"Source: Text/LieTheory/GrpCox.text";
"Line: 1128";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/LieTheory/GrpCox.text, line: 1128
// Example: H108E14 ()
print "Example: H108E14";
ei := GetEchoInput();
SetEchoInput(true);
W<[s]> := CoxeterGroup(GrpFPCox, "F4");
LongestElement(W);
CoxeterElement(W);
W := CoxeterGroup("E8");
Length(W, LongestElement(W));
assert $1 eq 120;
Length(W, CoxeterElement(W)); 
assert $1 eq 8;
W := CoxeterGroup("D5");                              
CoxeterNumber(W) eq Order(CoxeterElement(W));       
assert $1;
CoxeterNumber(W) eq #Roots(W) / Rank(W);              
assert $1;
R := RootDatum(W);
CoxeterNumber(W) eq &+Eltseq(HighestRoot(R)) + 1;
assert $1;
SetEchoInput(ei);
