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TitleSpeeding up cylindrical algebraic decomposition by Gr\"obner bases.
Author(s) Russell J. Bradford, James H. Davenport, David J. Wilson
TypeBook, Chapter in Book, Conference Proceeding
AbstractGröbner Bases [Buc70] and Cylindrical Algebraic Decomposition [Col75,CMMXY09] 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 Gröbner bases to 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.
ISBN978-3-642-31373-8/pbk
URL http://link.springer.com/chapter/10.1007%2F978-3-642-31374-5_19
LanguageEnglish
Pages280--294
PublisherBerlin: Springer
Year2012
Edition0
Translation No
Refereed No
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