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Version updates

Main features of the desing package in version:

1.0

 

• basic functionality ,
• text output for debugging ,
• HTML output ,
• partial result saving ,
• the CASA package is required.

1.1

 

• new architecture corresponding to the one described in [Bod00],
• speedup in the resolution (`desing/goodpoints`) ,
• either CASA or the new Groebner and Ore_algebra subpackages of the Mgfun package (version 2.2 or newer) are required ,
• extended chart description, which appears also in the HTML output blowing up and blowing down maps are included.
• fixed bugs in the singular locus computation routine for weighted basic objects, and in the procedure responsible for the preparation of the dimension reduction.
• a generalized blowup routine is added (`desing/blowupJ`) .

1.2

 

• revised handling of combinatorial information in the basic objects,
• possibility to output the maximum value of Villamayor's stratifying function locally over the current chart in the chart tree of the HTML output,
• in version 1.2.1 the calling sequence of the mgrobner procedures of CASA is automatically adjusted according to the version of CASA.

1.3

 

• extension of the scope of the algorithm to the non-hypersurface case after [EV01] (principalization of ideals is also supported),
• simplified handling of combinatorial information in the basic objects,
• simplified tests for deciding the necessity of separating components of a reducible hypersurface of maximal contact,
• it is possible to use a single variable to denote the inverse of several functions in the cover operations (optional feature),
• a new approach to cover blowing up varieties, which allows us to keep the dimension of the ambient space constant (optional feature),
• explicit test for normal crossing divisors which simplifies Villamayor's stratifying function, yielding sometimes much simpler resolutions (optional feature),
• new way of configuring the package, via the desingcfg table,
• computation of adjoints for hypersurfaces via the resolution of their singularities,
• computation of the dual hypergraph of the resolution,
• unification of the sequence of blowing ups of a resolution,
• generate resolution of singularities of projective varieties via dehomogenizations in each principal open subset automatically,
• possibility for the user to direct the algorithm (i.e. to tell it in which chart of the covering of the blowing up it should continue the resolution, or to choose from some predefined tree traversal strategies),
• Maple V Release 4 is not supported anymore,
• in version 1.3.1 a bug is removed from the algorithm that stops the resolution at the right moment in the non-hypersurface case (we thank S. Encinas for his help).

1.4

 

• this version requires Maple 8,
• a resolution strategy for reducible algebraic sets is introduced (dlocext and dlocsep subroutines),
• the package can be used without any other packages now, but it can use the Groebner and Ore_algebra subpackages of the Algolib package, or the Gröbner basis implementation of J. C. Faugère with the Gb interface Maple package,
• several bugs have been removed.

1.5

 

• the speedup strategy of normal crossings test has been rewritten, the corresponding feature is turned on by default now,
• computation of global sections of ideal sheaves on the variety W' (in the computed resolution W'->W) is introduced,
• computation of integral closure of idels via their principalization,
• a few minor bugs were fixed.