Dear Forum, Tim Kohl asked:
I am trying to do the following with GroupRing() gap> QC3:=GroupRing(Rationals,Group((1,2,3)));; gap> x:=Indeterminate(Rationals,"x");; gap> y:=Indeterminate(Rationals,"y");; gap> z:=Indeterminate(Rationals,"z");; gap> B:=Basis(QC3);; gap> Elements(B); [ (1)*(), (1)*(1,2,3), (1)*(1,3,2) ] So far so good, but the following doesn't work. gap> h := x*B[1]+y*B[2]+y*B[3] Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `*' on 2 arguments called from <function "HANDLE_METHOD_NOT_FOUND">( <arguments> ) called from read-eval loop at line 32 of *stdin* you can 'quit;' to quit to outer loop, or you can 'return;' to continue I want to do things like compute nilpotents etc by taking powers of 'generic' elements of a group ring (like h above) which will yield equations in the coefficients of the basis elements of the group ring. What is the correct way to do this?
I suppose what you would like to do is to compute in the group ring Q[x,y,z]C_3, rather than in QC_3: gap> R := PolynomialRing(Rationals,["x","y","z"]); Rationals[x,y,z] gap> RC3:=GroupRing(R,Group((1,2,3)));; gap> B := Basis(RC3);; gap> AsList(B); [ (1)*(), (1)*(1,2,3), (1)*(1,3,2) ] gap> h := x*B[1]+y*B[2]+y*B[3]; (x)*()+(y)*(1,2,3)+(y)*(1,3,2) Does this help you? Best regards, Stefan Kohl ----------------------------------------------------------------------------- https://stefan-kohl.github.io/ ----------------------------------------------------------------------------- _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
