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D.6.9 hnoether_lib

Hamburger-Noether (Puiseux) Expansion
Martin Lamm, lamm@mathematik.uni-kl.de
Christoph Lossen, lossen@mathematik.uni-kl.de

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.


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