D.6.15 hnoether_lib

Library:

hnoether.lib

Purpose:

Hamburger-Noether (Puiseux) Expansion

Authors:

Martin Lamm, [email protected]
Christoph Lossen, [email protected]

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.6.15.1 hnexpansion		Hamburger-Noether (HN) expansion of f
D.6.15.2 develop		HN expansion of irreducible plane curve germs
D.6.15.3 extdevelop		extension of the H-N expansion hne of f
D.6.15.4 param		parametrization of branches described by HN data
D.6.15.5 displayHNE		display HN expansion as an ideal
D.6.15.6 invariants		invariants of f, e.g. the characteristic exponents
D.6.15.7 displayInvariants		display invariants of f
D.6.15.8 multsequence		sequence of multiplicities
D.6.15.9 displayMultsequence		display sequence of multiplicities
D.6.15.10 intersection		intersection multiplicity of two local branches
D.6.15.11 is_irred		test whether f is irreducible as power series
D.6.15.12 delta		delta invariant of f
D.6.15.13 newtonpoly		(local) Newton polygon of f
D.6.15.14 is_NND		test whether f is Newton non-degenerate
D.6.15.15 stripHNE		reduce amount of memory consumed by hne
D.6.15.16 puiseux2generators		convert Puiseux pairs to generators of semigroup
D.6.15.17 separateHNE		number of quadratic transf. needed for separation
D.6.15.18 squarefree		a squarefree divisor of the polynomial f
D.6.15.19 allsquarefree		the maximal squarefree divisor of the polynomial f
D.6.15.20 further_hn_proc		show further procedures useful for interactive use