Am 12.08.2011 um 12:00 schrieb Cameo Cosmetics BG: > Dear forum members, > > I am working with subspaces of GF(2)^72 and I need to find the > subspace which is the intersection of two such subspaces V, W > and the compliment of V with regard of that intersection. I have > checked the manual but cannot find direct functions.
For the intersection you can use the "Intersection" command. Example: gap> spc:=GF(2)^72;; gap> V:=Subspace(spc, List([1..50], i->Random(spc)));; Dimension(V); 50 gap> W:=Subspace(spc, List([1..50], i->Random(spc)));; Dimension(W); 50 gap> U:=Intersection(V,W); <vector space of dimension 28 over GF(2)> (Of course this last dimension will vary, as W and U are random). For the complement: There are in general of course many complements to the intersection U of V and W inside V. Here is one way to get one of them, using basic linear algebra (continuing the example from above); it's main merit being that the code is short. gap> B:=SemiEchelonBasis(U);; gap> Ucomp:=Subspace(spc,List(Basis(V), v->SiftedVector(B,v))); <vector space over GF(2), with 50 generators> gap> Dimension(Ucomp); 22 gap> Dimension(U); 28 Cheers, Max _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
