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I'd like a software that I can use to work with commutative algebra, specifically to figure out S-Polynomials, Buchberger's Algorithm, etc.

I have Mathematica; if anyone could refer me to a package, it'd be awesome. Currently, I've checked out a package that the authors of Ideals, Varieties, and Algorithms have offered (it's from the Amherst College website) but there are way too many issues that need some cleaning up with the code.

Is there anything a bit more reliable?

I tried UIllinois' Macaulay2, but got stuck at installation. Otherwise, I'm literally open to trying anything (provided, of course, that the software is clean/virus-free).

I don't believe this question has been asked before; I tried looking this up on MSE and couldn't find an appropriate response. If there is one, please direct me to it- thank you in advance!

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    $\begingroup$ Nah, Mac OSX. If need be I could get access to a PC. $\endgroup$ – daOnlyBG Nov 6 '14 at 19:20
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    $\begingroup$ There's no need, M2 is designed to work well on OS X. I suggest you spend a bit more effort on installing M2, and also install Aquamacs for a better user interface. $\endgroup$ – Andrew Nov 6 '14 at 19:51
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    $\begingroup$ Try their web version, habanero.math.cornell.edu:3690 . $\endgroup$ – Youngsu Nov 6 '14 at 21:12
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    $\begingroup$ I have a Mac and use Macaulay2 all the time on it without problems. If you have problems, you could try to ask on the Google Group groups.google.com/forum/#!forum/macaulay2 . $\endgroup$ – Fredrik Meyer Nov 7 '14 at 16:02
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    $\begingroup$ The following site came to my mind SageMath Cloud wstein.org. It says it can handle both Macaulay2 and singular (and more). $\endgroup$ – Youngsu Nov 18 '14 at 5:24
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You may try a web version of Macaulay2, http://www.math.uiuc.edu/Macaulay2/TryItOut/, http://habanero.math.cornell.edu:3690/.

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  • $\begingroup$ Not a reliable link: that site is down relatively often. $\endgroup$ – user26857 Nov 16 '14 at 9:51
  • $\begingroup$ @user26857 I've noticed that the server is unstable these days. I've emailed Mike Stillman about this. It might be faster and better if you just email Mike or other people listed on the webpage. Also, the google forum mentioned above is a very helpful place for questions on Macaulay2. I believe all the authors for Macaulay2 check it often. At the same time, since I'm not part of the development team, there is not much I can tell you what's going on with the server right away. $\endgroup$ – Youngsu Nov 16 '14 at 20:35
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Try also Singular, a computer algebra system for polynomial computations.

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You may try CoCoA System, Computations in Commutative Algebra

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  • $\begingroup$ Thanks- I'll look into it right now $\endgroup$ – daOnlyBG Nov 6 '14 at 18:21
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You can use homalg, which is actually a GAP package, but it just uses GAP programming language. The main advantage of this is it can use Singular, Macaulay2, Maple, MAGMA, Sage as its compute machine. In other words, the objects defined in homalg (e.g. rings, modules, ideals, etc.) reside in GAP, whereas the low level computations are carried out by the underlying CAS.

homalg is truely object oriented, supports function overloading and operator overloading. More abstractly, you can also do category theory in homalg.

-- Mike

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