Dear Doug, On Fri, Dec 17, 2021 at 05:12:37AM -0600, D Brozovic wrote: > The general question is: given a matrix group G acting on Row space V, how > does one compute the stabilizer in G of a given subspace W of V? > > It's not quite clear to me how to set up the G-action on subspaces. For > example, if > > V:=FullRowSpace(GF(3),4) and > > X:=Subspaces(V,2), how does one obtain the action of G on this collection > of subspaces? If that's done, presumably I can just compute Stablizer(G, > W) with the usual gap command. The action you need to use in this case is OnSubspacesByCanonicalBasis.
gap> G:=GL(5,3); GL(5,3) gap> Length(Orbit(G,CanonicalBasis(Subspace(GF(3)^5,Z(3)^0*[[1,-1,0,0,0],[0,1,1,-1,0]])),OnSubspacesByCanonicalBasis)); 1210 gap> Stabilizer(G,CanonicalBasis(Subspace(GF(3)^5,Z(3)^0*[[1,-1,0,0,0],[0,1,1,-1,0]])),OnSubspacesByCanonicalBasis); <matrix group of size 393030144 with 7 generators> Hope this helps, Dima _______________________________________________ Forum mailing list Forum@gap-system.org https://mail.gap-system.org/mailman/listinfo/forum
