# Fundamental groups of plane quintics
Read("pi1sc.txt");

# relation at infinity
fixed := [(G.1*G.2)^2*G.3];

# regions to be used
list := [[], x, x^2, x*y*x^2, (x*y)^2*x^2];

## A_12
Size(DS(AA(list, [5, 9, 0, 0, 1])));

## 3A_4
Size(DS(AA(list, [5, 5, 0, 5])));
AbelianInvariants(h);
hh := DerivedSubgroup(h);
Size(hh);
AbelianInvariants(hh);
c := Center(g);
Size(c);
Size(Intersection(hh, c));
StructureDescription(h);

#Perturbations:
Size(DS(AA(list, [5, 1, 0, 5])));
Size(DS(AA(list, [5, 5, 0, 1])));
Size(DS(AA(list, [1, 5, 0, 5])));

## A_6 + 3A_2
DS(AA(list, [7, 3, 3]));

#Perturbations:
Size(DS(AA(list, [7, 1, 3])));
Size(DS(AA(list, [7, 3, 1])));
Size(DS(AA(list, [1, 3, 3])));
