Cylindrical Algebraic Decomposition I: The Basic Algorithm
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چکیده
منابع مشابه
Cylindrical Algebraic Decomposition I: The Basic Algorithm
Given I set of r-variatc integral polynomials, a cyllndrlt:al allebrtJJc decompoJition. (cad) of euclidean r-space E' partitioDIl E' into connected lubsets compatible with the zeros of tbe polynomials. Collins gave a cad construction algorithm in 1975, u part of • quantifier elimination procedure for real dosed fields. The algorithm has subsequently found diverse applications (optimization, cur...
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In this paper the idea of a Layered CAD is introduced, a truncation of a CAD to only high dimensional cells. Limiting to full-dimensional cells has already been investigated in the literature, but including another level can be beneficial for applications. A related topological property is defined and related to robotics motion planning. The distribution of cell dimensions in a CAD is investiga...
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We show that a strong well-based cylindrical algebraic decomposition P of a bounded semi-algebraic set is a regular cell decomposition, in any dimension and independently of the method by which P is constructed. Being well-based is a global condition on P that holds for the output of many widely used algorithms. We also show the same for S of dimension at most 3 and P a strong cylindrical algeb...
متن کاملAbstract Partial Cylindrical Algebraic Decomposition I: The Lifting Phase
Partial Cylindrical Algebraic Decomposition I: The Lifting Phase Grant Olney Passmore and Paul B. Jackson [email protected], [email protected] 1 Clare Hall, University of Cambridge 2 LFCS, University of Edinburgh Abstract. Though decidable, the theory of real closed fields (RCF) is Though decidable, the theory of real closed fields (RCF) is fundamentally infeasible. This is unfortunate...
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Cylindrical Algebraic Decomposition (CAD) was initially introduced to tackle the classic problem of quantifier elimination over real closed algebraic fields, however it has since seen many applications in its own right. Given a set of polynomials, multiple algorithms exist to produce a CAD such that over each cell the polynomials have constant sign. Inherently doubly exponential in the number o...
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ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 1984
ISSN: 0097-5397,1095-7111
DOI: 10.1137/0213054