"Source: Text/Group/GrpFP.text";
"Line: 3924";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpFP.text, line: 3924
// Example: H80E30 ()
print "Example: H80E30";
ei := GetEchoInput();
SetEchoInput(true);
F<x, y> := FreeGroup(2);
G<a, b> := quo<F | y^7, (x*y)^2, (x^-1*y)^3>;
H := sub<G | a>;
P := CosetEnumerationProcess(G, H);
StartEnumeration(~P : Print := true);
ExistsExcludedConjugate(P);
P1 := P;
for c in ExcludedConjugates(P) do
  AddSubgroupGenerator(~P1, c);
end for;
RedoEnumeration(~P1);
ExistsCosetSatisfying(P : Order := 2, Normalizing := true);
CosetsSatisfying(P : Order := 2, Normalizing := true);
ExistsCosetSatisfying(P : Order := 3, Normalizing := true);
assert not $1;
CosetSatisfying(P : Order := 3, Normalizing := true);
CosetsSatisfying(P : Order := 3, Normalizing := true);
SetEchoInput(ei);
