Dear Marc,
On 14.08.2012, at 18:12, Mbg Nimda wrote: > Dear Membres, > > I have constructed an algebra A, starting by defining a set of matrices > M,N, and P, with coefficients in the rationals. I used following commands: > * > * > *A:=Algebra(Rationals, [M,N,P]);* > <algebra over Rationals, with 3 generators> > *Dimension(A);inA,* > 24 > *R:=RadicalOfAlgebra(A);* > <algebra of dimension 18 over Rationals> > *Q:=A/R;* > <algebra of dimension 6 over Rationals> > *gQ:=GeneratorsOfAlgebra(Q);* > [ v.1, v.2, v.3, v.4, v.5, v.6 ] > > I would like to know if it is possible to either express the generators as > representatives or to construct some homomorphism of algebras from A:->Q. Please try the following code: gap> m:= [ [ 0, 1, 2 ], [ 0, 0, 3 ], [ 0, 0, 0 ] ];; gap> A:= AlgebraWithOneByGenerators( Rationals, [ m ] ); <algebra-with-one over Rationals, with 1 generators> gap> Dimension(A); 3 gap> R:=RadicalOfAlgebra(A); <algebra of dimension 2 over Rationals> gap> Dimension(R); 2 gap> hom:=NaturalHomomorphismByIdeal(A,R);; # Now we can compute Q as image of hom, and also lift elements from Q back to A. gap> Q:=Image(hom); <algebra of dimension 1 over Rationals> gap> gQ:=GeneratorsOfAlgebra(Q); [ v.1 ] gap> PreImagesRepresentative(hom, gQ[1]); [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ] Hope that helps, Max > > Thanks, > > Marc Bogaerts > _______________________________________________ > Forum mailing list > Forum@mail.gap-system.org > http://mail.gap-system.org/mailman/listinfo/forum > _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
