D.5.5 hnoether_lib

Library:

hnoether.lib

Purpose:

Hamburger-Noether (Puiseux) Development

Author:

Martin Lamm, lamm@mathematik.uni-kl.de

Overview:

A library for computing the Hamburger-Noether, resp. Puiseux, development of a 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.

Main procedures:

D.5.5.1 hnexpansion		Hamburger-Noether (H-N) development of f
D.5.5.2 sethnering		changes to the hnering created by hnexpansion
D.5.5.3 develop		H-N development of irreducible curves
D.5.5.4 extdevelop		extension of the H-N development hne of f
D.5.5.5 parametrisation		a parametrization of f
D.5.5.6 displayHNE		display H-N development as an ideal
D.5.5.7 invariants		invariants of f, e.g. the characteristic exponents
D.5.5.8 displayInvariants		display invariants of f
D.5.5.9 multsequence		sequence of multiplicities
D.5.5.10 displayMultsequence		display sequence of multiplicities
D.5.5.11 intersection		intersection multiplicity of two curves
D.5.5.12 stripHNE		reduce amount of memory consumed by hne
D.5.5.13 is_irred		test if f is irreducible
D.5.5.14 delta		delta invariant of f
D.5.5.15 newtonpoly		(local) Newton polygon of f
D.5.5.16 is_NND		test if f is Newton non-degenerate

Auxiliary procedures:

D.5.5.17 puiseux2generators		convert Puiseux pairs to generators of semigroup
D.5.5.18 separateHNE		number of quadratic transf. needed for separation
D.5.5.19 squarefree		a squarefree divisor of the poly f
D.5.5.20 allsquarefree		the maximal squarefree divisor of the poly f
D.5.5.21 further_hn_proc		show further procedures useful for interactive use