Thanks for the help, Everyone. Learning to construct the exact ring I wanted in Singular took some effort, but SuperCommutative() gave me the construction I needed and saved me piles of computation. (I don't know how to apply patches and so didn't attempt the 'native' solution, but I'm grateful for those comments anyway.)
(Also, hi again, Martin.) Best, Travis On Apr 17, 3:09 am, [email protected] wrote: > Hi Travis, > > On 17 Apr., 10:32, Travis Willse <[email protected]> wrote: > > > Is there a reasonable way to implement the exterior (alternating) > > algebra of a finite-dimensional vector space? One could do this with > > FreeAlgebraQuotient, but I want to compute the exterior algebra over > > QQ^7, which is large enough (dimension 128) that using that class > > would be tedious. > > I had a similar setting: Graded commutative rings, i.e., homogeneous > elements in odd degree anticommute among each other, and homogeneous > elements in even degree are in the center. An exterior algebra is just > a special case (all generators in degree one). > > My solution was to use Singular's "SuperCommutative" > (http://www.singular.uni-kl.de/Manual/3-0-4/sing_520.htm) in the background. > Here, one defines a polynomial ring, and SuperCommutative(m,n) then > yields a non-commutative ring in which variables m to n anticommute > and have square zero. > > Unfortunately, SuperCommutative isn't available in libsingular (yet, > hint hint...). So, you would need to use Singular directly via the > interface, using SuperCommutative(1,n) for implementing exteriour > algebra with n generators. > > SuperCommutative is quite efficiently implemented: Basic arithmetic > seems to be nearly as fast as in usual commutative polynomial rings, > and you have fast Gröbner basis computations. And the number of > generators shouldn't be a problem. > > Cheers, > Simon --~--~---------~--~----~------------~-------~--~----~ 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-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
