The goal of the subproject is to develop
mathematical theories, algorithms, and software for
efficiently proving/disproving algebraic statements and
solving algebraic constraints over the real numbers. The
statement/conditions may contain inequalities and
quantifiers. The importance of the goal comes from the
observation that many difficult problems in mathematics,
scientific, engineering and industrial computation can be
reduced to that of solving algebraic constraints.
- Parametrization: Some equational constraints can
be solved by giving an "algebraic" parametrization of the
solution set, i.e. a parametrization by rational functions.
We are developing algorithms for finding parametrizations
of algebraic surfaces, and for simplifying given
- Singularity Analysis: A solution set of
algebraic constraints does in general have singularities,
which are obstacles for identifying its topology or for
visualizing. Resolution is a standard way to analyze these
singularities. We are developing algorithms for singularity
resolution and studying applications (e.g. for the
- Box Approximation: Algebraic solution sets may
be approximated by rectangular floating point boxes.
|Mag. Brian Moore
List of Publications.
Please direct your comments
or eventual problem reports to webmaster.
SpezialForschungsBereich SFB F013 | Special Research
Program of the FWF - Austrian Science Fund