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.
The examples used in this paper are available in [Wil12]. This work was partially supported by the U.K.’s EPSRC under grant number EP/J003247/1.
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Wilson, D.J., Bradford, R.J., Davenport, J.H. (2012). Speeding Up Cylindrical Algebraic Decomposition by Gröbner Bases. In: Jeuring, J., et al. Intelligent Computer Mathematics. CICM 2012. Lecture Notes in Computer Science(), vol 7362. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31374-5_19
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DOI: https://doi.org/10.1007/978-3-642-31374-5_19
Publisher Name: Springer, Berlin, Heidelberg
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