#% -*- GAP:ASCII -*-
#% This file is marked for TeX processing
#[caption]"Computing $\pi_1$ for sextics with a type $\bD_p$ point"
#================================================================
#: The computation of the fundamental groups of plane sextics with a%
#: type $\bD_p$, $p\ge6$, singularity.
#----------------------------------------------------------------
Reread("pi1sc.txt");   #: (see \file{pi1sc})
#: Paths to be used
p := i -> (x*y)^i*x^2; #%
list := List([-1..8], p); #%
list[1] := x;
#: Relations \eqref{eq.Dp.1}, \eqref{eq.Dp.2}, and \eqref{eq.Dp.inf};%
#: $p$ is the path from~$e$ to $e\subroman2$ and $w=\width\rR2$.
inf := function(p, w)
 fixed := Braid(S.1^w, G, [G.3^-1*G.1*G.3, G.3^-1*G.2*G.3]);
 fixed := bm(p, [fixed[1]/G.1, fixed[2]/G.2, G.3]);
 fixed := [G.3*G.1*G.2/rho, fixed[1], fixed[2], rho^2*G.3/fixed[3]];
end;
#: Use "inf(p,w);" and then "size(n1,n2,...);"
#: Parameters are the braid indices of $\reg_-(e\ra\zeta)$%
#:   for $\zeta=\x$ and $\zeta=(\x\y)^i\x^2$, $i=0,1,\ldots$.
size := function(arg) return Size(DS(AA(list, arg))); end;
#================================================================
#[endinput]
