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D.15.8 classifyMapGerms_lib

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

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.

[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.


D.15.8.1 coDimMap  computes a bound of the A-determinacy of the map germ defined by I
D.15.8.2 coDim  computes the K-vectorspace dimension of A^r/M+N+maxideal(b)*A^r
D.15.8.3 vStd  computes a standard basis of M+N+maxideal(b)*A^r
D.15.8.4 modVStd  computes a standard basis of M+N+maxideal(bound)*A^r (modular)
D.15.8.5 modVStd0  computes a standard basis of M+N+maxideal(bound)*A^r (parallel)
D.15.8.6 classifySimpleMaps  computes the normal form of a germ in Riegers classification
D.15.8.7 classifySimpleMaps1  computes the normal form of a germ in Riegers classification
D.15.8.8 classifyUnimodalMaps  computes the normal form of a germ in Riegers classification