"Source: Text/LieTheory/GrpRfl.text";
"Line: 174";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/LieTheory/GrpRfl.text, line: 174
// Example: H109E2 ()
print "Example: H109E2";
ei := GetEchoInput();
SetEchoInput(true);
F<omega> := CyclotomicField(3);
r := Matrix(F,2,2,[1,omega^2,0,omega]);
IsReflection(r);
s := Matrix(F,2,2,[0,-1,1,0]);
IsReflection(s);
assert not $1;
G := MatrixGroup<2,F | r,s >;
IsReflectionGroup(G);
assert not $1;
IsReflectionGroup(G : Strict := false);
assert $1;
#G;
assert $1 eq 24;
exists(t){ t : t in G | IsReflection(t) and G eq sub<G|r,t> };
assert $1;
t;
SetEchoInput(ei);
