{Type} & \rm{Interpreted or Compiled}\\
> \hline
> \Axiom & General Purpose & both \\
> \Derive & General Purpose & \\
> \DoCon & General Purpose & Interpreted in Haskell \\
> \GAP & Group Theory & \\
> \Gmp & arb. prec. arithmetic & \\
> \Macsyma & General Purpose & \\
> \Magnus & Infinite Group Theory & \\
> \Maxima & General Purpose & \\
> \Maple & General Purpose & \\
> \Mathematica & General Purpose & \\
> \MuPAD & General Purpose & \\
> \Octave & Numerical Computing & \\
> \Pari & Number Theory & \\
> \Reduce & General Purpose & \\
> \Scilab & General Purpose & \\
> \Sumit & Functional Equations & \\
> \Yacas & General Purpose & \\
> \end{tabular} \\[10pt]
>
> \section{Programming and Miscellaneous}
>
> \begingroup
> \newcommand{\OR}{{\em or }}
> \newcommand{\fnm}{\footnotemark}
> \newcommand{\h}[1]{{\rm #1}}
> \newcommand{\m}[2]{\multicolumn{#1}{l}{#2}}
> \newcommand{\q}{\quad}
> \newcommand{\st}{\small\tt}
> \parindent=0pt
> \hfuzz=1pt
> \begin{tt}
>
> \begin{tabular}{l|ll}
> & \m{2}{\rm Unix/Microsoft user initialization file} \\
> \hline
> \Axiom & \~{}/axiom.input & \\
> \GAP & \~{}/.gaprc & GAP.RC \\
> \Gmp & & \\
> \DoCon & & \\
> \Derive & & derive.ini \\
> \Macsyma & \~{}/macsyma-init.macsyma & mac-init.mac \\
> \Magnus & & \\
> \Maxima & \~{}/macsyma-init.macsyma & mac-init.mac \\
> \Maple & \~{}/.mapleinit & maplev5.ini \\
> \Mathematica & \~{}/init.m & init.m \\
> \MuPAD & \~{}/.mupadinit &
> $\backslash$mupad$\backslash$bin$\backslash$userinit.mu \\
> \Octave & & \\
> \Pari & & \\
> \Reduce & \~{}/.reducerc & reduce.rc \\
> \Scilab & & \\
> \Sumit & & \\
> \Yacas & & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|ll}
> & \h{Describe {\em keyword}} & \h{Find keywords containing {\em pattern}} \\
> \hline
> \Axiom & & )what operations pattern \\
> \Derive & & \\
> \DoCon & & \\
> \GAP & ?keyword & ??keyword\\
> \Gmp & & \\
> \Macsyma & describe("keyword")\$ & apropos("pattern"); \\
> \Magnus & & \\
> \Maxima & describe("keyword")\$ & apropos("pattern"); \\
> \Maple & ?keyword & ?pattern\,\fnm \\
> \Mathematica & ?keyword & ?*pattern* \\
> \MuPAD & ?keyword & ?*pattern* \\
> \Octave & help -i keyword & \\
> \Pari & & \\
> \Reduce & & \\
> \Scilab & & \\
> \Sumit & & \\
> \Yacas & & \\
> \end{tabular} \\[10pt]
>
> \footnotetext{Only if the pattern is not a keyword and then the matches are
> simplistic.}
>
> \begin{tabular}{l|address@hidden }llll}
> & & & \h{Prev.} & \h{Case} & \h{Variables} \\
> & \h{Comment} & \h{Line continuation} & \h{expr.} & \h{sensitive} &
> \h{assumed}
> \\
> \hline
> \Axiom & -- comment & input \_<CR>input & \% & Yes & real \\
> \Derive & "comment" & input \~{}<CR>input & & No & real \\
> \DoCon & & & & & \\
> \GAP & \# comment & input$\backslash$<CR>input&last&Yes&no
> assumption\\
> \Gmp & & & & & \\
> \Macsyma & /* comment */ & input<CR>input; & \% & No & real \\
> \Magnus & & & & & \\
> \Maxima & /* comment */ & input<CR>input; & \% & No & real \\
> \Maple & \# comment & input<CR>input; & \% & Yes & complex \\
> \Mathematica & (* comment *) & input<CR>input & \% & Yes & complex \\
> \MuPAD & \# comment \# & input<CR>input; & \% & Yes & complex \\
> \Octave & \#\# & & & Yes & \\
> \Pari & & & & & \\
> \Reduce & \% comment & input<CR>input; & ws & No & complex \\
> \Scilab & & & & & \\
> \Sumit & & & & & \\
> \Yacas & & & & & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|lll}
> & \h{Load a file} & \h{Time a command} & \h{Quit} \\
> \hline
> \Axiom & )read "file" )quiet & )set messages time on & )quit \\
> \Derive & [Transfer Load Derive] & & [Quit] \\
> \DoCon & & & \\
> \GAP & Read("file"); & time; \h{(also see {\tt
> Runtime();})}&quit;\\
> \Gmp & & & \\
> \Macsyma & load("file")\$ & showtime: all\$ & quit(); \\
> \Magnus & & & \\
> \Maxima & load("file")\$ & showtime: all\$ & quit(); \\
> \Maple & read("file"): & readlib(showtime): on; & quit \\
> \Mathematica & << file & Timing[command] & Quit[] \\
> \MuPAD & read("file"): & time(command); & quit \\
> \Octave & load file & tic(); cmd ; toc() & quit \OR\
> exit\\
> \Pari & & & \\
> \Reduce & in "file"\$ & on time; & quit; \\
> \Scilab & & & quit \\
> \Sumit & & & \\
> \Yacas & & & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|lll}
> & \h{Display} & \h{Suppress} & \\
> & \h{output} & \h{output} & \h{Substitution: $f(x, y) \rightarrow f(z, w)$} \\
> \hline
> \Axiom & input & input; & subst(f(x, y), [x = z, y = w]) \\
> \Derive & input & var:= input & [Manage Substitute] \\
> \DoCon & & & \\
> \GAP & input; & input;; & Value(f,[x,y],[z,w]);\fnm \\
> \Gmp & & & \\
> \Macsyma & input; & input\$ & subst([x = z, y = w], f(x, y)); \\
> \Magnus & & & \\
> \Maxima & input; & input\$ & subst([x = z, y = w], f(x, y)); \\
> \Maple & input; & input: & subs(\{x = z, y = w\}, f(x, y)); \\
> \Mathematica & input & input; & f[x, y] /. \{x -> z, y -> w\} \\
> \MuPAD & input; & input: & subs(f(x, y), [x = z, y = w]); \\
> \Octave & input & input; & \\
> \Pari & & & \\
> \Reduce & input; & input\$ & sub(\{x = z, y = w\}, f(x, y)); \\
> \Scilab & & & \\
> \Sumit & & & \\
> \Yacas & & & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|lll}
> & \h{Set} & \h{List} & \h{Matrix} \\
> \hline
> \Axiom & set [1, 2] & [1, 2] & matrix([[1, 2],[3, 4]]) \\
> \Derive & \{1, 2\} & [1, 2] & [[1,2], [3,4]] \\
> \DoCon & & & \\
> \GAP & Set([1,2]) & [1, 2] & [[1,2], [3,4]]\fnm \\
> \Gmp & & & \\
> \Macsyma & [1, 2] & [1, 2] & matrix([1, 2], [3, 4]) \\
> \Magnus & & & \\
> \Maxima & [1, 2] & [1, 2] & matrix([1, 2], [3, 4]) \\
> \Maple & \{1, 2\} & [1, 2] & matrix([[1, 2], [3, 4]]) \\
> \Mathematica & \{1, 2\} & \{1, 2\} & \{\{1, 2\}, \{3, 4\}\} \\
> \MuPAD & \{1, 2\} & [1, 2] & export(Dom): \q export(linalg): \\
> & & & matrix:= ExpressionField(normal)): \\
> & & & matrix([[1, 2], [3, 4]]) \\
> \Octave & & & \\
> \Pari & & & \\
> \Reduce & \{1, 2\} & \{1, 2\} & mat((1, 2), (3, 4)) \\
> \Scilab & & list(1,2) & A=[1,2;3,4]\\
> \Sumit & & & \\
> \Yacas & & & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|llll}
> & \h{Equation} & \h{List element} & \h{Matrix element} & \h{Length of a list}
> \\
> \hline
> \Axiom & x = 0 & l . 2 & m(2, 3) & \#l \\
> \Derive & x = 0 & l SUB 2 & m SUB 2 SUB 3 & DIMENSION(l) \\
> \DoCon & & & & \\
> \GAP & x=0 & l[2] & m[2][3] & Length(l) \\
> \Gmp & & & & \\
> \Macsyma & x = 0 & l[2] & m[2, 3] & length(l) \\
> \Magnus & & & & \\
> \Maxima & x = 0 & l[2] & m[2, 3] & length(l) \\
> \Maple & x = 0 & l[2] & m[2, 3] & nops(l) \\
> \Mathematica & x == 0 & l[[2]] & m[[2, 3]] & Length[l] \\
> \MuPAD & x = 0 & l[2] & m[2, 3] & nops(l) \\
> \Octave & & & & \\
> \Pari & & & & \\
> \Reduce & x = 0 & part(l, 2) & m(2, 3) & length(l) \\
> \Scilab & & l(2) & & \\
> \Sumit & & & & \\
> \Yacas & & & & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|lll}
> & \m{2}{\rm Prepend/append an element to a list} & \h{Append two lists} \\
> \hline
> \Axiom & cons(e, l) & concat(l, e) & append(l1, l2) \\
> \Derive & APPEND([e], l) & APPEND(l, [e]) & APPEND(l1, l2) \\
> \DoCon & & & \\
> \GAP & Concatenation([e],l) & Add(l,e) & Append(l1, l2) \\
> \Gmp & & & \\
> \Macsyma & cons(e, l) & endcons(e, l) & append(l1, l2) \\
> \Magnus & & & \\
> \Maxima & cons(e, l) & endcons(e, l) & append(l1, l2) \\
> \Maple & [e, op(l)] & [op(l), e] & [op(l1), op(l2)] \\
> \Mathematica & Prepend[l, e] & Append[l, e] & Join[l1, l2] \\
> \MuPAD & [e, op(l)] & append(l, e) & l1 . l2 \\
> \Octave & & & \\
> \Pari & & & \\
> \Reduce & e . l & append(l, {e}) & append(l1, l2) \\
> \Scilab & & & \\
> \Sumit & & & \\
> \Yacas & & & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|ll}
> & \h{Matrix column dimension} & \h{Convert a list into a column vector} \\
> \hline
> \Axiom & ncols(m) & transpose(matrix([l])) \\
> \Derive & DIMENSION(m SUB 1) & [l]\`{} \\
> \DoCon & & \\
> \GAP & Length(mat[1]) & \h{objects are identical} \\
> \Gmp & & \\
> \Macsyma & mat\_\,ncols(m) & transpose(matrix(l)) \\
> \Magnus & & \\
> \Maxima & mat\_\,ncols(m) & transpose(matrix(l)) \\
> \Maple & linalg[coldim](m) & linalg[transpose](matrix([l])) \\
> \Mathematica & Dimensions[m][[2]] & Transpose[\{l\}] \\
> \MuPAD & linalg::ncols(m) & transpose(matrix([l]))\,\fnm \\
> \Octave & & \\
> \Pari & & \\
> \Reduce & load\_\,package(linalg)\$ & matrix v(length(l), 1)\$ \\
> & column\_dim(m) & for i:=1:length(l) do \\
> & & \q\q v(i, 1):= part(l, i) \\
> \Scilab & & \\
> \Sumit & & \\
> \Yacas & & \\
> \end{tabular} \\[10pt]
>
> \footnotetext{See the definition of {\tt matrix} above.}
>
> \begin{tabular}{l|l}
> & \h{Convert a column vector into a list} \\
> \hline
> \Axiom & [v(i, 1) for i in 1..nrows(v)] \\
> \Derive & v\`{} SUB 1 \\
> \DoCon & \\
> \GAP & \h{objects are identical} \\
> \Gmp & \\
> \Macsyma & part(transpose(v), 1) \\
> \Magnus & \\
> \Maxima & part(transpose(v), 1) \\
> \Maple & op(convert(linalg[transpose](v), listlist)) \\
> \Mathematica & Flatten[v] \\
> \MuPAD & [op(v)] \\
> \Octave & \\
> \Pari & \\
> \Reduce & load\_\,package(linalg)\$ \\
> & for i:=1:row\_\,dim(v) collect(v(i, 1)) \\
> \Scilab & \\
> \Sumit & \\
> \Yacas & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|lllllll}
> & \h{True} & \h{False} & \h{And} & \h{Or} & \h{Not} & \h{Equal} & \h{Not
> equal}
> \\
> \hline
> \Axiom & true & false & and & or & not & = & \~{}= \\
> \Derive & TRUE & FALSE & AND & OR & NOT & = & /= \\
> \DoCon & & & & & & & \\
> \GAP & true & false\fnm & and & or & not & = & <> \\
> \Gmp & & & & & & & \\
> \Macsyma & true & false & and & or & not & = & \# \\
> \Magnus & & & & & & & \\
> \Maxima & true & false & and & or & not & = & \# \\
> \Maple & true & false & and & or & not & = & <> \\
> \Mathematica & True & False & \&\& & || & ! & == & != \\
> \MuPAD & true & false & and & or & not & = & <> \\
> \Octave & & & & & & & \\
> \Pari & & & & & & & \\
> \Reduce & t & nil & and & or & not & = & neq \\
> \Scilab & \%t & \%f & & & & & \\
> \Sumit & & & & & & & \\
> \Yacas & & & & & & & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|ll}
> & \h{If+then+else statements} & \h{Strings (concatenated)} \\
> \hline
> \Axiom & if \_ then \_ else if \_ then \_ else \_ & concat(["x", "y"])
> \\
> \Derive & IF(\_, \_, IF(\_, \_, \_)) & "xy"
> \\
> \DoCon & & \\
> \GAP & if \_ then \_ elif \_ then \_ else \_ fi &
> Concatenation("x","y")\\
> \Gmp & & \\
> \Macsyma & if \_ then \_ else if \_ then \_ else \_ & concat("x", "y")
> \\
> \Magnus & & \\
> \Maxima & if \_ then \_ else if \_ then \_ else \_ & concat("x", "y")
> \\
> \Maple & if \_ then \_ elif \_ then \_ else \_ fi & "x" . "y"
> \\
> \Mathematica & If[\_, \_, If[\_, \_, \_]] & "x" <> "y"
> \\
> \MuPAD & if \_ then \_ elif \_ then \_ else \_ & "x" . "y"
> \\
> & \q\q end\_if & \\
> \Octave & & \\
> \Pari & & \\
> \Reduce & if \_ then \_ else if \_ then \_ else \_ & "xy" \OR\ mkid(x,
> y)\\
> \Scilab & & \\
> \Sumit & & \\
> \Yacas & & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|ll}
> & \h{Simple loop and Block} & \h{Generate the list $[1, 2, \ldots, n]$} \\
> \hline
> \Axiom & for i in 1..n repeat ( x; y ) & [f(i) for i in 1..n]
> \\
> \Derive & VECTOR([x, y], i, 1, n) & VECTOR(f(i), i, 1, n)
> \\
> \DoCon & & \\
> \GAP & for i in [1..n] do \_ od; & [1..n] {\rm or}
> [1,2..n]\\
> \Gmp & & \\
> \Macsyma & for i:1 thru n do (x, y); & makelist(f(i), i, 1, n);
> \\
> \Magnus & & \\
> \Maxima & for i:1 thru n do (x, y); & makelist(f(i), i, 1, n);
> \\
> \Maple & for i from 1 to n do x; y od; & [f(i) \$ i = 1..n];
> \\
> \Mathematica & Do[x; y, \{i, 1, n\}] & Table[f[i], \{i, 1, n\}]
> \\
> \MuPAD & for i from 1 to n do x; y & [f(i) \$ i = 1..n];
> \\
> & \q\q end\_for; & \\
> \Octave & & \\
> \Pari & & \\
> \Reduce & for i:=1:n do <<x; y>>; & for i:=1:n collect f(i);
> \\
> \Scilab & & \\
> \Sumit & & \\
> \Yacas & & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|l}
> & \h{Complex loop iterating on a list} \\
> \hline
> \Axiom & for x in [2, 3, 5] while x**2 < 10 repeat output(x) \\
> \Derive & \\
> \DoCon & \\
> \GAP & for x in [2, 3, 5] do while x\^{}2<10 do Print(x);od;od; \\
> \Gmp & \\
> \Macsyma & for x in [2, 3, 5] while x\^{}2 < 10 do print(x)\$ \\
> \Magnus & \\
> \Maxima & for x in [2, 3, 5] while x\^{}2 < 10 do print(x)\$ \\
> \Maple & for x in [2, 3, 5] while x\^{}2 < 10 do print(x) od: \\
> \Mathematica & For[l = \{2, 3, 5\}, l != \{\} \&\& l[[1]]\^{}2 < 10, \\
> & \q l = Rest[l], Print[l[[1]]] ] \\
> \MuPAD & for x in [2, 3, 5] do if x\^{}2 < 10 then print(x) end\_if \\
> & \q end\_for: \\
> \Octave & \\
> \Pari & \\
> \Reduce & for each x in \{2, 3, 5\} do if x\^{}2 < 10 then write(x)\$ \\
> \Scilab & \\
> \Sumit & \\
> \Yacas & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|lll}
> & \h{\small Assignment} & \h{Function definition} & \h{Clear vars and funs} \\
> \hline
> \Axiom & y:= f(x) & f(x, y) == x*y &
> {\small\tt )clear properties y f} \\
> \Derive & y:= f(x) & f(x, y):= x*y & y:= f:= \\
> \DoCon & & & \\
> \GAP & y:= f(x); & f:=function(x, y) return x*y; end; & \h{There are
> no symbolic variables}\\
> \Gmp & & & \\
> \Macsyma & y: f(x); & f(x, y):= x*y; & remvalue(y)\$ \\
> & & & remfunction(f)\$ \\
> \Magnus & & & \\
> \Maxima & y: f(x); & f(x, y):= x*y; & remvalue(y)\$ \\
> & & & remfunction(f)\$ \\
> \Maple & y:= f(x); & f:= proc(x, y) x*y end; & y:= 'y': f:= 'f': \\
> \Mathematica & y = f[x] & f[x\_, y\_\,]:= x*y & Clear[y, f] \\
> \MuPAD & y:= f(x); & f:= proc(x, y) & y:= NIL: f:= NIL: \\
> & & \q\q begin x*y end\_\,proc; & \\
> \Octave & & & \\
> \Pari & & & \\
> \Reduce & y:= f(x); & procedure f(x, y); x*y; & clear y, f; \\
> \Scilab & & & \\
> \Sumit & & & \\
> \Yacas & & & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|l}
> & \h{Function definition with a local variable} \\
> \hline
> \Axiom & f(x) == (local n; n:= 2; n*x) \\
> \Derive & \\
> \DoCon & \\
> \GAP & f:=function(x) local n; n:=2;return n*x; end; \\
> \Gmp & \\
> \Macsyma & f(x):= block([n], n: 2, n*x); \\
> \Magnus & \\
> \Maxima & f(x):= block([n], n: 2, n*x); \\
> \Maple & f:= proc(x) local n; n:= 2; n*x end; \\
> \Mathematica & f[x\_\,]:= Module[\{n\}, n = 2; n*x] \\
> \MuPAD & f:= proc(x) local n; begin n:= 2; n*x end\_\,proc; \\
> \Octave & \\
> \Pari & \\
> \Reduce & procedure f(x); begin scalar n; n:= 2; return(n*x) end; \\
> \Scilab & \\
> \Sumit & \\
> \Yacas & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|ll}
> & \h{Return unevaluated symbol} & \h{Define a function from an expression} \\
> \hline
> \Axiom & e:= x*y;\q 'e & function(e, f, x, y) \\
> \Derive & e:= x*y\q 'e & f(x, y):== e \\
> \DoCon & & \\
> \GAP & \h{No unevaluated symbols}\fnm&\\
> \Gmp & & \\
> \Macsyma & e: x*y\$\q 'e; & define(f(x, y), e); \\
> \Magnus & & \\
> \Maxima & e: x*y\$\q 'e; & define(f(x, y), e); \\
> \Maple & e:= x*y:\q 'e'; & f:= unapply(e, x, y); \\
> \Mathematica & e = x*y;\q HoldForm[e] & f[x\_, y\_\,] = e \\
> \MuPAD & e:= x*y:\q hold(e); & f:= hold(func)(e, x, y); \\
> \Octave & & \\
> \Pari & & \\
> \Reduce & e:= x*y\$ & for all x, y let f(x, y):= e; \\
> \Scilab & & \\
> \Sumit & & \\
> \Yacas & & \\
> \end{tabular} \\[10pt]
> \footnotetext{Variables can be assigned to generators of a suitable free
> object, for example {\tt x:=X(Rationals,"x");} or {\tt
> f:=FreeGroup(2);x:=f.1;}.}
> \addtocounter{footnote}{-1}%
>
> \begin{tabular}{l|ll}
> & \h{Fun.\ of an indefinite number of args} & \h{Apply ``+'' to sum a list} \\
> \hline
> \Axiom & & reduce(+, [1, 2])
> \\
> \Derive & LST l:= l & \\
> \DoCon & & \\
> \GAP & lst:=function(args) \_ end; & Sum([1,2])\\
> \Gmp & & \\
> \Macsyma & lst([l]):= l; & apply("+", [1, 2])
> \\
> \Magnus & & \\
> \Maxima & lst([l]):= l; & apply("+", [1, 2])
> \\
> \Maple & lst:=proc() [args[1..nargs]] end; & convert([1, 2], \`{}+\`{})
> \\
> \Mathematica & lst[l\_\,\_\,\_\,]:= \{l\} & Apply[Plus, \{1, 2\}]
> \\
> \MuPAD & lst:= proc(l) begin [args()] & \_\,plus(op([1, 2]))
> \\
> & \q\q\q end\_\,proc; & \\
> \Octave & & \\
> \Pari & & \\
> \Reduce & & xapply(+, \{1, 2\})\,\fnm
> \\
> \Scilab & & \\
> \Sumit & & \\
> \Yacas & & \\
> \end{tabular} \\[10pt]
>
> \footnotetext{\tt procedure xapply(f, lst); lisp(f . cdr(lst))\$}
> \addtocounter{footnote}{-1}%
>
> \begin{tabular}{l|ll}
> & \h{Apply a fun.\ to a} & \\
> & \h{list of its args} & \h{Map an anonymous function onto a list} \\
> \hline
> \Axiom & reduce(f, l) & map(x +-> x + y, [1, 2]) \\
> \Derive & & x:= [1, 2] \\
> & & VECTOR(x SUB i + y, i, 1, DIMENSION(x)) \\
> \DoCon & & \\
> \GAP & List(l,f) & List([1,2],x->x+y) \\
> \Gmp & & \\
> \Macsyma & apply(f, l) & map(lambda([x], x + y), [1, 2]) \\
> \Magnus & & \\
> \Maxima & apply(f, l) & map(lambda([x], x + y), [1, 2]) \\
> \Maple & f(op(l)) & map(x -> x + y, [1, 2]) \\
> \Mathematica & Apply[f, l] & Map[\# + y \&, \{1, 2\}] \\
> \MuPAD & f(op(l)) & map([1, 2], func(x + y, x)) \\
> \Octave & & \\
> \Pari & & \\
> \Reduce & xapply(f, l)\,\fnm & for each x in \{1, 2\} collect x + y \\
> \Scilab & & \\
> \Sumit & & \\
> \Yacas & & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|l}
> & \h{Pattern matching: $f(3 y) + f(z y) \rightarrow 3 f(y) + f(z y)$} \\
> \hline
> \Axiom & f:= operator('f); \\
> & ( rule f((n | integer?(n)) * x) == n*f(x) )( \_ \\
> & \q\q f(3*y) + f(z*y)) \\
> \Derive & \\
> \DoCon & \\
> \GAP & \\
> \Gmp & \\
> \Macsyma & matchdeclare(n, integerp, x, true)\$ \\
> & defrule(fnx, f(n*x), n*f(x))\$ \\
> & apply1(f(3*y) + f(z*y), fnx); \\
> \Magnus & \\
> \Maxima & matchdeclare(n, integerp, x, true)\$ \\
> & defrule(fnx, f(n*x), n*f(x))\$ \\
> & apply1(f(3*y) + f(z*y), fnx); \\
> \Maple & map(proc(q) local m; \\
> & \q\q\q if match(q = f(n*y), y, 'm') and \\
> & \q\q\q\q\q type(rhs(op(m)), integer) then \\
> & \q\q\q\q subs(m, n * f(y)) else q fi \\
> & \q\q end, \\
> & \q\q f(3*y) + f(z*y)); \\
> \Mathematica & f[3*y] + f[z*y] /. f[n\_Integer * x\_\,] -> n*f[x] \\
> \MuPAD & d:= domain("match"): \q d::FREEVARIABLE:= TRUE: \\
> & n:= new(d, "n", func(testtype(m, DOM\_INT), m)): \\
> & x:= new(d, "x", TRUE): \\
> & map(f(3*y) + f(z*y), \\
> & \q\q proc(q) local m; begin m:= match(q, f(n*x)); \\
> & \q\q\q if m = FAIL then q \\
> & \q\q\q else subs(hold("n" * f("x")), m) end\_if \\
> & \q\q end\_\,proc); \\
> \Octave & \\
> \Pari & \\
> \Reduce & operator f; \\
> & f(3*y) + f(z*y) \\
> & \q\q where \{f(\~{}n * \~{}x) => n*f(x) when fixp(n)\}; \\
> \Scilab & \\
> \Sumit & \\
> \Yacas & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|l}
> & \h{Define a new infix operator and then use it} \\
> \hline
> \Axiom & \\
> \Derive & \\
> \DoCon & \\
> \GAP &\h{One can overload existing infix operators for ones own
> purposes}\\
> \Gmp & \\
> \Macsyma & infix("\~{}")\$ \q "\~{}"(x, y):= sqrt(x\^{}2 + y\^{}2)\$ \q
> 3 \~{} 4; \\
> \Magnus & \\
> \Maxima & infix("\~{}")\$ \q "\~{}"(x, y):= sqrt(x\^{}2 + y\^{}2)\$ \q
> 3 \~{} 4; \\
> \Maple & \`{}\&\~{}\`{}:= (x, y) -> sqrt(x\^{}2 + y\^{}2): \q 3 \&\~{}
> 4;
> \\
> \Mathematica & x\_ $\backslash$[Tilde] y\_:= Sqrt[x\^{}2 + y\^{}2]; \q
> 3 $\backslash$[Tilde] 4 \\
> \MuPAD & tilde:= proc(x, y) begin sqrt(x\^{}2 + y\^{}2) end\_\,proc: \\
> & \q 3 \&tilde 4; \\
> \Octave & \\
> \Pari & \\
> \Reduce & infix |\$ \q procedure |(x, y); sqrt(x\^{}2 + y\^{}2)\$ \q
> 3 | 4; \\
> \Scilab & \\
> \Sumit & \\
> \Yacas & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|lll}
> & \h{Main expression} & & \\
> & \h{operator} & \h{\nth{1} operand} & \h{List of expression operands} \\
> \hline
> \Axiom\fnm & & kernels(e) . 1 & kernels(e) \\
> \Derive & & & {\em various}\fnm \\
> \DoCon & & & \\
> \GAP &\m{3}{\rm There are no formal unevaluated expressions}\\
> \Gmp & & & \\
> \Macsyma & part(e, 0) & part(e, 1) & args(e) \\
> \Magnus & & & \\
> \Maxima & part(e, 0) & part(e, 1) & args(e) \\
> \Maple & op(0, e) & op(1, e) & [op(e)] \\
> \Mathematica & Head[e] & e[[1]] & ReplacePart[e, List, 0] \\
> \MuPAD & op(e, 0) & op(e, 1) & [op(e)] \\
> \Octave & & & \\
> \Pari & & & \\
> \Reduce & part(e, 0) & part(e, 1) & for i:=1:arglength(e) \\
> & & & \q\q collect part(e, i) \\
> \Scilab & & & \\
> \Sumit & & & \\
> \Yacas & & & \\
> \end{tabular} \\[10pt]
>
> \addtocounter{footnote}{-1}%
> \footnotetext{The following commands work only on expressions that consist of
> a
> single level (e.g., $x + y + z$ but not $a/b + c/d$).}
> \addtocounter{footnote}{-1}%
> \footnotetext{{\tt TERMS}, {\tt FACTORS}, {\tt NUMERATOR}, {\tt LHS}, etc.}
>
> \begin{tabular}{l|l}
> & \h{Print text and results} \\
> \hline
> \Axiom & output(concat(["sin(", string(0), ") = ", \\
> & \q string(sin(0))])); \\
> \Derive & "sin(0)" = sin(0) \\
> \DoCon & \\
> \GAP & Print("There is no sin, but factors(10)= ",Factors(10),
> "$\backslash$n")\\
> \Gmp & \\
> \Macsyma & print("sin(", 0, ") =", sin(0))\$ \\
> \Magnus & \\
> \Maxima & print("sin(", 0, ") =", sin(0))\$ \\
> \Maple & printf("sin(\%a) = \%a$\backslash$n", 0, sin(0)): \\
> \Mathematica & Print[StringForm["sin(\`{}\`{}) = \`{}\`{}", 0, Sin[0]]]; \\
> \MuPAD & print(Unquoted, "sin(".0.")" = sin(0)): \\
> \Octave & \\
> \Pari & \\
> \Reduce & write("sin(", 0, ") = ", sin(0))\$ \\
> \Scilab & \\
> \Sumit & \\
> \Yacas & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|ll}
> & \h{Generate FORTRAN} & \h{Generate \TeX/\LaTeX} \\
> \hline
> \Axiom & outputAsFortran(e) & outputAsTex(e) \\
> \Derive & [Transfer Save Fortran] & \\
> \DoCon & & \\
> \GAP &&Print(LaTeX(e));\\
> \Gmp & & \\
> \Macsyma & fortran(e)\$ \OR gentran(eval(e))\$ & tex(e); \\
> \Magnus & & \\
> \Maxima & fortran(e)\$ \OR gentran(eval(e))\$ & tex(e); \\
> \Maple & fortran([e]); & latex(e); \\
> \Mathematica & FortranForm[e] & TexForm[e] \\
> \MuPAD & generate::fortran(e); & generate::TeX(e); \\
> \Octave & & \\
> \Pari & & \\
> \Reduce & on fort; \q e; \q off fort; \OR & load\_\,package(tri)\$
> \\
> & load\_\,package(gentran)\$ gentran e; & on TeX; e; off TeX; \\
> \Scilab & & \\
> \Sumit & & \\
> \Yacas & & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|l}
> & \h{Import two space separated columns of integers from {\tt file}} \\
> \hline
> \Axiom & \\
> \Derive & [Transfer Load daTa] ({\rm from} file.dat) \\
> \DoCon & \\
> \GAP & \\
> \Gmp & \\
> \Macsyma & xy: read\_num\_data\_to\_matrix("file", nrows, 2)\$ \\
> \Magnus & \\
> \Maxima & xy: read\_num\_data\_to\_matrix("file", nrows, 2)\$ \\
> \Maple & xy:= readdata("file", integer, 2): \\
> \Mathematica & xy = ReadList["file", Number, RecordLists -> True] \\
> \MuPAD & \\
> \Octave & \\
> \Pari & \\
> \Reduce & \\
> \Scilab & \\
> \Sumit & \\
> \Yacas & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|l}
> & \h{Export two space separated columns of integers to {\tt file}\fnm} \\
> \hline
> \Axiom & )set output algebra "file" \q ({\rm creates} file.spout)
> \\
> & for i in 1..n repeat output( \_
> \\
> & \q concat([string(xy(i, 1)), " ", string(xy(i, 2))]) )
> \\
> & )set output algebra console
> \\
> \Derive & xy [Transfer Print Expressions File]\q({\rm creates}
> file.prt)\\
> \DoCon & \\
> \GAP & PrintTo("file");for i in [1..n] do\\
> &\q AppendTo("file",xy[i][1]," ",xy[i][2],"$\backslash$n");od;\\
> \Gmp & \\
> \Macsyma & writefile("file")\$ \q for i:1 thru n do
> \\
> & \q print(xy[i, 1], xy[i, 2])\$ \q closefile()\$
> \\
> \Magnus & \\
> \Maxima & writefile("file")\$ \q for i:1 thru n do
> \\
> & \q print(xy[i, 1], xy[i, 2])\$ \q closefile()\$
> \\
> \Maple & writedata("file", xy);
> \\
> \Mathematica & outfile = OpenWrite["file"];
> \\
> & Do[WriteString[outfile,
> \\
> & \q xy[[i, 1]], " ", xy[[i, 2]], "$\backslash$n"], \{i, 1, n\}]
> \\
> & Close[outfile];
> \\
> \MuPAD & fprint(Unquoted, Text, "file",
> \\
> & \q ("$\backslash$n", xy[i, 1], xy[i, 2]) \$ i = 1..n):
> \\
> \Octave & \\
> \Pari & \\
> \Reduce & out "file"; \q for i:=1:n do
> \\
> & \q write(xy(i, 1), " ", xy(i, 2)); \q shut "file";
> \\
> \Scilab & \\
> \Sumit & \\
> \Sumit & \\
> \Yacas & \\
> \end{tabular} \\[10pt]
>
> \footnotetext{Some editing of {\tt file} will be necessary for all systems but
> \Maple\ and \Mathematica.}
>
> \section{Mathematics and Graphics}
>
> {\rm Since {\GAP} aims at discrete mathematics, it does not provide much of
> the calculus functionality listed in the following section.}
>
> \begin{tabular}{l|llllll}
> & $e$ & $\pi$ & $i$ & $+\infty$ & $\sqrt{2}$ & $2^{1/3}$ \\
> \hline
> \Axiom & \%e & \%pi & \%i & \%plusInfinity & sqrt(2) & 2**(1/3) \\
> \Derive & \#e & pi & \#i & inf & SQRT(2) & 2\^{}(1/3) \\
> \DoCon & & & & & & \\
> \GAP & & & E(4) & infinity & ER(2)\fnm &\\
> \Gmp & & & & & & \\
> \Macsyma & \%e & \%pi & \%i & inf & sqrt(2) & 2\^{}(1/3) \\
> \Magnus & & & & & & \\
> \Maxima & \%e & \%pi & \%i & inf & sqrt(2) & 2\^{}(1/3) \\
> \Maple & exp(1) & Pi & I & infinity & sqrt(2) & 2\^{}(1/3) \\
> \Mathematica & E & Pi & I & Infinity & Sqrt[2] & 2\^{}(1/3) \\
> \MuPAD & E & PI & I & infinity & sqrt(2) & 2\^{}(1/3) \\
> \Octave & & & & & & \\
> \Pari & & & & & & \\
> \Reduce & e & pi & i & infinity & sqrt(2) & 2\^{}(1/3) \\
> \Scilab & & & & & & \\
> \Sumit & & & & & & \\
> \Yacas & & & & & & \\
> \end{tabular} \\[10pt]
> \footnotetext{{\tt ER} represents special cyclotomic numbers and is not a
> root function.}
> \addtocounter{footnote}{-1}%
>
> \begin{tabular}{l|llll}
> & \h{Euler's constant} & \h{Natural log} & \h{Arctangent} & $n!$ \\
> \hline
> \Axiom & & log(x) & atan(x) & factorial(n) \\
> \Derive & euler\_\,gamma & LOG(x) & ATAN(x) & n! \\
> \DoCon & & & & \\
> \GAP & & LogInt(x,base) && Factorial(n) \\
> \Gmp & & & & \\
> \Macsyma & \%gamma & log(x) & atan(x) & n! \\
> \Magnus & & & & \\
> \Maxima & \%gamma & log(x) & atan(x) & n! \\
> \Maple & gamma & log(x) & arctan(x) & n! \\
> \Mathematica & EulerGamma & Log[x] & ArcTan[x] & n! \\
> \MuPAD & EULER & ln(x) & atan(x) & n! \\
> \Octave & & & & \\
> \Pari & & & & \\
> \Reduce & Euler\_\,Gamma & log(x) & atan(x) & factorial(n) \\
> \Scilab & & & & \\
> \Sumit & & & & \\
> \Yacas & & & & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|ll}
> & \h{Legendre polynomial} & \h{Chebyshev poly.\ of the \nth{1} kind} \\
> \hline
> \Axiom & legendreP(n, x) & chebyshevT(n, x) \\
> \Derive & LEGENDRE\_\,P(n, x) & CHEBYCHEV\_\,T(n, x) \\
> \DoCon & & \\
> \GAP & & \\
> \Gmp & & \\
> \Macsyma & legendre\_\,p(n, x) & chebyshev\_\,t(n, x) \\
> \Magnus & & \\
> \Maxima & legendre\_\,p(n, x) & chebyshev\_\,t(n, x) \\
> \Maple & orthopoly[P](n, x) & orthopoly[T](n, x) \\
> \Mathematica & LegendreP[n, x] & ChebyshevT[n, x] \\
> \MuPAD & orthpoly::legendre(n, x) & orthpoly::chebyshev1(n, x) \\
> \Octave & & \\
> \Pari & & \\
> \Reduce & LegendreP(n, x) & ChebyshevT(n, x) \\
> \Scilab & & \\
> \Sumit & & \\
> \Yacas & & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|ll}
> & \h{Fibonacci number} & \h{Elliptic integral of the \nth{1} kind} \\
> \hline
> \Axiom & fibonacci(n) & \\
> \Derive & FIBONACCI(n) & ELLIPTIC\_\,E(phi, k\^{}2) \\
> \DoCon & & \\
> \GAP & Fibonacci(n) & \\
> \Gmp & & \\
> \Macsyma & fib(n) & elliptic\_\,e(phi, k\^{}2) \\
> \Magnus & & \\
> \Maxima & fib(n) & elliptic\_\,e(phi, k\^{}2) \\
> \Maple & combinat[fibonacci](n) & EllipticE(sin(phi), k) \\
> \Mathematica & Fibonacci[n] & EllipticE[phi, k\^{}2] \\
> \MuPAD & numlib::fibonacci(n) & \\
> \Octave & & \\
> \Pari & & \\
> \Reduce & & EllipticE(phi, k\^{}2) \\
> \Scilab & & \\
> \Sumit & & \\
> \Yacas & & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|llll}
> & $\Gamma(x)$ & $\psi(x)$ & \h{Cosine integral} & \h{Bessel fun.\ (\nth{1})}
> \\
> \hline
> \Axiom & Gamma(x) & psi(x) & real(Ei(\%i*x)) & besselJ(n, x)
> \\
> \Derive & GAMMA(x) & PSI(x) & CI(x) & BESSEL\_\,J(n, x)
> \\
> \DoCon & & & & \\
> \GAP & & & & \\
> \Gmp & & & & \\
> \Macsyma & gamma(x) & psi[0](x) & cos\_\,int(x) & bessel\_j[n](x)
> \\
> \Magnus & & & & \\
> \Maxima & gamma(x) & psi[0](x) & cos\_\,int(x) & bessel\_j[n](x)
> \\
> \Maple & GAMMA(x) & Psi(x) & Ci(x) & BesselJ(n, x)
> \\
> \Mathematica & Gamma[x] & PolyGamma[x] & CosIntegral[x] & BesselJ[n, x]
> \\
> \MuPAD & gamma(x) & psi(x) & & besselJ(n, x)
> \\
> \Octave & & & & \\
> \Pari & & & & \\
> \Reduce & Gamma(x) & Psi(x) & Ci(x) & BesselJ(n, x)
> \\
> \Scilab & & & & \\
> \Sumit & & & & \\
> \Yacas & & & & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|lll}
> & \h{Hypergeometric fun.\ ${}_2F_1(a, b; c; x)$} & \h{Dirac delta} &
> \h{Unit step fun.} \\
> \hline
> \Axiom & & & \\
> \Derive & GAUSS(a, b, c, x) & & STEP(x) \\
> \DoCon & & & \\
> \GAP & & & \\
> \Gmp & & & \\
> \Macsyma & hgfred([a, b], [c], x) & delta(x) & unit\_\,step(x)
> \\
> \Magnus & & & \\
> \Maxima & hgfred([a, b], [c], x) & delta(x) & unit\_\,step(x)
> \\
> \Maple & hypergeom([a, b], [c], x) & Dirac(x) & Heaviside(x) \\
> \Mathematica & HypergeometricPFQ[\{a,b\},\{c\},x] &
> \m{2}{<< Calculus\`{}DiracDelta\`{}} \\
> \MuPAD & & dirac(x) & heaviside(x) \\
> \Octave & & & \\
> \Pari & & & \\
> \Reduce & hypergeometric(\{a, b\}, \{c\}, x) & & \\
> \Scilab & & & \\
> \Sumit & & & \\
> \Yacas & & & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|l}
> & \h{Define $|x|$ via a piecewise function} \\
> \hline
> \Axiom & \\
> \Derive & a(x):= -x*CHI(-inf, x, 0) + x*CHI(0, x, inf) \\
> \DoCon & \\
> \GAP & \\
> \Gmp & \\
> \Macsyma & a(x):= -x*unit\_\,step(-x) + x*unit\_\,step(x)\$ \\
> \Magnus & \\
> \Maxima & a(x):= -x*unit\_\,step(-x) + x*unit\_\,step(x)\$ \\
> \Maple & a:= x -> piecewise(x < 0, -x, x): \\
> \Mathematica & << Calculus\`{}DiracDelta\`{} \\
> & a[x\_]:= -x*UnitStep[-x] + x*UnitStep[x] \\
> \MuPAD & a:= proc(x) begin -x*heaviside(-x) + x*heaviside(x) \\
> & \q\q end\_\,proc: \\
> \Octave & \\
> \Pari & \\
> \Reduce & \\
> \Scilab & \\
> \Sumit & \\
> \Yacas & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|ll}
> & \h{Assume $x$ is real} & \h{Remove that assumption} \\
> \hline
> \Axiom & & \\
> \Derive & x :epsilon Real & x:= \\
> \DoCon & & \\
> \GAP & & \\
> \Gmp & & \\
> \Macsyma & declare(x, real)\$ & remove(x, real)\$ \\
> \Magnus & & \\
> \Maxima & declare(x, real)\$ & remove(x, real)\$ \\
> \Maple & assume(x, real); & x:= 'x': \\
> \Mathematica & x/: Im[x] = 0; & Clear[x] \\
> \MuPAD & assume(x, Type::RealNum): & unassume(x, Type::RealNum): \\
> \Octave & & \\
> \Pari & & \\
> \Reduce & & \\
> \Scilab & & \\
> \Sumit & & \\
> \Yacas & & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|ll}
> & \h{Assume $0 < x \le 1$} & \h{Remove that assumption} \\
> \hline
> \Axiom & & \\
> \Derive & x :epsilon (0, 1] & x:= \\
> \DoCon & & \\
> \GAP & & \\
> \Gmp & & \\
> \Macsyma & assume(x > 0, x <= 1)\$ & forget(x > 0, x <= 1)\$ \\
> \Magnus & & \\
> \Maxima & assume(x > 0, x <= 1)\$ & forget(x > 0, x <= 1)\$ \\
> \Maple & assume(x > 0); & x:= 'x': \\
> & additionally(x <= 1); & \\
> \Mathematica & Assumptions -> 0 < x <= 1\,\fnm & \\
> \MuPAD & assume(x > 0): assume(x <= 1): & unassume(x): \\
> \Octave & & \\
> \Pari & & \\
> \Reduce & & \\
> \Scilab & & \\
> \Sumit & & \\
> \Yacas & & \\
> \end{tabular} \\[10pt]
>
> \footnotetext{This is an option for {\tt Integrate}.}
>
> \begin{tabular}{l|l}
> & \h{Basic simplification of an expression $e$} \\
> \hline
> \Axiom & simplify(e) \OR\ normalize(e) \OR\ complexNormalize(e) \\
> \Derive & e \\
> \DoCon & \\
> \GAP & e \\
> \Gmp & \\
> \Macsyma & ratsimp(e) \OR\ radcan(e) \\
> \Magnus & \\
> \Maxima & ratsimp(e) \OR\ radcan(e) \\
> \Maple & simplify(e) \\
> \Mathematica & Simplify[e] \OR\ FullSimplify[e] \\
> \MuPAD & simplify(e) \OR\ normal(e) \\
> \Octave & \\
> \Pari & \\
> \Reduce & e \\
> \Scilab & \\
> \Sumit & \\
> \Yacas & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|ll}
> & \h{Use an unknown function} & \h{Numerically evaluate an expr.} \\
> \hline
> \Axiom & f:= operator('f); \q f(x) & exp(1) :: Complex Float \\
> \Derive & f(x):= & Precision:= Approximate \\
> & f(x) & APPROX(EXP(1)) \\
> & & Precision:= Exact \\
> \DoCon & & \\
> \GAP & & EvalF(123/456)\\
> \Gmp & & \\
> \Macsyma & f(x) & sfloat(exp(1)); \\
> \Magnus & & \\
> \Maxima & f(x) & sfloat(exp(1)); \\
> \Maple & f(x) & evalf(exp(1)); \\
> \Mathematica & f[x] & N[Exp[1]] \\
> \MuPAD & f(x) & float(exp(1)); \\
> \Octave & & \\
> \Pari & & \\
> \Reduce & operator f; \q f(x) & on rounded; \q exp(1); \\
> & & off rounded; \\
> \Scilab & & \\
> \Sumit & & \\
> \Yacas & & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|ll}
> & $ n \bmod m$ & \h{Solve $e \equiv 0 \bmod m$ for $x$} \\
> \hline
> \Axiom & rem(n, m) & solve(e = 0 :: PrimeField(m), x) \\
> \Derive & MOD(n, m) & SOLVE\_\,MOD(e = 0, x, m) \\
> \DoCon & & \\
> \GAP & n mod m & \h{solve using finite fields}\\
> \Gmp & & \\
> \Macsyma & mod(n, m) & modulus: m\$ \q solve(e = 0, x) \\
> \Magnus & & \\
> \Maxima & mod(n, m) & modulus: m\$ \q solve(e = 0, x) \\
> \Maple & n mod m & msolve(e = 0, m) \\
> \Mathematica & Mod[n, m] & Solve[\{e == 0, Modulus == m\}, x] \\
> \MuPAD & n mod m & solve(poly(e = 0, [x], IntMod(m)), x) \\
> \Octave & & \\
> \Pari & & \\
> \Reduce & on modular; & load\_\,package(modsr)\$ \q on modular; \\
> & setmod m\$ \q n & setmod m\$ \q m\_solve(e = 0, x) \\
> \Scilab & & \\
> \Sumit & & \\
> \Yacas & & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|ll}
> & \h{Put over common denominator} & \h{Expand into separate fractions} \\
> \hline
> \Axiom & a/b + c/d & (a*d + b*c)/(b*d) :: \_ \\
> & & \q MPOLY([a], FRAC POLY INT) \\
> \Derive & FACTOR(a/b + c/d, Trivial) & EXPAND((a*d + b*c)/(b*d)) \\
> \DoCon & & \\
> \GAP & a/b+c/d &\\
> \Gmp & & \\
> \Macsyma & xthru(a/b + c/d) & expand((a*d + b*c)/(b*d)) \\
> \Magnus & & \\
> \Maxima & xthru(a/b + c/d) & expand((a*d + b*c)/(b*d)) \\
> \Maple & normal(a/b + c/d) & expand((a*d + b*c)/(b*d)) \\
> \Mathematica & Together[a/b + c/d] & Apart[(a*d + b*c)/(b*d)] \\
> \MuPAD & normal(a/b + c/d) & expand((a*d + b*c)/(b*d)) \\
> \Octave & & \\
> \Pari & & \\
> \Reduce & a/b + c/d & on div; (a*d + b*c)/(b*d) \\
> \Scilab & & \\
> \Sumit & & \\
> \Yacas & & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|l}
> & \h{Manipulate the root of a polynomial} \\
> \hline
> \Axiom & a:= rootOf(x**2 - 2); \q a**2 \\
> \Derive & \\
> \DoCon & \\
> \GAP & x:=X(Rationals,"x");\\
> &\q a:=RootOfDefiningPolynomial(AlgebraicExtension(Rationals,x\^{}2-2));
> a\^{}2\\
> \Gmp & \\
> \Macsyma & algebraic:true\$ \q tellrat(a\^{}2 - 2)\$ \q rat(a\^{}2); \\
> \Magnus & \\
> \Maxima & algebraic:true\$ \q tellrat(a\^{}2 - 2)\$ \q rat(a\^{}2); \\
> \Maple & a:= RootOf(x\^{}2 - 2): \q simplify(a\^{}2); \\
> \Mathematica & a = Root[\#\^{}2 - 2 \&, 2] \q a\^{}2 \\
> \MuPAD & \\
> \Octave & \\
> \Pari & \\
> \Reduce & load\_\,package(arnum)\$ \q defpoly(a\^{}2 - 2); \q a\^{}2; \\
> \Scilab & \\
> \Sumit & \\
> \Yacas & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|ll}
> & \h{Noncommutative multiplication} & \h{Solve a pair of equations} \\
> \hline
> \Axiom & & solve([eqn1, eqn2], [x, y]) \\
> \Derive & x :epsilon Nonscalar & SOLVE([eqn1, eqn2], [x, y]) \\
> & y :epsilon Nonscalar & \\
> & x . y & \\
> \DoCon & & \\
> \GAP &*&\\
> \Gmp & & \\
> \Macsyma & x . y & solve([eqn1, eqn2], [x, y]) \\
> \Magnus & & \\
> \Maxima & x . y & solve([eqn1, eqn2], [x, y]) \\
> \Maple & x \&* y & solve(\{eqn1, eqn2\}, \{x, y\}) \\
> \Mathematica & x ** y & Solve[\{eqn1, eqn2\}, \{x, y\}] \\
> \MuPAD & & solve(\{eqn1, eqn2\}, \{x, y\}) \\
> \Octave & & \\
> \Pari & & \\
> \Reduce & operator x, y; & solve(\{eqn1, eqn2\}, \{x, y\}) \\
> & noncom x, y; & \\
> & x() * y() & \\
> \Scilab & & \\
> \Sumit & & \\
> \Yacas & & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|ll}
> & \m{2}{\rm Decrease/increase angles in trigonometric functions} \\
> \hline
> \Axiom & \m{2}{simplify(normalize(sin(2*x)))} \\
> \Derive & Trigonometry:= Expand & Trigonometry:= Collect \\
> & sin(2*x) & 2*sin(x)*cos(x) \\
> \DoCon & & \\
> \GAP & & \\
> \Gmp & & \\
> \Macsyma & trigexpand(sin(2*x)) & trigreduce(2*sin(x)*cos(x)) \\
> \Magnus & & \\
> \Maxima & trigexpand(sin(2*x)) & trigreduce(2*sin(x)*cos(x)) \\
> \Maple & expand(sin(2*x)) & combine(2*sin(x)*cos(x)) \\
> \Mathematica & TrigExpand[Sin[2*x]] & TrigReduce[2*Sin[x]*Cos[x]] \\
> \MuPAD & expand(sin(2*x)) & combine(2*sin(x)*cos(x),
> sincos)
> \\
> \Octave & & \\
> \Pari & & \\
> \Reduce & load\_\,package(assist)\$ \\
> & trigexpand(sin(2*x)) & trigreduce(2*sin(x)*cos(x)) \\
> \Scilab & & \\
> \Sumit & & \\
> \Yacas & & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|l}
> & \h{Gr\"obner basis} \\
> \hline
> \Axiom & groebner([p1, p2, ...]) \\
> \Derive & \\
> \DoCon & \\
> \GAP & \\
> \Gmp & \\
> \Macsyma & grobner([p1, p2, ...]) \\
> \Magnus & \\
> \Maxima & grobner([p1, p2, ...]) \\
> \Maple & Groebner[gbasis]([p1, p2, ...], plex(x1, x2, ...)) \\
> \Mathematica & GroebnerBasis[\{p1, p2, ...\}, \{x1, x2, ...\}] \\
> \MuPAD & groebner::gbasis([p1, p2, ...]) \\
> \Octave & \\
> \Pari & \\
> \Reduce & load\_\,package(groebner)\$ \q groebner(\{p1, p2, ...\}) \\
> \Scilab & \\
> \Sumit & \\
> \Yacas & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|l}
> & \h{Factorization of $e$ over $i = \sqrt{-1}$} \\
> \hline
> \Axiom & factor(e, [rootOf(i**2 + 1)]) \\
> \Derive & FACTOR(e, Complex) \\
> \DoCon & \\
> \GAP & Factors(GaussianIntegers,e)\\
> \Gmp & \\
> \Macsyma & gfactor(e); \OR\ factor(e, i\^{}2 + 1); \\
> \Magnus & \\
> \Maxima & gfactor(e); \OR\ factor(e, i\^{}2 + 1); \\
> \Maple & factor(e, I); \\
> \Mathematica & Factor[e, Extension -> I] \\
> \MuPAD & QI:= Dom::AlgebraicExtension(Dom::Rational, i\^{}2 + 1); \\
> & QI::name:= "QI": \q Factor(poly(e, QI)); \\
> \Octave & \\
> \Pari & \\
> \Reduce & on complex, factor; \q e; \q off complex, factor; \\
> \Scilab & \\
> \Sumit & \\
> \Yacas & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|ll}
> & \h{Real part} & \h{Convert a complex expr.\ to rectangular form} \\
> \hline
> \Axiom & real(f(z)) & complexForm(f(z)) \\
> \Derive & RE(f(z)) & f(z) \\
> \DoCon & & \\
> \GAP & (f(z)+GaloisCyc(f(z),-1))/2&\\
> \Gmp & & \\
> \Macsyma & realpart(f(z)) & rectform(f(z)) \\
> \Magnus & & \\
> \Maxima & realpart(f(z)) & rectform(f(z)) \\
> \Maple & Re(f(z)) & evalc(f(z)) \\
> \Mathematica & Re[f[z]] & ComplexExpand[f[z]] \\
> \MuPAD & Re(f(z)) & rectform(f(z)) \\
> \Octave & & \\
> \Pari & & \\
> \Reduce & repart(f(z)) & repart(f(z)) + i*impart(f(z)) \\
> \Scilab & & \\
> \Sumit & & \\
> \Yacas & & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|lll}
> & \h{Matrix addition} & \h{Matrix multiplication} & \h{Matrix transpose} \\
> \hline
> \Axiom & A + B & A * B & transpose(A) \\
> \Derive & A + B & A . B & A\`{} \\
> \DoCon & & & \\
> \GAP & A + B & A * B & TransposedMat(A)\\
> \Gmp & & & \\
> \Macsyma & A + B & A . B & transpose(A) \\
> \Magnus & & & \\
> \Maxima & A + B & A . B & transpose(A) \\
> \Maple & evalm(A + B) & evalm(A \&* B) & linalg[transpose](A) \\
> \Mathematica & A + B & A . B & Transpose[A] \\
> \MuPAD & A + B & A * B & transpose(A) \\
> \Octave & & & \\
> \Pari & & & \\
> \Reduce & A + B & A * B & tp(A) \\
> \Scilab & & & \\
> \Sumit & & & \\
> \Yacas & & & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|l}
> & \h{Solve the matrix equation $A x = b$} \\
> \hline
> \Axiom & solve(A, transpose(b)) . 1 . particular :: Matrix \_\_\_ \\
> \Derive & \\
> \DoCon & \\
> \GAP & SolutionMat(TransposedMat(A),b)\\
> \Gmp & \\
> \Macsyma & xx: genvector('x, mat\_nrows(b))\$ \\
> & x: part(matlinsolve(A . xx = b, xx), 1, 2) \\
> \Magnus & \\
> \Maxima & xx: genvector('x, mat\_nrows(b))\$ \\
> & x: part(matlinsolve(A . xx = b, xx), 1, 2) \\
> \Maple & x:= linalg[linsolve](A, b) \\
> \Mathematica & x = LinearSolve[A, b] \\
> \MuPAD & \\
> \Octave & \\
> \Pari & \\
> \Reduce & \\
> \Scilab & \\
> \Sumit & \\
> \Yacas & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|ll}
> & \h{Sum: $\sum_{i = 1}^n f(i)$} & \h{Product: $\prod_{i = 1}^n f(i)$} \\
> \hline
> \Axiom & sum(f(i), i = 1..n) & product(f(i), i = 1..n) \\
> \Derive & SUM(f(i), i, 1, n) & PRODUCT(f(i), i, 1, n) \\
> \DoCon & & \\
> \GAP & Sum([1..n],f) & Product([1..n],f)\\
> \Gmp & & \\
> \Macsyma & closedform( & closedform( \\
> & \q sum(f(i), i, 1, n)) & \q product(f(i), i, 1, n)) \\
> \Magnus & & \\
> \Maxima & closedform( & closedform( \\
> & \q sum(f(i), i, 1, n)) & \q product(f(i), i, 1, n)) \\
> \Maple & sum(f(i), i = 1..n) & product(f(i), i = 1..n) \\
> \Mathematica & Sum[f[i], \{i, 1, n\}] & Product[f[i], \{i, 1, n\}] \\
> \MuPAD & sum(f(i), i = 1..n) & product(f(i), i = 1..n) \\
> \Octave & & \\
> \Pari & & \\
> \Reduce & sum(f(i), i, 1, n) & prod(f(i), i, 1, n) \\
> \Scilab & & \\
> \Sumit & & \\
> \Yacas & & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|ll}
> & \h{Limit: $\lim_{x \rightarrow 0-} f(x)$} & \h{Taylor/Laurent/etc.\ series}
> \\
> \hline
> \Axiom & limit(f(x), x = 0, "left") & series(f(x), x = 0, 3) \\
> \Derive & LIM(f(x), x, 0, -1) & TAYLOR(f(x), x, 0, 3) \\
> \DoCon & & \\
> \GAP & & \\
> \Gmp & & \\
> \Macsyma & limit(f(x), x, 0, minus) & taylor(f(x), x, 0, 3) \\
> \Magnus & & \\
> \Maxima & limit(f(x), x, 0, minus) & taylor(f(x), x, 0, 3) \\
> \Maple & limit(f(x), x = 0, left) & series(f(x), x = 0, 4) \\
> \Mathematica & Limit[f[x], x->0, Direction->1] & Series[f[x],\{x, 0, 3\}] \\
> \MuPAD & limit(f(x), x = 0, Left) & series(f(x), x = 0, 4) \\
> \Octave & & \\
> \Pari & & \\
> \Reduce & limit!-(f(x), x, 0) & taylor(f(x), x, 0, 3) \\
> \Scilab & & \\
> \Sumit & & \\
> \Yacas & & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|ll}
> & \h{Differentiate: $\frac{d^3 f(x, y)}{dx \, dy^2}$} &
> \h{Integrate: $\int_0^1 f(x) \, dx$} \\
> \hline
> \Axiom & D(f(x, y), [x, y], [1, 2]) & integrate(f(x), x = 0..1) \\
> \Derive & DIF(DIF(f(x, y), x), y, 2) & INT(f(x), x, 0, 1) \\
> \DoCon & & \\
> \GAP & & \\
> \Gmp & & \\
> \Macsyma & diff(f(x, y), x, 1, y, 2) & integrate(f(x), x, 0, 1) \\
> \Magnus & & \\
> \Maxima & diff(f(x, y), x, 1, y, 2) & integrate(f(x), x, 0, 1) \\
> \Maple & diff(f(x, y), x, y\$2) & int(f(x), x = 0..1) \\
> \Mathematica & D[f[x, y], x, \{y, 2\}] & Integrate[f[x], \{x, 0, 1\}] \\
> \MuPAD & diff(f(x, y), x, y\$2) & int(f(x), x = 0..1) \\
> \Octave & & \\
> \Pari & & \\
> \Reduce & df(f(x, y), x, y, 2) & int(f(x), x, 0, 1) \\
> \Scilab & & \\
> \Sumit & & \\
> \Yacas & & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|ll}
> & \h{Laplace transform} & \h{Inverse Laplace transform} \\
> \hline
> \Axiom & laplace(e, t, s) & inverseLaplace(e, s, t) \\
> \Derive & LAPLACE(e, t, s) & \\
> \DoCon & & \\
> \GAP & & \\
> \Gmp & & \\
> \Macsyma & laplace(e, t, s) & ilt(e, s, t) \\
> \Magnus & & \\
> \Maxima & laplace(e, t, s) & ilt(e, s, t) \\
> \Maple & inttrans[laplace](e,t,s) & inttrans[invlaplace](e,s,t) \\
> \Mathematica & \m{2}{\q << Calculus\`{}LaplaceTransform\`{}} \\
> & LaplaceTransform[e, t, s] & {\st
> InverseLaplaceTransform[e,s,t]}
> \\
> \MuPAD & transform::laplace(e,t,s) & transform::ilaplace(e, s, t) \\
> \Octave & & \\
> \Pari & & \\
> \Reduce & \m{2}{\q load\_\,package(laplace)\$ \q
> load\_\,package(defint)\$}
> \\
> & laplace(e, t, s) & invlap(e, t, s) \\
> \Scilab & & \\
> \Sumit & & \\
> \Yacas & & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|l}
> & \h{Solve an ODE (with the initial condition $y'(0) = 1$)} \\
> \hline
> \Axiom & solve(eqn, y, x) \\
> \Derive & APPLY\_\,IC(RHS(ODE(eqn, x, y, y\_)), [x, 0], [y, 1]) \\
> \DoCon & \\
> \GAP & \\
> \Gmp & \\
> \Macsyma & ode\_ibc(ode(eqn, y(x), x), x = 0, diff(y(x), x) = 1) \\
> \Magnus & \\
> \Maxima & ode\_ibc(ode(eqn, y(x), x), x = 0, diff(y(x), x) = 1) \\
> \Maple & dsolve(\{eqn, D(y)(0) = 1\}, y(x)) \\
> \Mathematica & DSolve[\{eqn, y'[0] == 1\}, y[x], x] \\
> \MuPAD & solve(ode(\{eqn, D(y)(0) = 1\}, y(x))) \\
> \Octave & \\
> \Pari & \\
> \Reduce & odesolve(eqn, y(x), x) \\
> \Scilab & \\
> \Sumit & \\
> \Yacas & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|l}
> & \h{Define the differential operator $L = D_x + I$ and apply it to $\sin x$}
> \\
> \hline
> \Axiom & DD : LODO(Expression Integer, e +-> D(e, x)) := D(); \\
> & L:= DD + 1; \q L(sin(x)) \\
> \Derive & \\
> \DoCon & \\
> \GAP & \\
> \Gmp & \\
> \Macsyma & load(opalg)\$ \q L: (diffop(x) - 1)\$ \q L(sin(x)); \\
> \Magnus & \\
> \Maxima & load(opalg)\$ \q L: (diffop(x) - 1)\$ \q L(sin(x)); \\
> \Maple & id:= x -> x: \q L:= (D + id): \q L(sin)(x); \\
> \Mathematica & L = D[\#, x]\& + Identity; \q Through[L[Sin[x]]] \\
> \MuPAD & L:= (D + id): \q L(sin)(x); \\
> \Octave & \\
> \Pari & \\
> \Reduce & \\
> \Scilab & \\
> \Sumit & \\
> \Yacas & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|l}
> & \h{2D plot of two separate curves overlayed} \\
> \hline
> \Axiom & draw(x, x = 0..1); \q draw(acsch(x), x = 0..1); \\
> \Derive & [Plot Overlay] \\
> \DoCon & \\
> \GAP & \\
> \Gmp & \\
> \Macsyma & plot(x, x, 0, 1)\$ \q plot(acsch(x), x, 0, 1)\$ \\
> \Magnus & \\
> \Maxima & plot(x, x, 0, 1)\$ \q plot(acsch(x), x, 0, 1)\$ \\
> \Maple & plot(\{x, arccsch(x)\}, x = 0..1): \\
> \Mathematica & Plot[\{x, ArcCsch[x]\}, \{x, 0, 1\}]; \\
> \MuPAD & plotfunc(x, acsch(x), x = 0..1): \\
> \Octave & \\
> \Pari & \\
> \Reduce & load\_\,package(gnuplot)\$ \q plot(y = x, x = (0 .. 1))\$ \\
> & plot(y = acsch(x), x = (0 .. 1))\$ \\
> \Scilab & \\
> \Sumit & \\
> \Yacas & \\
> \end{tabular} \\[10pt]
>
> \begin{tabular}{l|l}
> & \h{Simple 3D plotting} \\
> \hline
> \Axiom & draw(abs(x*y), x = 0..1, y = 0..1); \\
> \Derive & [Plot Overlay] \\
> \DoCon & \\
> \GAP & \\
> \Gmp & \\
> \Macsyma & plot3d(abs(x*y), x, 0, 1, y, 0, 1)\$ \\
> \Magnus & \\
> \Maxima & plot3d(abs(x*y), x, 0, 1, y, 0, 1)\$ \\
> \Maple & plot3d(abs(x*y), x = 0..1, y = 0..1): \\
> \Mathematica & Plot3D[Abs[x*y], \{x, 0, 1\}, \{y, 0, 1\}]; \\
> \MuPAD & plotfunc(abs(x*y), x = 0..1, y = 0..1): \\
> \Octave & \\
> \Pari & \\
> \Reduce & load\_\,package(gnuplot)\$ \\
> & plot(z = abs(x*y), x = (0 .. 1), y = (0 .. 1))\$ \\
> \Scilab & \\
> \Sumit & \\
> \Yacas & \\
> \end{tabular} \\[10pt]
>
> %\begin{tabular}{l|l}
> %& \h{} \\
> %\hline
> %\Axiom & \\
> %\Derive & \\
> %\DoCon & \\
> %\GAP & \\
> %\Gmp & \\
> %\Macsyma & \\
> %\Magnus & \\
> %\Maxima & \\
> %\Maple & \\
> %\Mathematica & \\
> %\MuPAD & \\
> %\Octave & \\
> %\Pari & \\
> %\Reduce & \\
> %\Scilab & \\
> %\Sumit & \\
> %\Yacas & \\
> %\end{tabular} \\[10pt]
>
> \end{tt}
> \endgroup
> \end{document}
>
>
>
--
The relationship between the computed price and reality is as yet unknown.
-- From the pac(8) manual page
- [Axiom-mail] (no subject), root, 2004/03/12
- [Axiom-mail] Re: Axiom, Rosetta and Quantian, Dirk Eddelbuettel, 2004/03/13
- [Axiom-mail] Re: Axiom, Rosetta and Quantian, root, 2004/03/13
- [Axiom-mail] Re: Axiom, Rosetta and Quantian,
Dirk Eddelbuettel <=
- [Axiom-mail] Re: Axiom, Rosetta and Quantian, A.J. Rossini, 2004/03/13
- [Axiom-mail] Re: Axiom, Rosetta and Quantian, root, 2004/03/12
- [Axiom-mail] Re: Axiom, Rosetta and Quantian, A.J. Rossini, 2004/03/12