"Source: Text/Group/GrpMatGen.text";
"Line: 927";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpMatGen.text, line: 927
// Example: H66E7 ()
print "Example: H66E7";
ei := GetEchoInput();
SetEchoInput(true);
K<w> := FiniteField(4);
GL34 := GeneralLinearGroup(3, K);
x := GL34 ! [1,w,0, 0,w,1, w^2,0,1];
y := GL34 ! [1,0,0, 1,w,0, 1,1,w];
x;
y;
x*y;
x^10;
x^-1;
x^y;
x/y;
(x, y);
(x,y,y);
P<a,b,c,m,x,y,z> := FunctionField(RationalField(), 7);
S := MatrixGroup< 3, P | [1,a,b,0,1,c,0,0,1],    
                         [1,0,m,0,1,0,0,0,1],   
                         [1,x,y,0,1,z,0,0,1] >;

t := S.1 * S.2;
t;
t^-1;
Determinant(t); 
assert $1 eq 1;
t^2;
SetEchoInput(ei);
