#% -*- GAP -*-
#% This file is marked for TeX processing
#[caption]"Computing $\pi_1$ for sextics with a type $\bD_4$ point"
#================================================================
#: The computation of the fundamental groups of plane sextics with a%
#:   type $\bD_4$ singularity.
#: Parameters: $n_1$ and $n_2$ are the braid indices of $\reg e$ and%
#:   $\reg(e\ra\x)$, respectively, and $l_i$ is the exponent~$l$ in%
#:   the chain \smash{$\y(\xy)^l$} from~$e$ to $e_i$ in the boundary%
#:   of the outer region, $i=1,2,3$.
#----------------------------------------------------------------
Reread("pi1sc.txt");   #: (see \file{pi1sc})
#[skiplines] % just bind the variable
b := [];
#[endskip] %
group := function(n1, n2, l1, l2, l3)
 b := List([l1, l2, l3], i -> bm(y*(x*y)^i, [G.3])[1]);
 b := Union(List(b, i -> rho*i/(i*rho)), [rho*b[3]*b[2]*b[1]]);
 return DS(AA([[], x], [n1, n2]), b);
end;
size := function(arg) return Size(CallFuncList(group, arg)); end;
#================================================================
#[endinput]
