About the Software (desing v1.5 for Maple)
The software package contains an implementation of Villamayor's
algorithm for embedded resolution of singularities of schemes embedded
into smooth varieties, where the base field is of characteristic zero.
It comes as a precompiled Maple package with the full
source code available under the GNU
desing v1.5 is available for:
The package can use the Groebner and Ore_algebra packages of the Algolib package or the Gb
C++ implementation via the Gb Maple interface-library.
For more information about the installation of desing, please,
take a look at the README file.
Main features of the desing package in version:
- basic functionality,
- text output for debugging,
- HTML exporter,
- partial result saving,
package is required.
- new architecture corresponding to the one described in [Bodnar2000],
- applying Abhyankar's "good points" strategy in the resolution
- distributed computation is possible,
- either CASA or the new
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`.
- revised handling of combinatorial information in the basic
- 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.
- extension of the scope of the algorithm to the
non-hypersurface case after [Encinas and
Villamayor2001] (principalization of ideals is also supported),
- simplified handling of combinatorial information in the basic
- 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 (experimental, 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
- 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
- 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).
- 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.
- the speedup strategy of normal crossings test has been
rewritten, the corresponding feature is turned on by default now,
- omputation of global sections of ideal sheaves on the variety
W' (in the computed resolution W'->W) is introduced,
- computation of integral closure of ideals via their principalization,
- a few minor bugs were fixed.
At any feedback, bug report, etc., please write to the following