### Abstract

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.

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.

Original language | English |
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Title of host publication | Mathematical Software - ICMS 2020 |

Publisher | Springer International Publishing |

Pages | (In-Press) |

Number of pages | 10 |

Volume | (In-Press) |

Publication status | Accepted/In press - 20 May 2020 |

Event | International Congress on Mathematical Software 2020 - Braunschweig, Germany Duration: 13 Jul 2020 → 16 Jul 2020 |

### Publication series

Name | Lecture Notes in Computational Science and Engineering |
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ISSN (Print) | 1439-7358 |

### Conference

Conference | International Congress on Mathematical Software 2020 |
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Abbreviated title | ICMS 2020 |

Country | Germany |

City | Braunschweig |

Period | 13/07/20 → 16/07/20 |

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## Cite this

Florescu, D., & England, M. (Accepted/In press). A machine learning based software pipeline to pick the variable ordering for algorithms with polynomial inputs. In

*Mathematical Software - ICMS 2020*(Vol. (In-Press), pp. (In-Press)). (Lecture Notes in Computational Science and Engineering). Springer International Publishing.