Home Online Manual
Top
Back: member
Forward: curveDeltaInv
FastBack:
FastForward:
Up: Singular Manual
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

D.15.10 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.15.10.1 curveDeltaInv  computes the delta invariant of R/I for a given ideal I
D.15.10.2 curveConductorMult  returns the multiplicity of the conductor of R/I
D.15.10.3 curveDeligneNumber  computes the Deligne number of R/I
D.15.10.4 curveColengthDerivations  returns the colength of derivations, the length of Der(Normalization(R/I))/Der(R/I)