"Source: Text/LieTheory/GrpCox.text";
"Line: 1848";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/LieTheory/GrpCox.text, line: 1848
// Example: H108E23 ()
print "Example: H108E23";
ei := GetEchoInput();
SetEchoInput(true);
W := CoxeterGroup("B3");
IsReflection(W.1*W.2);
assert not $1;
mx := ReflectionMatrix(W, 4);
perm := Reflection(W, 4);
wd := ReflectionWord(W, 4);
rt := VectorSpace(Rationals(), 3) ! Root(W,2);
RootPosition(W, rt * mx) eq 2^perm;
assert $1;
perm eq &*[ Reflection(W, r) : r in wd ];
assert $1;

mx := CoreflectionMatrix(W, 4);
CorootPosition(W, Coroot(W,2) * mx) eq 2^perm;
assert $1;
SetEchoInput(ei);
