"Source: Text/Group/GrpFP.text";
"Line: 10753";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpFP.text, line: 10753
// Example: H80E86 ()
print "Example: H80E86";
ei := GetEchoInput();
SetEchoInput(true);
F := FreeGroup(2);
rel := (F.1 * F.2 * F.1 * F.2 * F.1 * F.2 * F.1 * F.2 * F.1 * F.2 *
  F.1 * F.2 * F.1 * F.2 * F.1 * F.2^-1 * F.1 * F.2 * F.1 * F.2^-1)^2;
G := quo<F | [F.1^2 ,F.2^3, rel]>;
HasInfinitePSL2Quotient(G : Full := true);
assert $1;
HasInfinitePSL2Quotient(G : Full := true, Signs := [-1,1,0]);
assert $1;
G := quo<F | [F.1^2 ,F.2^3, (F.1*F.2)^5]>;
HasInfinitePSL2Quotient(G);
assert not $1;
HasInfinitePSL2Quotient(G : Full := true, Signs := [-1,1,0]);
assert not $1;
SetEchoInput(ei);
