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 Title Involutive Bases for Polynomial Ideals Author(s) Ralf Hemmecke Type PhD Theses 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 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 Calix. Keywords involutive basis; involutive criteria; Gröbner basis; Buchberger criteria; sliced division; involutive division File URL ftp://ftp.risc.uni-linz.ac.at/pub/techreports/2003/03-02.ps.gz Language English Address 4040 Linz, Austria, Europe Year 2003 Edition 0 Translation No Refereed No Sponsors Austrian Science Foundation (FWF), SFB F013, project 1304
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