### Abstract

An algorithm we have introduced has a great effect on quantifier elimination of a first order formula containing many equalities. When the parametric ideal generated by the underlying equalities is not radical, however, our algorithm tends to produce an unnecessarily complicated formula. In this short paper, we show a result concerning Hermitian quadratic forms. It enables us to improve our algorithm so that we can get a simple formula without any radical computation.

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 | 258-263 |

Number of pages | 6 |

ISBN (Print) | 9783319724522 |

DOIs | |

Publication status | Published - Jan 1 2017 |

Externally published | Yes |

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

### 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 | 11/15/17 → 11/17/17 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Mathematical Aspects of Computer and Information Sciences - 7th International Conference, MACIS 2017, Proceedings*(pp. 258-263). (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_18

**On real roots counting for non-radical parametric ideals.** / Fukasaku, Ryoya; Sato, Yosuke.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Mathematical Aspects of Computer and Information Sciences - 7th International Conference, MACIS 2017, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10693 LNCS, Springer Verlag, pp. 258-263, 7th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2017, Vienna, Austria, 11/15/17. https://doi.org/10.1007/978-3-319-72453-9_18

}

TY - GEN

T1 - On real roots counting for non-radical parametric ideals

AU - Fukasaku, Ryoya

AU - Sato, Yosuke

PY - 2017/1/1

Y1 - 2017/1/1

N2 - An algorithm we have introduced has a great effect on quantifier elimination of a first order formula containing many equalities. When the parametric ideal generated by the underlying equalities is not radical, however, our algorithm tends to produce an unnecessarily complicated formula. In this short paper, we show a result concerning Hermitian quadratic forms. It enables us to improve our algorithm so that we can get a simple formula without any radical computation.

AB - An algorithm we have introduced has a great effect on quantifier elimination of a first order formula containing many equalities. When the parametric ideal generated by the underlying equalities is not radical, however, our algorithm tends to produce an unnecessarily complicated formula. In this short paper, we show a result concerning Hermitian quadratic forms. It enables us to improve our algorithm so that we can get a simple formula without any radical computation.

UR - http://www.scopus.com/inward/record.url?scp=85039415126&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85039415126&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-72453-9_18

DO - 10.1007/978-3-319-72453-9_18

M3 - Conference contribution

AN - SCOPUS:85039415126

SN - 9783319724522

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 258

EP - 263

BT - Mathematical Aspects of Computer and Information Sciences - 7th International Conference, MACIS 2017, Proceedings

A2 - Kotsireas, Ilias S.

A2 - Blomer, Johannes

A2 - Simos, Dimitris E.

A2 - Kutsia, Temur

PB - Springer Verlag

ER -