### D.6.6 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

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 Singularities. Institute of Mathematics of the Polish Academy of Sciences,Preprint 664(2006)

Procedures:

> D.6.6.1 sagbiAlg |  | Compute the Sagbi-basis of the Algebra.
> D.6.6.2 sagbiMod |  | Compute the Sagbi- basis of the Module.
> D.6.6.3 semiGroup |  | Compute the Semi-Group of the Algebra provided the input is Sagbi Bases of the Algebra.
> D.6.6.4 semiMod |  | Compute the Semi-Module provided that the input are the Sagbi Bases of the Algebra resp.Module.
> D.6.6.5 planeCur |  | Compute the type of the Simple Plane Curve singularity.
> D.6.6.6 spaceCur |  | Compute the type of the simple Space Curve singularity.
> D.6.6.7 HHnormalForm |  | computes for the parametrization defined by I normal form, semi group, semi module of differentials, Zariski number and moduli
> D.6.6.8 modSagbiAlg |  | modular variant of sagbiAlg
> D.6.6.9 classSpaceCurve |  | normal form of I if I is simple

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