Alexander, Thanks, that works. I don’t need anything more efficient than that at the moment – I was able to use it to verify something I thought was happening based on some other computations. It beats trying to compute by hand an orbit under the action of a group with 20,160 elements!
--Steve From: Hulpke,Alexander <alexander.hul...@colostate.edu> Date: Monday, December 28, 2020 at 6:04 PM To: Steven R. Costenoble <steven.r.costeno...@hofstra.edu>, forum@gap-system.org <forum@gap-system.org> Subject: Re: [GAP Forum] Action of general linear group on polynomials EXTERNAL MESSAGE Dear Steven Costenoble, Dear Forum, > Apologies if this is elementary: Related to a research project, I’d like to > do some computations involving the action of GL(n,2) on the ring of > polynomials over GF(2) in n variables. (Specifically n=4 at the moment.) I > know how to compute with the action of SymmetricGroup(n), using > OnIndeterminates, but is there an easy/standard way in Gap to let all of > GL(n,2) act on polynomials? At this point, this action is not implemented -- the issue being that it *should* be done better than just using `Value', but doing so requires a bit more thought. (And so far nobody had asked for it.) I append a basic kludgy implementation of such an action that *does* use `Value' after all. It is not as good/fast as I would like, and does no test of parameters, but might be better than nothing. All the best, Alexander Hulpke # basic action on polynomials. No check of characteristic etc. OnPolynomials:=function(pol,mat) local n,v,r; r:=DefaultRing(OneImmutable(CoefficientsFamily(FamilyObj(pol)))); n:=Length(mat); v:=List([1..n],x->X(r,x)); return Value(pol,v,List([1..n],i->Sum([1..n],j->v[j]*mat[i][j]))); end; **** CAUTION: This email originated from outside of Hofstra University. Do not click links or open attachments unless you recognize the sender and know the content is safe. **** _______________________________________________ Forum mailing list Forum@gap-system.org https://mail.gap-system.org/mailman/listinfo/forum
