Dear all, I need to construct the action of a matrix algebra A on an A-invariant subspace, which is spanned by an eigenvector of one of matrix generators. And I get a weird type clash that I don't know how to get around:
regmats := [ [ [ 0, 2, 0, 0 ], [ 1, 1, 0, 0 ], [ 0, 0, 0, 2 ], [ 0, 0, 1, 1 ] ], [ [ -2, 0, -4, -4 ], [ 0, 0, 0, 4 ], [ 1, 1, 0, 2 ], [ 0, -1, 0, -2 ] ], [ [ 0, 0, 0, 8 ], [ -2, 0, -4, 0 ], [ 0, -2, 0, -4 ], [ 1, 0, 0, 0 ] ], [ [ 0, 0, 4, 0 ], [ 1, -2, 2, -4 ], [ -1, 0, -2, 0 ], [ -1/2, 1, 0, 0 ] ], [ [ 1, -2, 0, -4 ], [ 0, 0, 2, 0 ], [ 0, 1, 1, 0 ], [ -1/2, 0, -1, 0 ] ] ]; es := First(Eigenspaces(Rationals, TransposedMat(regmats[1])),x->Dimension(x)=2); A := AlgebraWithOne(Rationals, regmats); M:=LeftAlgebraModule(A,\*,Rationals^4); V:=SubAlgebraModule(M,[Basis(es)[1]]); and I get at the last line: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `SubAlgebraModule' on 2 arguments called\ from <function>( <arguments> ) called from read-eval-loop Entering break read-eval-print loop ... you can 'quit;' to quit to outer loop, or you can 'return;' to continue brk> while gap> Basis(es)[1]; [ 1, 1, 0, 0 ] and also gap> BM:=Basis(M); Basis( <4-dimensional left-module over <algebra-with-one over Rationals, with 5 generators>>, [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ] ) gap> V:=SubAlgebraModule(M,[BM[1]+BM[2]]); <left-module over <algebra-with-one over Rationals, with 5 generators>> gap> MatrixOfAction(Basis(V),regmats[1]); [ [ 2, 2 ], [ 0, -1 ] ] does what it should. But I do not understand how to write GAP code to compute the decomposition of my vector Basis(es)[1] in the basis BM of M ! Many thanks in advance, Dmitrii Pasechnik CONFIDENTIALITY: This email is intended solely for the person(s) named and may be confidential and/or privileged. If you are not the intended recipient, please delete it, notify us and do not copy, use, or disclose its content. Thank you. Towards A Sustainable Earth: Print Only When Necessary _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
