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Title: On the regularity of cylindrical algebraic decompositions
Author: Locatelli, Acyr
ISNI:       0000 0004 5923 1874
Awarding Body: University of Bath
Current Institution: University of Bath
Date of Award: 2016
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Cylindrical algebraic decomposition is a powerful algorithmic technique in semi-algebraic geometry. Nevertheless, there is a disparity between what algorithms output and what the abstract definition of a cylindrical algebraic decomposition allows. Some work has been done in trying to understand what the ideal class of cylindrical algebraic decom- positions should be — especially from a topological point of view. We prove a special case of a conjecture proposed by Lazard in [22]; the conjecture relates a special class of cylindrical algebraic decompositions to regular cell complexes. Moreover, we study the properties that define this special class of cell decompositions, as well as their implications for the actual topology of the cells that make up the cell decompositions.
Supervisor: Sankaran, Gregory ; Davenport, James Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Cylindrical Algebraic Decomposition ; regularity