Speeding up cylindrical algebraic decomposition by gröbner bases

Authors:
David J. Wilson;Russell J. Bradford;James H. Davenport
Affiliations:
Department of Computer Science, University of Bath, Bath, U.K.;Department of Computer Science, University of Bath, Bath, U.K.;Department of Computer Science, University of Bath, Bath, U.K.
Venue:
CICM'12 Proceedings of the 11th international conference on Intelligent Computer Mathematics
Year:
2012

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Abstract

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.