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TitleInvolutive Bases for Polynomial Ideals
Author(s) Ralf Hemmecke
TypePhD Theses
AbstractThis 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 division}. The thesis is
built on this generalised approach. Secondly, we
treat the question of choosing a ``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} algoritm. 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
Keywordsinvolutive basis; involutive criteria; Gröbner basis; Buchberger criteria; sliced division; involutive division
URL ftp://ftp.risc.uni-linz.ac.at/pub/techreports/2003/03-02.ps.gz
Address4040 Linz, Austria, Europe
Translation No
Refereed No
SponsorsAustrian Science Foundation (FWF), SFB F013, project 1304