Singular

D.15.9 curveInv_lib

Library:

curveInv.lib

Purpose:

A library for computing invariants of curves

Author:

Peter Chini, chini@rhrk.uni-kl.de

Overview:

This library provides a collection of procedures for computing invariants of curve singularities. Invariants that can be computed are: - the delta invariant
- the multiplicity of the conductor: the length of Normalization(R)/C, where C denotes the conductor
- the Deligne number
- the colength of derivations along the normalization - the length of Der(Normalization(R/I)) / R/I

In addition, it is possible to compute the conductor of a ring S = R/I, where R is a (localized) polynomial ring.

Theory:

Computing the Deligne number of curve singularities and an algorithmic framework for differential algebras in SINGULAR;
Chapter 5 - Master's Thesis of Peter Chini - August 2015

Procedures:

D.15.9.1 curveDeltaInv		computes the delta invariant of R/I for a given ideal I
D.15.9.2 curveConductorMult		returns the multiplicity of the conductor of R/I
D.15.9.3 curveDeligneNumber		computes the Deligne number of R/I
D.15.9.4 curveColengthDerivations		returns the colength of derivations, the length of Der(Normalization(R/I))/Der(R/I)