Singular

D.15.4 classify_aeq_lib

Library:

classifyAeq.lib

Purpose:

Simple Space Curve singularities in characteristic 0

Authors:

Faira Kanwal Janjua fairakanwaljanjua@gmail.com
Gerhard Pfister pfister@mathematik.uni-kl.de Khawar Mehmood khawar1073@gmail.com NEU

Overview:

A library for classifying the simple singularities
with respect to A equivalence in characteristic 0.
Simple Surface singularities in characteristic O have been classified by Bruce and Gaffney [4] resp. Gibson and Hobbs [1] with respect to A equivalence. If the input is one of the simple singularities in [1] it returns a normal form otherwise a zero ideal(i.e not simple).

References:

[1] Gibson,C.G; Hobbs,C.A.:Simple SIngularities of Space Curves. Math.Proc. Comb.Phil.Soc.(1993),113,297.
[2] Hefez,A;Hernandes,M.E.:Standard bases for local rings of branches and their modules of differentials. Journal of Symbolic Computation 42(2007) 178-191. [3] Hefez,A;Hernandes,M.E.:The Analytic Classification Of Plane Branches. Bull.Lond Math Soc.43.(2011) 2,289-298. [4] Bruce, J.W.,Gaffney, T.J.: Simple singularities of mappings (C, 0) ->(C2,0). J. London Math. Soc. (2) 26 (1982), 465-474.
[5] Ishikawa,G; Janeczko,S.: The Complex Symplectic Moduli Spaces of Unimodal Parametric Plane Curve NEU Singularities. Insitute of Mathematics of the Polish Academy of Sciences,Preprint 664(2006)

Procedures:

D.15.4.1 sagbiAlg		Compute the Sagbi-basis of the Algebra.
D.15.4.2 sagbiMod		Compute the Sagbi- basis of the Module.
D.15.4.3 semiGroup		Compute the Semi-Group of the Algebra provided the input is Sagbi Bases of the Algebra.
D.15.4.4 semiMod		Compute the Semi-Module provided that the input are the Sagbi Bases of the Algebra resp.Module.
D.15.4.5 planeCur		Compute the type of the Simple Plane Curve singularity.
D.15.4.6 spaceCur		Compute the type of the simple Space Curve singularity.
D.15.4.7 HHnormalForm		computes for the parametrization defined by I normal form, semi group, semi module of differentials, Zariski number and moduli