Singular

D.6.7 gmssing_lib

Library:

gmssing.lib

Purpose:

Gauss-Manin System of Isolated Singularities

Author:

Mathias Schulze, mschulze at mathematik.uni-kl.de

Overview:

A library for computing invariants related to the Gauss-Manin system of an isolated hypersurface singularity.

References:

[Sch01] M. Schulze: Algorithms for the Gauss-Manin connection. J. Symb. Comp. 32,5 (2001), 549-564.
[Sch02] M. Schulze: The differential structure of the Brieskorn lattice. In: A.M. Cohen et al.: Mathematical Software - ICMS 2002. World Scientific (2002).
[Sch03] M. Schulze: Monodromy of Hypersurface Singularities. Acta Appl. Math. 75 (2003), 3-13.
[Sch04] M. Schulze: A normal form algorithm for the Brieskorn lattice. J. Symb. Comp. 38,4 (2004), 1207-1225.

Procedures:

D.6.7.1 gmsring		Gauss-Manin system of t with variable s
D.6.7.2 gmsnf		Gauss-Manin normal form of p
D.6.7.3 gmscoeffs		Gauss-Manin basis representation of p
D.6.7.4 bernstein		Bernstein-Sato polynomial of t
D.6.7.5 monodromy		Jordan data of complex monodromy of t
D.6.7.6 spectrum		singularity spectrum of t
D.6.7.7 sppairs		spectral pairs of t
D.6.7.8 vfilt		V-filtration of t on Brieskorn lattice
D.6.7.9 vwfilt		weighted V-filtration of t on Brieskorn lattice
D.6.7.10 tmatrix		matrix of t w.r.t. good basis of Brieskorn lattice
D.6.7.11 endvfilt		endomorphism V-filtration on Jacobian algebra
D.6.7.12 sppnf		spectral pairs normal form of (a,w[,m])
D.6.7.13 sppprint		print spectral pairs spp
D.6.7.14 spadd		sum of spectra sp1 and sp2
D.6.7.15 spsub		difference of spectra sp1 and sp2
D.6.7.16 spmul		linear combination of spectra sp
D.6.7.17 spissemicont		semicontinuity test of spectrum sp
D.6.7.18 spsemicont		semicontinuous combinations of spectra sp0 in sp
D.6.7.19 spmilnor		Milnor number of spectrum sp
D.6.7.20 spgeomgenus		geometrical genus of spectrum sp
D.6.7.21 spgamma		gamma invariant of spectrum sp