About the Software (desing v1.2 for Singular)
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 Singular
library, so that the full source code is released under the GNU GPL licence.
desing v1.2 is available for:
Please use versions of Singular which are newer than the fix of 2-0-4
which was released February 2003. This version contains bugfixes which
are crucial for the package.
For more information about the installation of desing, please,
take a look at the README file.
Main features of the desing package in version:
- 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,
- minor bugfixes.
- using FOCUS is made optional via the DCFG[DCFOCUS] config variable,
- a bug is removed from the computation of suitable covers in 'case 5'
- the explicit normal crossings test (NCTEST) has been finalized
(the theoretical background is to be presented in a forthcoming
- if one wants to resolve singularities of reducible algebraic
sets, it is possible to build superposed resolutions of the
irreducible components by a new resolution strategy which achieves
embedded resolution by a final component separation phase (the
theoretical background is to be presented in a forthcoming paper),
- the resolution stops now always when an embedded resolution is
reached and no unnecessary finishing blowing ups are computed,
- minor bugfixes.
- basic functionality (resolution of hypersurfaces and pure dimensional varieties, principalization of ideals),
- text output for debugging,
- HTML exporter,
- applying the standard basis computation facility of Singular in semilocal rings (optional),
- applying the "normal crossing test" for nonsingular hypersurfaces to avoid unnecessary blowing ups (optional),
- in 1.0.1 bugs are fixed in the singular locus computation for weighted objects and in the equi-order computation (thanks to S. Encinas),
- in 1.0.2 a bug is removed from the blowup routine for the localized
version of the algorithm so that the charts of the blowing up variety
are generated in the right order now, moreover in the monomial case
the localization became the usual one.
At any feedback, bug report, etc., please write to the following