### D.6.9 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.6.9.1 gmsring |  | Gauss-Manin system of t with variable s
> D.6.9.2 gmsnf |  | Gauss-Manin normal form of p
> D.6.9.3 gmscoeffs |  | Gauss-Manin basis representation of p
> D.6.9.4 bernstein |  | Bernstein-Sato polynomial of t
> D.6.9.5 monodromy |  | Jordan data of complex monodromy of t
> D.6.9.6 spectrum |  | singularity spectrum of t
> D.6.9.7 sppairs |  | spectral pairs of t
> D.6.9.8 vfilt |  | V-filtration of t on Brieskorn lattice
> D.6.9.9 vwfilt |  | weighted V-filtration of t on Brieskorn lattice
> D.6.9.10 tmatrix |  | matrix of t w.r.t. good basis of Brieskorn lattice
> D.6.9.11 endvfilt |  | endomorphism V-filtration on Jacobian algebra
> D.6.9.12 sppnf |  | spectral pairs normal form of (a,w[,m])
> D.6.9.13 sppprint |  | print spectral pairs spp
> D.6.9.14 spadd |  | sum of spectra sp1 and sp2
> D.6.9.15 spsub |  | difference of spectra sp1 and sp2
> D.6.9.16 spmul |  | linear combination of spectra sp
> D.6.9.17 spissemicont |  | semicontinuity test of spectrum sp
> D.6.9.18 spsemicont |  | semicontinuous combinations of spectra sp0 in sp
> D.6.9.19 spmilnor |  | Milnor number of spectrum sp
> D.6.9.20 spgeomgenus |  | geometrical genus of spectrum sp
> D.6.9.21 spgamma |  | gamma invariant of spectrum sp

See also: dmod_lib; gmspoly_lib; mondromy_lib; spectrum_lib.

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