"Source: Text/LieTheory/RootSys.text";
"Line: 1122";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/LieTheory/RootSys.text, line: 1122
// Example: H106E12 ()
print "Example: H106E12";
ei := GetEchoInput();
SetEchoInput(true);
R := RootSystem("B3");
mx := ReflectionMatrix(R, 4);
perm := ReflectionPermutation(R, 4);
wd := ReflectionWord(R, 4);
RootPosition(R, Root(R,2) * mx) eq 2^perm;
assert $1;
perm eq &*[ ReflectionPermutation(R, r) : r in wd ];
assert $1;

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