"Source: Text/LieTheory/GrpRfl.text";
"Line: 2155";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/LieTheory/GrpRfl.text, line: 2155
// Example: H109E25 ()
print "Example: H109E25";
ei := GetEchoInput();
SetEchoInput(true);
Q := RationalField();
W := ReflectionGroup("A3");
mx := ReflectionMatrix(W, 4);
perm := ReflectionPermutation(W, 4);
RootPosition(W, Vector(Q, Eltseq(Root(W,2))) * mx) eq 2^perm;
assert $1;
mx := CoreflectionMatrix(W, 4);
CorootPosition(W, Coroot(W,2) * mx) eq 2^perm;
assert $1;
SetEchoInput(ei);
