=ADD=
=reftype=
14
=number=
99-33
=url=
ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1999/99-33.ps.gz
=year=
1999
=month=
11
=author=
Heiss; Werner
=title=
An Implementation for the Rational Parametrization of Surfaces
=abstract=
The parametrization problem for rational algebraic surfaces had been
solved algorithmically only for a very limited class of surfaces until
the first complete algorithm was formulated and proven in $1995$. This
algorithm parametrizes an implicitly given surface by first computing a
birational map to  an easier-to-parametrize surface of one of five
different types. Then this surface is parametrized and the
parametrization is composed with the inverse of the birational map to
obtain a parametrization of the original surface.

The method used by the parametrization algorithm is based on the concept
of adjoints. In the first step the parametrization algorithm computes
adjoint vectorspaces of a given surface to construct a birational map
to a simpler surface. The second part of the parametrization
then consists in the parametrization of the birationally equivalent
surface. 

The topic of this thesis was the implementation of this second part of
the
entire algorithm. The goal was reached, i.e. we now have an
implementation
computing the parametrization of a given rational surface, using an
interface to an algorithm that computes the adjoint vectorspaces of an
implicitly given surface. 

We will not go into technical details for the first part of the
algorithm,
adjoints computation.
We will just briefly sketch an algorithm
and use adjoints as a black box for the rest of the paper.

During the implementation  several theoretical and practical changes
and refinements turned out to be useful. We describe here this second
part of the algorithm
 in detail, discuss the underlying theory and practical aspects of
the implementation. Detailed proofs for  the various subalgorithms
we use are given.

=keywords=
parametrization, rational, surfaces
=note=
Master Thesis (supervisor J. Schicho)
=sponsor=
FWF (adjoints)