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: 11th 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, J. , 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.

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