Singular

D.6.1.1 resolutiongraph

Usage:

resolutiongraph(INPUT); INPUT poly or list

Assume:

INPUT is either a REDUCED bivariate polynomial defining a plane curve singularity, or the output of hnexpansion(f[,"ess"]), or the list hne in the ring created by hnexpansion(f[,"ess"]), or the output of develop(f) resp. of extdevelop(f,n), or a list containing the contact matrix and a list of integer vectors with the characteristic exponents of the branches of a plane curve singularity, or an integer vector containing the characteristic exponents of an irreducible plane curve singularity.

Return:

intmat, the incidence matrix of the resolution graph of the plane curve defined by INPUT, where the entries on the diagonal are the weights of the vertices of the graph and a negative entry corresponds to the strict transform of a branch of the curve.

Note:

In case the Hamburger-Noether expansion of the curve f is needed for other purposes as well it is better to calculate this first with the aid of hnexpansion and use it as input instead of the polynomial itself.
If you are not sure whether the INPUT polynomial is reduced or not, use squarefree(INPUT) as input instead.

LIB "alexpoly.lib";
ring r=0,(x,y),ls;
poly f1=(y2-x3)^2-4x5y-x7;
poly f2=y2-x3;
poly f3=y3-x2;
resolutiongraph(f1*f2*f3);
==> 1,0,1,0,0,0,0,0,1,0,
==> 0,2,1,0,0,0,0,0,0,0,
==> 1,1,3,0,1,0,0,0,0,0,
==> 0,0,0,4,1,0,1,0,0,0,
==> 0,0,1,1,5,1,0,0,0,0,
==> 0,0,0,0,1,-1,0,0,0,0,
==> 0,0,0,1,0,0,-2,0,0,0,
==> 0,0,0,0,0,0,0,2,1,0,
==> 1,0,0,0,0,0,0,1,3,1,
==> 0,0,0,0,0,0,0,0,1,-3