Recommendations for Commutative Algebra Software?

Question

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!

Answer 1

You may try a web version of Macaulay2, http://www.math.uiuc.edu/Macaulay2/TryItOut/, http://habanero.math.cornell.edu:3690/.

Answer 2

You may try CoCoA System, Computations in Commutative Algebra

Answer 3

Try also Singular, a computer algebra system for polynomial computations.

Answer 4

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