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We are interested in the application of Machine Learning (ML) technology toimprove mathematical software. It may seem that the probabilistic nature of MLtools would invalidate the exact results prized by such software, however, thealgorithms which underpin the software often come with a range of choices whichare good candidates for ML application. We refer to choices which have noeffect on the mathematical correctness of the software, but do impact itsperformance.  In the past we experimented with one such choice: the variable ordering touse when building a Cylindrical Algebraic Decomposition (CAD). We used thePython library Scikit-Learn (sklearn) to experiment with different ML models,and developed new techniques for feature generation and hyper-parameterselection.  These techniques could easily be adapted for making decisions other than ourimmediate application of CAD variable ordering. Hence in this paper we presenta software pipeline to use sklearn to pick the variable ordering for analgorithm that acts on a polynomial system. The code described is freelyavailable online.

A machine learning based software pipeline to pick the variable ordering for algorithms with polynomial inputs