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What software would you recommend for working with chain complexes? In particular I'd like to be able to compute cohomology of a finite complex of free modules over polynomial ring. Is it possible in principle? (I hope so.) Here by "compute" I mean get a presentation as a cokernel of a map of free modules.

I've never used seriously any of the mathematical software yet, but I've checked manuals for Macaulay, Singular, Gap and Sage and I can't seem to find what I want. Maybe I wasn't looking very well?

Thanks.

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  • $\begingroup$ Strange, I'd say all the software you mention would do what you're looking for, although not much more, I should say. I've recently been looking for software to deal with DGAs but I haven't been successful. $\endgroup$ Jun 10, 2012 at 22:12
  • $\begingroup$ Which polynomial ring are you working over? There is no Euclidean algorithm for $\mathbb{Z}[t]$ for instance. $\endgroup$ Jun 10, 2012 at 22:58
  • $\begingroup$ Check out the following chapter of the book "Computations with Macaulay2". Isn't that what you are looking for? math.uiuc.edu/Macaulay2/Book/ComputationsBook/chapters/… $\endgroup$ Jun 10, 2012 at 23:00
  • $\begingroup$ GAP has a homological algebra library that might answer your questions... The description of the library is here: hamilton.nuigalway.ie/Hap/www/index.html $\endgroup$ Jun 10, 2012 at 23:43
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    $\begingroup$ Fernando, have you tried the DGAlgebras package for Macaulay2? Also as an aside - I'm working on "cleaning up" and adding new bits to the homological algebra packages in M2 this summer, and I'd be interested if you have any particular suggestions. $\endgroup$ Jun 11, 2012 at 7:07

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