### D.5.9 reszeta_lib

Library:
  reszeta.lib
Purpose:
  topological Zeta-function and some other applications of desingularization

Authors:
  A. Fruehbis-Krueger, anne@mathematik.uni-kl.de,
  G. Pfister, pfister@mathematik.uni-kl.de

References:
  [1] Fruehbis-Krueger,A., Pfister,G.: Some Applications of Resolution of
  Singularities from a Practical Point of View, in Computational
  Commutative and Non-commutative Algebraic Geometry,
  NATO Science Series III, Computer and Systems Sciences 196, 104-117 (2005) [2] Fruehbis-Krueger: An Application of Resolution of Singularities:
  Computing the topological Zeta-function of isolated surface singularities
  in (C^3,0), in D.Cheniot, N.Dutertre et al.(Editors): Singularity Theory,
  World Scientific Publishing (2007)

Procedures:

> D.5.9.1 intersectionDiv |  | computes intersection form and genera of exceptional divisors (isolated singularities of surfaces)
> D.5.9.2 spectralNeg |  | computes negative spectral numbers (isolated hypersurface singularity)
> D.5.9.3 discrepancy |  | computes discrepancy of given resolution
> D.5.9.4 zetaDL |  | computes Denef-Loeser zeta function (hypersurface singularity of dimension 2)
> D.5.9.5 collectDiv |  | identify exceptional divisors in different charts (embedded and non-embedded case)
> D.5.9.6 prepEmbDiv |  | prepare list of divisors (including components of strict transform, embedded case)
> D.5.9.7 abstractR |  | pass from embedded to non-embedded resolution
> D.5.9.8 computeV |  | multiplicities of divisors in pullback of volume form
> D.5.9.9 computeN |  | multiplicities of divisors in total transform of resolution

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