"Source: Text/Group/GrpFP.text";
"Line: 3783";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpFP.text, line: 3783
// Example: H80E28 ()
print "Example: H80E28";
ei := GetEchoInput();
SetEchoInput(true);
F<x, y> := FreeGroup(2);
G<a, b> := quo<F | x^8, y^7, (x*y)^2, (x^-1*y)^3>;
H := sub<G | >;
P := CosetEnumerationProcess(G, H : Print := true);
StartEnumeration(~P);
P1 := P;
AddSubgroupGenerator(~P1, a^-1*b);
Subgroup(P1);
CanRedoEnumeration(P1);
assert $1;
RedoEnumeration(~P1);

P2 := P;
AddSubgroupGenerator(~P2, a^2);
Subgroup(P2);
CanRedoEnumeration(P2);
assert $1;
RedoEnumeration(~P2);          
P3 := P2;
AddRelator(~P3, a^4);
CanContinueEnumeration(P3);
assert $1;
ContinueEnumeration(~P3);
G3<a3,b3> := Group(P3);
G3;
H3<u3, v3> := Subgroup(P3);
H3;
SetEchoInput(ei);
