/*
A5 as 3 x 3 matrices over Z[b5].
Representation 3a in ATLAS.
*/

F<r5>:=QuadraticField(5);b5:=(-1+r5)/2;
// R<z>:=PolynomialRing(Integers());F<b5>:=NumberField(z^2+z-1);r5:=1+2*b5;

G<x,y>:=MatrixGroup<3,F|[
-1,0,0,
0,-1,0,
-b5,-b5,1]
,[
0,1,0,
0,0,1,
1,0,0]
>;

a:=x;b:=y;