  Cylindrical Algebraic Decomposition (CAD) is a key tool in computational
algebraic geometry, particularly for quantifier elimination over real-closed
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 human-made heuristic.
