### D.6.15 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.6.15.1 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

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