The Complexity of Cylindrical Algebraic Decomposition with Respect to Polynomial Degree

Matthew England, James H. Davenport

    Research output: Chapter in Book/Report/Conference proceedingConference proceedingpeer-review

    17 Citations (Scopus)
    34 Downloads (Pure)


    Cylindrical algebraic decomposition (CAD) is an important tool for working with polynomial systems, particularly quantifier elimination. However, it has complexity doubly exponential in the number of variables. The base algorithm can be improved by adapting to take advantage of any equational constraints (ECs): equations logically implied by the input. Intuitively, we expect the double exponent in the complexity to decrease by one for each EC. In ISSAC 2015 the present authors proved this for the factor in the complexity bound dependent on the number of polynomials in the input. However, the other term, that dependent on the degree of the input polynomials, remained unchanged. In the present paper the authors investigate how CAD in the presence of ECs could be further refined using the technology of Gr¨obner Bases to move towards the intuitive bound for polynomial degree.
    Original languageEnglish
    Title of host publicationComputer Algebra in Scientific Computing
    EditorsVladimir P. Gerdt, Wolfram Koepf, Werner M. Seiler, Evgenii V. Vorozhtsov
    Place of PublicationSwitzerland
    PublisherSpringer Verlag
    Number of pages21
    ISBN (Electronic)978-3-319-45641-6
    ISBN (Print)978-3-319-45640-9
    Publication statusPublished - 9 Sept 2016
    EventInternational Workshop on Computer Algebra in Scientific Computing - Bucharest, Romania
    Duration: 19 Sept 201623 Sept 2016

    Publication series

    NameLecture Notes in Computer Science
    PublisherSpringer Verlag
    ISSN (Print)0302-9743


    ConferenceInternational Workshop on Computer Algebra in Scientific Computing

    Bibliographical note

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    Lecture Notes in Computer Science ISSN 0302-9743


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