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What are the pluses and minuses of different software packages? Anything new worth checking out?

I'm especially interested in open source packages.

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If you haven't already, you should try Sage.

Advantages:

  • Open source.
  • Includes many different packages (including GAP, Maxima, Singular, PARI/GP, and R, just to name a few), and provides a common interface for them.
  • Has a built-in Python interpreter.
  • You can install it on a server and allow people to run it remotely, through a web browser.
  • Is still actively being developed.

(Possible) Disadvantage:

  • No native Windows version. (You can still run it on Windows, but you have to run it under a virtual machine. This is fairly straightforward, though.)
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Someone should also mention Axiom, which started out as commercial package developed by IBM but after a long and tortuous journey is now open source. As I understand it, it is built on a strongly typed, mathematically oriented and user extensible type hierarchy. So it knows what groups, rings and fields are, and it lets you define your own and do computation in them.

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  • $\begingroup$ I don't actually use Axiom myself – but I have watched from afar with interest, and it's on my list of software to try sometime. If someone does use it, feel free to flesh out and/or correct the description above. $\endgroup$
    – Harald Hanche-Olsen
    Commented Jul 7, 2010 at 3:15
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    $\begingroup$ note that there are two forks of Axiom, namely OpenAxiom open-axiom.org and FriCAS fricas.sourceforge.net - shameless plug: FriCAS contains a guessing package similar to the well known GFUN algo.inria.fr/libraries/papers/gfun.html for Maple and Guess risc.jku.at/research/combinat/software/Guess for Mathematica, but more general and much faster in many situations. Also, as far as I know this is the only freely available guessing package. $\endgroup$
    – Martin Rubey
    Commented Jul 7, 2010 at 6:28
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I tend to use Macaulay2 for research related stuff

Some points about it.

  1. It is open source
  2. It is specific to algebraic geometry/commutative algebra (but since this is a large community on mathoverflow...)
  3. Is actively being developed (it seems to have several conferences devoted to it each year in recent years).
  4. It is a unix program so you need cygwin to run it on windows.
  5. The preferred environment to run it seems to be in an emacs window (although various people are working on other interfaces I understand).

I've also heard good things about Sage but haven't tried it.

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I suggest you to try Reduce, it is OpenSource and there are RPM packeges. It looks like this:

alt text http://static.itmages.ru/i/10/1012/h_1286887665_4af06aa049.png

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The only open-source CAS (Computer Algebra System) that I know of is called Maxima, but as I have not used it, I cannot say whether it is any good. I own a copy of Mathematica 7.0, and can say that it is superb. The programming language is easy to learn, and in many ways quite similar to that of the TI-89. The university I attend uses Maple 13, which from my experience is not as strong as Mathematica in the area of purely symbolic manipulation, but is superior in terms of numerical modeling.

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For quick calculations, I use Wolfram|Alpha, which is not open source but is a free web service.

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  • $\begingroup$ Limited and buggy, but also free and convenient. $\endgroup$
    – Charles
    Commented Nov 4, 2010 at 0:55
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    $\begingroup$ A big plus for W|A is that I can access it through my cell phone. $\endgroup$
    – Kevin O'Bryant
    Commented Nov 4, 2010 at 3:04

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