D.6.9 classifyMapGerms_lib

Library:

classifyMapGerms.lib

Authors:

Gerhard Pfister, [email protected]
Deeba Afzal, [email protected]
Shamsa Kanwal, [email protected]

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