Layered Cylindrical Algebraic Decomposition

D. J. Wilson, M. England

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Abstract

In this report the idea of a Layered CAD is introduced: a
truncation of a CAD to cells of dimension higher than a prescribed
value. Limiting to full-dimensional cells has already been
investigated in the literature, but including more levels is shown to
also be beneficial for applications. Alongside a direct algorithm, a
recursive algorithm is provided. A related topological property is
defined and related to robot motion planning. The distribution of cell
dimensions in a CAD is investigated and layered CAD ideas are combined
with other research. All research is fully implemented within a freely
available Maple package, and all results are corroborated with
experimental results.
Original languageEnglish
Place of PublicationBath, U. K.
PublisherDepartment of Computer Science, University of Bath
Publication statusPublished - Aug 2013

Publication series

NameDepartment of Computer Science Technical Report Series
PublisherDepartment of Computer Science, University of Bath
No.CSBU-2013-05
ISSN (Print)1740-9497

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    Wilson, D. J., & England, M. (2013). Layered Cylindrical Algebraic Decomposition. (Department of Computer Science Technical Report Series; No. CSBU-2013-05). Department of Computer Science, University of Bath.