  There are a variety of choices to be made in both computer algebra systems
(CASs) and satisfiability modulo theory (SMT) solvers which can impact
performance without affecting mathematical correctness. Such choices are
candidates for machine learning (ML) approaches, however, there are
difficulties in applying standard ML techniques, such as the efficient
identification of ML features from input data which is typically a polynomial
system. Our focus is selecting the variable ordering for cylindrical algebraic
decomposition (CAD), an important algorithm implemented in several CASs, and
now also SMT-solvers. We created a framework to describe all the previously
identified ML features for the problem and then enumerated all options in this
framework to automatically generation many more features. We validate the
usefulness of these with an experiment which shows that an ML choice for CAD
variable ordering is superior to those made by human created heuristics, and
further improved with these additional features. We expect that this technique
of feature generation could be useful for other choices related to CAD, or even
choices for other algorithms with polynomial systems for input.
