### D.4.5 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.4.5.1 curveDeltaInv |  | computes the delta invariant of R/I for a given ideal I
> D.4.5.2 curveConductorMult |  | returns the multiplicity of the conductor of R/I
> D.4.5.3 curveDeligneNumber |  | computes the Deligne number of R/I
> D.4.5.4 curveColengthDerivations |  | returns the colength of derivations, the length of Der(Normalization(R/I))/Der(R/I)

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