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D.6.9 gmssing_lib

Gauss-Manin System of Isolated Singularities

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

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

[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.


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.