desing v1.5
Maple Library for Desingularization of Subschemes of Smooth Varieties
after O. Villamayor
by Josef Schicho and Gabor Bodnar
ABOUT
-----
The package is an implementation of the algorithm extracted from the
constructive proof of the existence of embedded resolution of
singularities for hypersurfaces, published by Villamayor (1989). The
main source of his proof for this work was the paper: S. Encinas and
O. Villamayor, A course on constructive desingularization and
equivariance, In Resolution of singularities, A research textbook in
tribute to Oscar Zariski, editors H. Hauser, J. Lipman, F. Oort and
A. Quiros, Progress in Mathematics 181, Birkhauser (2000). The
fundamentals of the implementation was published in: G. Bodnar and
J. Schicho, Automated resolution of singularities for hypersurfaces,
Journal of Symbolic Computation 30(4): 401-428, Academic Press (2000).
The implementation works in arbitrary dimensions. The package offers
several advanced features beside its basic functionality. Please
consult the manual and the online help for more information on these.
VERSION
-------
This version 1.5
Release feature history:
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 the paper
"Two computational techniques for singularity resolution" referred
above, application of the "goodpoints" strategy for speedup in the
resolution,
- distributed computation,
- 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 with name `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: S. Encinas and O. Villamayor, A new theorem of
desingularization over fields of characteristic zero, Preprint
2001, (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--it is recommended to be turned on),
- 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 exceptional divisors,
- 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
Groebner basis implementation of J. C. Faugere 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 ideals via their principalization,
- a few minor bugs were fixed.
The development of the algorithm is being continued and new versions,
optimizations are to be released on the web site:
http://www.risc.uni-linz.ac.at/projects/basic/adjoints/blowup
REQUIREMENTS
------------
The package is written for Maple 8 or more recent versions.
INSTALLATION
------------
This software package is also available via ftp, at
ftp.risc.uni-linz.ac.at/pub/adjoints/blowup
The package comes also as a precompiled Maple library, so the
installation requires only the following steps:
* Choose (or create) a directory where the package is to be placed.
(e.g. /home/mylogin/maplestuff/)
* Unpack and untar the downloaded file in the created directory.
(mv desingv1.4.tar.gz /home/mylogin/maplestuff/;
cd /home/mylogin/maplestuff/;
tar xfz desingv1.4.tar.gz)
* Extend the `libname' variable in your `.mapleinit' file so that it
also points to the directory of the package.
(libname := `/home/mylogin/maplestuff/desing/lib`,libname:)
When you start Maple next time you should be able to reach the help
and to use the package via the Maple command `with(desing);'.
The following directories and files are created:
lib directory for the precompiled maple package,
source directory for the source code
GPL the text of GNU General public license
README this file
maunal.ps the manual of the package (also available online)
Makefile the make file to compile the source provided that the
commands `maple' and `march' are available without any path
specification (you can also edit the makefile as you need).
COMMENTS
--------
For more detailed description of the HTML output, and other topics
related to the algorithm, please visit the web page
http://www.risc.uni-linz.ac.at/projects/basic/adjoints/blowup
Bug reports, feedbacks should be sent to adjoints@risc.uni-linz.ac.at
COPYRIGHT NOTICE
----------------
Copyright (C) 1998-2004 by
Research Institute for Symbolic Computation
Johannes Kepler University
A-4040 Linz, Austria.
The system is freely distributed under the following conditions: Any
research activity which uses `desing' should cite the authors and the
system explicitly. The system can be freely distributed to other
users. New users are encouraged to notify the authors via the email
address adjoints@risc.uni-linz.ac.at to be kept informed about the
further development and releases of the system.
NOTE: This system is not a part of Maple share library.