Singular

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