[GAP Forum] Indeterminates and GroupRing elements

[tkohl at math.bu.edu]

Dear Stefan,

 think I can use this. If I compute h^2

gap> h^2;
(x^2+2*y^2)*()+(2*x*y+y^2)*(1,2,3)+(2*x*y+y^2)*(1,3,2)

then it's a matter of extracting the coefficients on the
group elements by using Coefficients(B,h^2).

Thank you very much!

	-Tim

On Mon, 25 Sep 2017, Stefan Kohl wrote:

> Dear Forum,
> 
> Tim Kohl asked:
>  
> 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
> 
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