### D.6.9 classifyMapGerms_lib

Library:
  classifyMapGerms.lib
Authors:
  Gerhard Pfister, pfister@mathematik.uni-kl.de
  Deeba Afzal, deebafzal@gmail.com
  Shamsa Kanwal, lotus_zone16@yahoo.com

Overview:
  A library for computing the standard basis of the tangent space at the orbit of an algebraic group action. The tangent space is usually described as the sum of two modules over different rings. It computes the standard basis using modular methods and parallel modular methods. It also computes the normal form of the germ given by Riegers classification.

References:
  [1] Idrees N.; Pfister, G.; Steidel, S.: Parallelization of modular algorithms. J. Symbolic Comput. 46(2011), no. 6, 672-684.
  [2] Gibson,C.G; Hobbs,C.A.: Simple SIngularities of Space Curves. Math.Proc. Comb.Phil.Soc.(1993),113,297.
  [3] Bruce, J.W.,Gaffney, T.J.: Simple singularities of mappings (C, 0) ->(C2,0). J. London Math. Soc. (2) 26 (1982), 465-474.
  [4] Rieger, J. H.: Families of maps from the plane to the plane. J. London Math. Soc. (2)36(1987), no. 2. 351-369.

Procedures:

> D.6.9.1 coDimMap |  | computes a bound of the A-determinacy of the map germ defined by I
> D.6.9.2 coDim |  | computes the K-vectorspace dimension of A^r/M+N+maxideal(b)*A^r
> D.6.9.3 vStd |  | computes a standard basis of M+N+maxideal(b)*A^r
> D.6.9.4 modVStd |  | computes a standard basis of M+N+maxideal(bound)*A^r (modular)
> D.6.9.5 modVStd0 |  | computes a standard basis of M+N+maxideal(bound)*A^r (parallel)
> D.6.9.6 classifySimpleMaps |  | computes the normal form of a germ in Riegers classification
> D.6.9.7 classifySimpleMaps1 |  | computes the normal form of a germ in Riegers classification
> D.6.9.8 classifyUnimodalMaps |  | computes the normal form of a germ in Riegers classification

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