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Erschienen in:
2014 | OriginalPaper | Buchkapitel
Using the Regular Chains Library to Build Cylindrical Algebraic Decompositions by Projecting and Lifting
verfasst von : Matthew England, David Wilson, Russell Bradford, James H. Davenport
Erschienen in: Mathematical Software – ICMS 2014
Verlag: Springer Berlin Heidelberg
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Cylindrical algebraic decomposition (CAD) is an important tool, both for quantifier elimination over the reals and a range of other applications. Traditionally, a CAD is built through a process of projection and lifting to move the problem within Euclidean spaces of changing dimension. Recently, an alternative approach which first decomposes complex space using triangular decomposition before refining to real space has been introduced and implemented within the
RegularChains
Library of
Maple
. We here describe a freely available package
ProjectionCAD
which utilises the routines within the
RegularChains
Library to build CADs by projection and lifting. We detail how the projection and lifting algorithms were modified to allow this, discuss the motivation and survey the functionality of the package.