Computing the Cylindrical Algebraic Decomposition Adapted to a Set of Equalities

Neila Gonzalez-Campos () and Laureano Gonzalez-Vega ()
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Neila Gonzalez-Campos: Universidad de Cantabria, Departamento de Matemática Aplicada y Ciencias de la Computación
Laureano Gonzalez-Vega: Universidad de Cantabria, Departamento de Matemáticas, Estadística y Computación

A chapter in Computer Algebra in Scientific Computing, 2000, pp 203-217 from Springer

Abstract: Abstract The Cylindrical Algebraic Decomposition algorithm, in its projection phase, proceeds by eliminating one variable from a given set of polynomials P by means of the computation of the principal subresultant coefficients of a certain set of pairs of polynomials in P (including their derivatives and reducta). Since this method produces usually a big number of polynomials, and since the process must be iterated several times, any improvement in the projection phase would convey to dramatically speed up the efficiency of the Cylindrical Algebraic Decomposition algorithm. The purpose of this paper is to present two approaches allowing, in some cases, to simplify the projection phase in the Cylindrical Algebraic Decomposition algorithm when some of the involved polynomials are prescribed to have a particular sign behaviour.

Keywords: Projection Operator; Real Root; Boolean Combination; Quantifier Elimination; Real Algebraic Geometry (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-57201-2_17

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DOI: 10.1007/978-3-642-57201-2_17

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