=ADD=
=reftype=
14
=number=
00-07
=url=
ftp://ftp.risc.uni-linz.ac.at/pub/techreports/2000/00-07.ps.gz
=year=
2000
=month=
03
=author=
Mittermaier ; Christian
=title=
Parallel Algorithms in Constructive Algebraic Geometry
=abstract=
The computer algebra software library CASA provides numerous
algorithms for constructive algebraic geometry on the top of the Maple
system.
Usually, CASA functions operate on polynomials or rational functions
and the algorithms work fine for inputs of moderate degree.
However, when the degree increases, computing time explodes
dramatically, making interactive usage of the system almost
impossible.

In this work we investigate parallelization ideas for three important
CASA algorithms, namely for plotting plane algebraic curves, plotting
surface-to-surface intersections and for resolution of singularities. 
Besides the parallel algorithms we also give some improvements of the
sequential programs which already reduce computing time significantly.

We have systematically tested and benchmarked our algorithms using the
{\em Distributed Maple} environment on various machine configurations
employing different numbers of processors. 
We have achieved significant speedups which  reduce computing time to
a moderate size.
=note=
Diploma Thesis
=sponsor=
FWF project P11160-TEC and SFB013 project number F1304
=keywords=
computer algebra, maple, parallel algorithm, cluster