"Source: Text/Group/GrpMatFF.text";
"Line: 2782";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpMatFF.text, line: 2782
// Example: H67E17 ()
print "Example: H67E17";
ei := GetEchoInput();
SetEchoInput(true);
G := CGOPlus(4, 5^2);

T := CompositionTree(G);

DisplayCompTreeNodes (G: Leaves:=true);
H := CompositionTreeNiceGroup(G);
W := CompositionTreeSLPGroup(G);
CompositionTreeFastVerification(G);
assert $1;

f, R := CompositionTreeVerify(G);
Set(Evaluate(R, [H.i:i in [1..Ngens(H)]]));
CompositionTreeOrder(G);                                
assert $1 eq 11681280000;
g := Random(G);
f, w := CompositionTreeElementToWord(G, g);
Evaluate(w, [H.i:i in [1..Ngens(H)]]) eq g;
assert $1;
tau := CompositionTreeNiceToUser(G);
tau;
v := tau(w);
Evaluate (v, [G.i : i in [1..Ngens(G)]]) eq g;
assert $1;
x := Random(Generic(G));
f, w := CompositionTreeElementToWord(G, x);
f; 
assert not $1;
CS, _, _, _, flag := CompositionTreeSeries(G);
"Series is composition series? ", flag;
"Length is ", #CS;

g := Random(G);
CompositionTreeFactorNumber(G, g);
SetEchoInput(ei);
