Hi Kyle, This is one area in which Sage (and GAP4 for that matter) could use some work -- there hasn't really been anyone been working on it. Right now, there is a FreeAlgebraQuotient ( http://www.sagemath.org/doc/html/ref/module-sage.algebras.free-algebra-quotient.html ) in Sage which allows you to work with these objects assuming you have a faithful representation for the algebra. The vector enumeration algorithms allow one to go from a description of the underlying two sided ideal like you have with a*b-b*a-a to a representation that could be plugged into FreeAlgebraQuotient. There is a free software implementation in C by Steve Linton, and we should definitely think about including it in Sage. It comes with the GAP3 package "ve".
The other way to go about doing things is with noncommutative Grobner bases which I would be pretty interested in. But, Sage does not have any support for these at the moment. The only real algorithm that I know of is due to Mora, but this is probably due to my relative unfamiliarity with the area. I do know that Bergman ( http://servus.math.su.se/bergman/ ) and the GAP4 package GBNP ( http://www.mathdox.org/products/gbnp/ ) can carry out these computations. I have no idea on their relative efficiency though. It may come as no surprise, but Magma is probably the best software now in this area. Reading Magma's docs on this stuff is a good place to start http://www.math.uiuc.edu/Software/magma/text433.html . --Mike P.S. I'm not sure what you (specifically) want when you say factoring or gcd in these algebras. On Dec 26, 2007 1:03 AM, Kyle Schalm <[EMAIL PROTECTED]> wrote: > > > what's the status of noncommutative algebra in sage? > > suppose i want to play with expressions in the free algebra Z<a,b> modulo > the relation ab=ba+a. i'd also like to factor and gcd, ideally. er... no > pun intended. > > how do i do this -- or if sage can't do this (yet), what are my > options? > thanks > kyle > > > > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-forum URLs: http://sage.math.washington.edu/sage/ and http://sage.scipy.org/sage/ -~----------~----~----~----~------~----~------~--~---
