Speeding up cylindrical algebraic decomposition by Gröebner Bases

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Abstract

Gröebner Bases and Cylindrical Algebraic Decomposition are generally thought of as two, rather different, methods of looking at systems of equations and, in the case of Cylindrical Algebraic Decomposition, inequalities. However, even for a mixed system of equalities and inequalities, it is possible to apply Gröebner basesto the (conjoined) equalities before invoking CAD. We see that this is, quite often but not always, a beneficial preconditioning of the CAD problem. It is also possible to precondition the (conjoined) inequalities with respect to the equalities, and this can also be useful in many cases.
Original languageEnglish
Title of host publicationIntelligent Computer Mathematics
EditorsJohan Jeuring, John A Campbell, Jacques Carette, Gabriel Dos Reis, Petr Sojka, Makarius Wenzel, Volker Sorge
Place of PublicationHeidelberg
Pages280-294
Number of pages15
Volume7362
ISBN (Electronic)9783642313745
DOIs
Publication statusPublished - 2012
Event11th International Conference, AISC 2012, 19th Symposium, Calculemus 2012, 5th International Workshop, DML 2012, 11th International Conference, MKM 2012, Systems and Projects, held as part of CICM 2012 - Bremen, Germany
Duration: 8 Jul 201213 Jul 2012

Publication series

NameLecture Notes in Computer Science
Volume7362
ISSN (Print)0302-9743

Conference

Conference11th International Conference, AISC 2012, 19th Symposium, Calculemus 2012, 5th International Workshop, DML 2012, 11th International Conference, MKM 2012, Systems and Projects, held as part of CICM 2012
Abbreviated titleCICM 2012
CountryGermany
CityBremen
Period8/07/1213/07/12

Keywords

  • Groebner basis
  • Cylindrical Algebraic Decomposition

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    Wilson, D. J., Bradford, R. J., & Davenport, J. H. (2012). Speeding up cylindrical algebraic decomposition by Gröebner Bases. In J. Jeuring, J. A. Campbell, J. Carette, G. Dos Reis, P. Sojka, M. Wenzel, & V. Sorge (Eds.), Intelligent Computer Mathematics (Vol. 7362, pp. 280-294). (Lecture Notes in Computer Science; Vol. 7362).. https://doi.org/10.1007/978-3-642-31374-5_19