On Dec 26, 9:57 am, "Mike Hansen" <[EMAIL PROTECTED]> wrote:
> 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-algebr...
> ) 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/)
Bergman hasn't been updated in well over a year and doesn't run on any
clisp newer than the 2.32 release. I have complained about that, but
nothing happened. You can use other lisp implementations to get it to
run, though. As fas as I can remember Bergman is also limited to
homogeneous ideals when computing those nc-GBases, but I wouldn't
swear on it.
A much more plausible candidate to do nc operations and GBasis
computations would be Singular. It should also be possible to use
libSingular for that, but I guess malb has to fill in the details.
Cheers,
Michael
> 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 starthttp://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
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