# Fundamental groups of universal curves
Read("pi1sc.txt");

## Z_7
tmp := [RA([], 7), RA((y*x^2)^2, 1)];
Size(DS(tmp, bm(x, tmp), bm(x^2, tmp), [rho^4]));


## Z_9
tmp := [RA([], 9), RA(x^2*(y*x^2)^2, 1)];
DS(tmp, bm(x*y, tmp), bm((x*y)^2, tmp), [RA(x, 3), rho^6]);
simplify(g.1/g.3, g.2/g.3);
TzPrintRelators(P);
DS(tmp, bm(x*y, tmp), bm((x*y)^2, tmp), [RA(x, 3), rho^2]);
simplify(g.1/g.3, g.2/g.3);
TzPrintRelators(P);


## Z_5 + Z_5
tmp := [RA([], 5), RA(x^2*y*x^2, 5)];
tmp := Union(List([0..4], i -> bm((x*y)^i, tmp)));
DS(tmp, [RA(x, 5), rho^10]);
AbelianInvariants(h);
DS(tmp, [RA(x, 5), rho^2]);
AbelianInvariants(h);
hh := DerivedSubgroup(h);
AbelianInvariants(hh);
