### Abstract

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.

Original language | English |
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Title of host publication | 18th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing |

Place of Publication | California |

Publisher | IEEE Computer Society |

Pages | 45-52 |

ISBN (Print) | 978-1-5090-5707-8 |

DOIs | |

Publication status | Published - 26 Jan 2017 |

Event | International Symposium on Symbolic and Numeric Algorithms for Scientific Computing - Timisoara, Romania Duration: 24 Sep 2016 → 27 Sep 2016 |

### Conference

Conference | International Symposium on Symbolic and Numeric Algorithms for Scientific Computing |
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Country | Romania |

City | Timisoara |

Period | 24/09/16 → 27/09/16 |

### Bibliographical note

© 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. ISSN 2470-881X### Keywords

- preconditioning
- machine learning
- support vector machine
- computer algebra
- cylindrical algebraic decomposition
- groebner bases
- Computers
- Algebra
- Machine learning algorithms
- Support vector machines
- Measurement
- Electronic mail
- Complexity theory

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## Cite this

Huang, Z., England, M., Davenport, J. H., & Paulson, L. C. (2017). Using Machine Learning to Decide When to Precondition Cylindrical Algebraic Decomposition With Groebner Bases. In

*18th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing*(pp. 45-52). California: IEEE Computer Society. https://doi.org/10.1109/SYNASC.2016.020