Singular

D.6.9 hnoether_lib

Library:

hnoether.lib

Purpose:

Hamburger-Noether (Puiseux) Expansion

Authors:

Martin Lamm, lamm@mathematik.uni-kl.de
Christoph Lossen, lossen@mathematik.uni-kl.de

Overview:

A library for computing the Hamburger-Noether expansion (analogue of Puiseux expansion over fields of arbitrary characteristic) of a reduced plane curve singularity following [Campillo, A.: Algebroid curves in positive characteristic, Springer LNM 813 (1980)].
The library contains also procedures for computing the (topological) numerical invariants of plane curve singularities.

Procedures:

D.6.9.1 hnexpansion		Hamburger-Noether (HN) expansion of f
D.6.9.2 develop		HN expansion of irreducible plane curve germs
D.6.9.3 extdevelop		extension of the H-N expansion hne of f
D.6.9.4 param		parametrization of branches described by HN data
D.6.9.5 displayHNE		display HN expansion as an ideal
D.6.9.6 invariants		invariants of f, e.g. the characteristic exponents
D.6.9.7 displayInvariants		display invariants of f
D.6.9.8 multsequence		sequence of multiplicities
D.6.9.9 displayMultsequence		display sequence of multiplicities
D.6.9.10 intersection		intersection multiplicity of two local branches
D.6.9.11 is_irred		test whether f is irreducible as power series
D.6.9.12 delta		delta invariant of f
D.6.9.13 newtonpoly		(local) Newton polygon of f
D.6.9.14 is_NND		test whether f is Newton non-degenerate
D.6.9.15 stripHNE		reduce amount of memory consumed by hne
D.6.9.16 puiseux2generators		convert Puiseux pairs to generators of semigroup
D.6.9.17 separateHNE		number of quadratic transf. needed for separation
D.6.9.18 squarefree		a squarefree divisor of the polynomial f
D.6.9.19 allsquarefree		the maximal squarefree divisor of the polynomial f
D.6.9.20 further_hn_proc		show further procedures useful for interactive use