=ADD=
=reftype=
14
=number=
03-02
=url=
ftp://ftp.risc.uni-linz.ac.at/pub/techreports/2003/03-02.ps.gz
=year=
2003
=month=
05
=author=
Hemmecke; Ralf
=title=
Involutive Bases for Polynomial Ideals
=abstract=
This thesis contributes to the theory of polynomial involutive bases. 
Firstly, we present the two existing theories of involutive divisions,
compare them, and come up with a generalised approach of
\emph{suitable partial divisions}.
The thesis is built on this generalised approach.
Secondly, we treat the question of choosing a \vague{good}
suitable partial division in each iteration of the involutive basis
algorithm. We devise an efficient and flexible algorithm for this
purpose, the \emph{Sliced Division} algorithm.
During the involutive basis algorithm, the Sliced Division algorithm
contributes to an early detection of the involutive basis property and
a minimisation of the number of critical elements.
Thirdly, we give new criteria to avoid unnecessary reductions in an
involutive basis algorithm.
We show that the termination property of an involutive basis algorithm
which applies our criteria is independent of the prolongation
selection strategy used during its run.
Finally, we present an implementation of the algorithms and results of
this thesis in our software package Calix.
=note=
PhD Thesis
=sponsor=
FWF, SFB F013, project 1304
=keywords=
involutive basis, involutive division, suitable partial division