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D.5.8 resolve_lib

Resolution of singularities (Desingularization) Algorithm of Villamayor
A. Fruehbis-Krueger, anne@mathematik.uni-kl.de,
G. Pfister, pfister@mathematik.uni-kl.de

[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)


D.5.8.1 blowUp  computes the blowing up of the variety V(J) (considered as embedded in V(W)) in the (smooth) center V(C),
D.5.8.2 blowUp2  computes the blowing up of the variety V(J) in the (possibly singular) center V(C)
D.5.8.3 Center  computes 'Villamayor'-center for blow up
D.5.8.4 resolve  computes the desingularization of the variety V(J)
D.5.8.5 showBO  prints the content of a BO in more human readable form
D.5.8.6 presentTree  prints the final charts in more human readable form
D.5.8.7 showDataTypes  prints help text for output data types
D.5.8.8 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.5.8.9 createBO  creates basic object from input data
D.5.8.10 CenterBO  computes the center for the next blow-up of the given basic object
D.5.8.11 Delta  apply the Delta-operator of [Bravo,Encinas,Villamayor]
D.5.8.12 DeltaList  list of results of Delta^0 to Delta^bmax