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Erschienen in:
2012 | OriginalPaper | Buchkapitel
Speeding Up Cylindrical Algebraic Decomposition by Gröbner Bases
verfasst von : David J. Wilson, Russell J. Bradford, James H. Davenport
Erschienen in: Intelligent Computer Mathematics
Verlag: Springer Berlin Heidelberg
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Gröbner 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.