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Quantifier elimination and cylindrical algebraic decomposition

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Published by Springer in Wien, New York .
Written in English

Subjects:

  • Algebra -- Data processing -- Congresses.,
  • Decomposition method -- Data processing -- Congresses.,
  • Algorithms -- Congresses.

Book details:

Edition Notes

Other titlesQuantifier elimination
StatementB.F. Caviness, J.R. Johnson (eds.).
SeriesTexts and monographs in symbolic computation,
ContributionsCaviness, Bob F., Johnson, J. R.
Classifications
LC ClassificationsQA155.7.E4 Q36 1998
The Physical Object
Paginationxix, 431 p. :
Number of Pages431
ID Numbers
Open LibraryOL1003901M
ISBN 103211827943
LC Control Number96043590

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George Collins’ discovery of Cylindrical Algebraic Decomposition (CAD) as a method for Quantifier Elimination (QE) for the elementary theory of real closed fields brought a major breakthrough in automating mathematics with recent important applications in high-tech areas (e.g. robot motion), also stimulating fundamental research in computer algebra over the past three decades. Such a decomposition is therefore called an ~-invariant cylindrical algebraic decomposition. The sign of a polynomial in ~in a cell of the decomposition can be determined by computing its sign at a sample point belonging to the cell. In the application of cylindrical algebraic de- composition to quantifier elimination, we assume that we are given aCited by: Collins G.E. () Quantifier Elimination for Real Closed Fields by Cylindrical Algebraic Decomposition. In: Caviness B.F., Johnson J.R. (eds) Quantifier Elimination and Cylindrical Algebraic by: A quantifier elimination algorithm by cylindrical algebraic decomposition based on regular chains is presented. The main idea is to refine a complex cylindrical tree until the signs of polynomials appearing in the tree are sufficient to distinguish the true and false by:

George Collins' discovery of Cylindrical Algebraic Decomposition (CAD) as a method for Quantifier Elimination (QE) for the elementary theory of real closed fields brought a major breakthrough in automating mathematics with recent important applications in high-tech areas (e.g. robot motion), also stimulating fundamental research in computer algebra over the past three decades. A quantifier elimination algorithm by cylindrical algebraic decomposition based on regular chains is presented. The main idea is to refine a complex cylindrical tree until the signs of polynomials. The method of cylindrical algebraic decomposition (CAD) of the k-dimensional space constitutes a classical technique for the efficient solution of quantifier elimination (QE) problems in algorithmic, computer-aided we apply this method to some applied mechanics problems under appropriate by: CylindricalDecomposition[ineqs, {x1, x2, }] finds a decomposition of the region represented by the inequalities ineqs into cylindrical parts whose directions correspond to the successive xi. CylindricalDecomposition[ineqs, {x1, x2, }, op] finds a decomposition of the result of applying the topological operation op to the region represented by the inequalities ineqs.

QEPCAD is an implementation of quantifier elimination by partial cylindrical algebraic decomposition due orginally to Hoon Hong, and subsequently added on to by many others. It is an interactive command-line program written in C, and based on the SACLIB library of computer algebra functions. a quantifier elimination method for reat closed fields ([TAR4B]). Hence a subset of E. T. is semi-algebraic. if. and only if it is definable. A decomposition is algebraic if each of its regions is a semi-algebraic set. A cylindrical algebraic decomposition of £T is a decompositionwhichis both cylindrical and algebraic. LetX be a subset of g;r. Quantifier Elimination and Cylindrical Algebraic Decomposition | George Collins' discovery of Cylindrical Algebraic Decomposition (CAD) as a method for Quantifier Elimination (QE) for the elementary theory of real closed fields brought a major breakthrough in automating mathematics with recent important applications in high-tech areas (e.g. Quanti er Elimination by Cylindrical Algebraic Decomposition Based on Regular Chains Changbo Chen1 and Marc Moreno Maza2 (Gratitude goes to James Davenport for presenting this talk) 1 Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences 2 ORCCA, University of Western Ontario J ISSAC , Kobe, Japan.