"Source: Text/Group/GrpMatFF.text";
"Line: 2100";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpMatFF.text, line: 2100
// Example: H67E12 ()
print "Example: H67E12";
ei := GetEchoInput();
SetEchoInput(true);
G := MatrixGroup ("G25", 6);
G: Minimal;
f, m1, m2, m3, m4, E, W := ExceptionalConstructiveRecognition( G, "G", 2, 5 );
Q, R := ExceptionalStandardPresentation ("G", 2, 5);
X := E[1]; Xm := E[2];
#Set (Evaluate( R, &cat X cat &cat Xm)) eq 1;
x := Random (G);
m1;
y := m1 (x);
m3;
w := m3 (x);
Evaluate (w, [G.i: i in [1..Ngens (G)]]) eq x;
&cat X eq Evaluate( &cat W[1], [G.i : i in [ 1 .. Ngens( G )]]);     
&cat Xm eq Evaluate( &cat W[2], [G.i : i in [ 1 .. Ngens( G )]]);     

G := ChevalleyGroup ("3D", 4, 4);
G := RandomConjugate (G);
G: Minimal;
f, m1, m2, m3, m4, E, W := ExceptionalConstructiveRecognition( G, "3D", 4, 4);
Q, R := ExceptionalStandardPresentation ("3D", 4, 4);
X := E[1]; Xm := E[2];
#Set (Evaluate( R, &cat X cat &cat Xm)) eq 1;
SetEchoInput(ei);
