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Local Box Adjacency Algorithms for Cylindrical Algebraic Decompositions

✍ Scribed by Scott M c Callum; George E. Collins

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
372 KB
Volume
33
Category
Article
ISSN
0747-7171

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✦ Synopsis

We describe new algorithms for determining the adjacencies between zero-dimensional cells and those one-dimensional cells that are sections (not sectors) in cylindrical algebraic decompositions (cad). Such adjacencies constitute a basis for determining all other cell adjacencies. Our new algorithms are local, being applicable to a specified 0D cell and the 1D cells described by specified polynomials. Particularly efficient algorithms are given for the 0D cells in spaces of dimensions two, three and four. Then an algorithm is given for a space of arbitrary dimension. This algorithm may on occasion report failure, but it can then be repeated with a modified isolating interval and a likelihood of success.

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