most recent 30 from http://mathoverflow.net 2013-05-22T15:10:31Z http://mathoverflow.net/feeds/question/117 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/117/is-there-a-good-computer-package-for-working-with-complexes-over-non-commutative Ben Webster 2009-10-05T14:47:37Z 2010-10-26T22:22:05Z

<p>I'm interested in doing computations with certain non-commutative rings, most of which involve taking derived tensor products. Does anyone know of a computer algebra package which will find projective resolutions of complexes of modules over a finite-dimensional non-commutative ring, tensor with a bimodule, and do it all over again?</p>

http://mathoverflow.net/questions/117/is-there-a-good-computer-package-for-working-with-complexes-over-non-commutative/220#220 Mikael Vejdemo-Johansson 2009-10-09T06:17:46Z 2009-10-09T06:17:46Z

<p>I don't know whether Magma can handle all you ask for, but if I remember my coding for Magma correctly, at least the projective resolutions of modules over a non-commutative ring should be covered by that - for nice enough non-commutative rings. It's all been developed there as part of Jon F. Carlson's work on computing group cohomology rings.</p> <p>If there is a system that does all you ask for, and does it efficiently, it is probably been written in connection to a group cohomology computation effort - which narrows the candidates down significantly: Magma and GAP do group cohomology rings, and SAGE now with the work of Simon King and David Green.</p> <p>In contrast, I'm reasonably certain that Macaulay only does commutative things, and Singular doesn't have resolutions as a naturally occuring object at all.</p> <p>Bergman might be able to deal with what you ask for, though.</p> <p>To conclude: I'd recommend you to take a look at the homological algebra modules in Magma, GAP, SAGE and Bergman - I'd be highly surprised to see any other packages deal with the case you describe, and I'm not entirely convinced either of these do it well either.</p>

http://mathoverflow.net/questions/117/is-there-a-good-computer-package-for-working-with-complexes-over-non-commutative/43733#43733 Mohamed Barakat 2010-10-26T22:22:05Z 2010-10-26T22:22:05Z

<p>Which non-commutative rings are you interested in? Tensor product over non-commutative rings is computationally a delicate issue, since the resulting module is in general only an Abelian group, which is very often infinitely generated. So could you please be more specific.</p>