### Abstract

We present upper bounds on the bit-size of coefficients of non-radical purely lexicographical Gröbner bases (triangular sets) in dimension zero. This extends a previous work [4], constrained to radical triangular sets; it follows the same technical steps, based on interpolation. However, key notion of height of varieties is not available for points with multiplicities; therefore the bounds obtained are thus less universal and depend on some input data. We also introduce a related family of non-monic polynomials that have smaller coefficients, and smaller bounds. It is not obvious to compute them from the initial triangular set though.

Original language | English |
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Title of host publication | Mathematical Aspects of Computer and Information Sciences - 7th International Conference, MACIS 2017, Proceedings |

Editors | Ilias S. Kotsireas, Johannes Blomer, Dimitris E. Simos, Temur Kutsia |

Publisher | Springer Verlag |

Pages | 264-269 |

Number of pages | 6 |

ISBN (Print) | 9783319724522 |

DOIs | |

Publication status | Published - 2017 Jan 1 |

Externally published | Yes |

Event | 7th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2017 - Vienna, Austria Duration: 2017 Nov 15 → 2017 Nov 17 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 10693 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 7th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2017 |
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Country | Austria |

City | Vienna |

Period | 17/11/15 → 17/11/17 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

Dahan, X. (2017). On the bit-size of non-radical triangular sets. In I. S. Kotsireas, J. Blomer, D. E. Simos, & T. Kutsia (Eds.),

*Mathematical Aspects of Computer and Information Sciences - 7th International Conference, MACIS 2017, Proceedings*(pp. 264-269). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10693 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-72453-9_19