[GAP Forum] element in ideal (more specific)

b-eide at juno.com b-eide at juno.com
Thu Aug 21 06:59:34 BST 2008

>I was asked to be more specific about my "element in ideal" question:  >This is what I am trying to do:

> I have a matrix group with 3 generators (3 by 3 matrices), G.
> Then R is the Group Ring over the integers,
> R:=GroupRing(Integers,G);
> Then I have
> emb:=Embedding(G,R);
> so that I could create 4 elements in R such as,
> R3:=A^emb+B^emb+C^emb;
> b;
> where A, B, and C are 3 by 3 matrices.
> Next, I created a right ideal, I, by generators(R3,R13,R6,R10) in R,
> I:=RightIdealByGenerators(R,R3,R13,R6,R10);
> Finally I have 3 more elements in R which look similar to R3 and I'd like to 
determine if they are in the ideal I.
> I tried "in":
> R7 in I;
> and I got the error
> Error, no method found! For debuggin hints type ?Recovery from NoMethodFound.
> Error, no 1st choice method found for 'Basis' on 1 arguments called from 
NiceBasis(B) called from BasisVectors(MB!.immutableBasis ) called from BasisVectors(MB) 
called from NrBasisVectors(MB) called from...

If GAP cannot do this, does anyone know a software package that will?

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