Using Machine Learning to Decide When to Precondition Cylindrical Algebraic Decomposition With Groebner Bases
Abstract
Cylindrical Algebraic Decomposition (CAD) is a key tool in computational algebraic geometry, particularly for quantifier elimination over realclosed fields. However, it can be expensive, with worst case complexity doubly exponential in the size of the input. Hence it is important to formulate the problem in the best manner for the CAD algorithm. One possibility is to precondition the input polynomials using Groebner Basis (GB) theory. Previous experiments have shown that while this can often be very beneficial to the CAD algorithm, for some problems it can significantly worsen the CAD performance. In the present paper we investigate whether machine learning, specifically a support vector machine (SVM), may be used to identify those CAD problems which benefit from GB preconditioning. We run experiments with over 1000 problems (many times larger than previous studies) and find that the machine learned choice does better than the humanmade heuristic.
 Publication:

arXiv eprints
 Pub Date:
 August 2016
 arXiv:
 arXiv:1608.04219
 Bibcode:
 2016arXiv160804219H
 Keywords:

 Computer Science  Symbolic Computation;
 Computer Science  Machine Learning;
 68W30;
 68T05;
 I.2.6;
 I.1.0
 EPrint:
 Proceedings of the 18th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC '16), pp. 4552. IEEE, 2016