2026-09-19T21:30:14Z https://opus4.kobv.de/opus4-uni-passau/oai

oai:kobv.de-opus4-uni-passau:46 2025-08-13 bibliography:false doc-type:PhDThesis status-type:publishedVersion open_access ddc ddc:510

Cylindrical Decomposition Under Application-Oriented Paradigms Zylindrische Dekomposition unter anwendungsorientierten Paradigmen Andreas Seidl 510 Quantorenelimination cylindrical algebraic decomposition CAD cylindrical subdecomposition SCAD quantifier elimination QE Quantifier elimination (QE) is a powerful tool for problem solving. Once a problem is expressed as a formula, such a method converts it to a simpler, quantifier-free equivalent, thus solving the problem. Particularly many problems live in the domain of real numbers, which makes real QE very interesting. Among the so far implemented methods, QE by cylindrical algebraic decomposition (CAD) is the most important complete method. The aim of this thesis is to develop CAD-based algorithms, which can solve more problems in practice and/or provide more interesting information as output. An algorithm that satisfies these standards would concentrate on generic cases and postpone special and degenerated ones to be treated separately or to be abandoned completely. It would give a solution, which is locally correct for a region the user is interested in. It would give answers, which can provide much valuable information in particular for decision problems. It would combine these methods with more specialized ones, for subcases that allow for. It would exploit degrees of freedom in the algorithms by deciding to proceed in a way that promises to be efficient. It is the focus of this dissertation to treat these challenges. Algorithms described here are implemented in the computer logic system REDLOG and ship with the computer algebra system REDUCE. Universität Passau Passau Innstrasse 29, 94032 Passau Volker Weispfenning Prof. Dr. 2006-11-30 2006-12-06 PhDThesis Text publishedVersion urn:nbn:de:bvb:739-opus-816 application/pdf eng Standardbedingung laut Einverständniserklärung thesis.doctoral Universität Passau Passau Fakultät für Informatik und Mathematik 1 https://opus4.kobv.de/opus4-uni-passau/oai/container/index/docId/46 https://opus4.kobv.de/opus4-uni-passau/frontdoor/index/index/docId/46