### D.5.15 resolve_lib

Library:
  resolve.lib
Purpose:
  Resolution of singularities (Desingularization) Algorithm of Villamayor
Authors:
  A. Fruehbis-Krueger, anne@mathematik.uni-kl.de,
  G. Pfister, pfister@mathematik.uni-kl.de

References:
  [1] J.Kollar: Lectures on Resolution of Singularities, Princeton University Press (2007)
  (contains large overview over various known methods for curves and surfaces as well as
  a detailed description of the approach in the general case)
  [2] A.Bravo, S.Encinas, O.Villamayor: A Simplified Proof of Desingularisation and
  Applications, Rev. Math. Iberoamericana 21 (2005), 349-458
  (description of the algorithmic proof of desingularization in characteristic zero which underlies this implementation)
  [3] A.Fruehbis-Krueger: Computational Aspects of Singularities, in J.-P. Brasselet, J.Damon et al.: Singularities in Geometry and Topology, World Scientific Publishing, 253--327 (2007)
  (chapter 4 contains a detailed discussion on algorithmic desingularization and efficiency aspects thereof)

Procedures:

> D.5.15.1 blowUp |  | computes the blowing up of the variety V(J) (considered as embedded in V(W)) in the (smooth) center V(C),
> D.5.15.2 blowUp2 |  | computes the blowing up of the variety V(J) in the (possibly singular) center V(C)
> D.5.15.3 Center |  | computes 'Villamayor'-center for blow up
> D.5.15.4 resolve |  | computes the desingularization of the variety V(J)
> D.5.15.5 showBO |  | prints the content of a BO in more human readable form
> D.5.15.6 presentTree |  | prints the final charts in more human readable form
> D.5.15.7 showDataTypes |  | prints help text for output data types
> D.5.15.8 blowUpBO |  | computes the blowing up of the variety V(BO[1]) in the center V(C). BO is a list (basic object), C is an ideal
> D.5.15.9 createBO |  | creates basic object from input data
> D.5.15.10 CenterBO |  | computes the center for the next blow-up of the given basic object
> D.5.15.11 Delta |  | apply the Delta-operator of [Bravo,Encinas,Villamayor]
> D.5.15.12 DeltaList |  | list of results of Delta^0 to Delta^bmax

User manual for Singular version 4.4.1, 2025, generated by texi2html.