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Speeding up cylindrical algebraic decomposition by Gröebner Bases


Reference:

Wilson, D. J., Bradford, R. J. and Davenport, J. H., 2012. Speeding up cylindrical algebraic decomposition by Gröebner Bases. In: Jeuring, J., Campbell, J. A., Carette, J., Dos Reis, G., Sojka, P., Wenzel, M. and Sorge, V., eds. Intelligent Computer Mathematics. Vol. 7362. Heidelberg: , pp. 280-294. (Lecture Notes in Computer Science; 7362)

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    Official URL:

    http://dx.doi.org/10.1007/978-3-642-31374-5_19

    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.

    Details

    Item Type Book Sections
    CreatorsWilson, D. J., Bradford, R. J. and Davenport, J. H.
    EditorsJeuring, J., Campbell, J. A., Carette, J., Dos Reis, G., Sojka, P., Wenzel, M. and Sorge, V.
    DOI10.1007/978-3-642-31374-5_19
    Uncontrolled Keywordsgroebner basis, cylindrical algebraic decomposition
    DepartmentsFaculty of Science > Computer Science
    Publisher StatementCICM2012-v9-EasyChair.pdf: The original publication is available at www.springerlink.com
    StatusPublished
    ID Code29509
    Additional Information11th 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, July 8-13, 2012. Proceedings

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