### D.6.1 alexpoly_lib

Library:
  alexpoly.lib
Purpose:
  Resolution Graph and Alexander Polynomial
Author:
  Fernando Hernando Carrillo, hernando@agt.uva.es
  Thomas Keilen, keilen@mathematik.uni-kl.de

Overview:
  A library for computing the resolution graph of a plane curve singularity f, the total multiplicities of the total transforms of the branches of f along the exceptional divisors of a minimal good resolution of f, the Alexander polynomial of f, and the zeta function of its monodromy operator.

Procedures:

> D.6.1.1 resolutiongraph |  | resolution graph f
> D.6.1.2 totalmultiplicities |  | resolution graph, total multiplicities and strict multiplicities of f
> D.6.1.3 alexanderpolynomial |  | Alexander polynomial of f
> D.6.1.4 semigroup |  | calculates generators for the semigroup of f
> D.6.1.5 proximitymatrix |  | calculates the proximity matrix of f
> D.6.1.6 multseq2charexp |  | converts multiplicity sequence to characteristic exponents
> D.6.1.7 charexp2multseq |  | converts characteristic exponents to multiplicity sequence
> D.6.1.8 charexp2generators |  | converts characteristic exponents to generators of the semigroup
> D.6.1.9 charexp2inter |  | converts contact matrix and charact. exp. to intersection matrix
> D.6.1.10 charexp2conductor |  | converts characteristic exponents to conductor
> D.6.1.11 charexp2poly |  | calculates a polynomial f with characteristic exponents v
> D.6.1.12 tau_es2 |  | equisingular Tjurina number of f

User manual for Singular version 4.4.1, 2025, generated by texi2html.