Speeding up Cylindrical Algebraic Decomposition by Gr\"obner Bases
Symbolic Computation
2012-07-30 v1 Algebraic Geometry
Abstract
Gr\"obner 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 Gr\"obner 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.
Keywords
Cite
@article{arxiv.1205.6285,
title = {Speeding up Cylindrical Algebraic Decomposition by Gr\"obner Bases},
author = {David J. Wilson and Russell J. Bradford and James H. Davenport},
journal= {arXiv preprint arXiv:1205.6285},
year = {2012}
}
Comments
To appear in Proc. CICM 2012, LNCS 7362