We are interested in the application of Machine Learning (ML) technology to
improve mathematical software. It may seem that the probabilistic nature of ML
tools would invalidate the exact results prized by such software, however, the
algorithms which underpin the software often come with a range of choices which
are good candidates for ML application. We refer to choices which have no
effect on the mathematical correctness of the software, but do impact its
performance.
In the past we experimented with one such choice: the variable ordering to
use when building a Cylindrical Algebraic Decomposition (CAD). We used the
Python library Scikit-Learn (sklearn) to experiment with different ML models,
and developed new techniques for feature generation and hyper-parameter
selection.
These techniques could easily be adapted for making decisions other than our
immediate application of CAD variable ordering. Hence in this paper we present
a software pipeline to use sklearn to pick the variable ordering for an
algorithm that acts on a polynomial system. The code described is freely
available online.Comment: Accepted into Proc ICMS 202