On real roots counting for non-radical parametric ideals

Ryoya Fukasaku; Yosuke Sato

doi:10.1007/978-3-319-72453-9_18

On real roots counting for non-radical parametric ideals

Ryoya Fukasaku, Yosuke Sato

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

1 Citation (Scopus)

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
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	https://doi.org/10.1007/978-3-319-72453-9_18
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)
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
Country	Austria
City	Vienna
Period	11/15/17 → 11/17/17

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

Access to Document

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

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Cite this

Fukasaku, R., & Sato, Y. (2017). On real roots counting for non-radical parametric ideals. 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. 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.

Mathematical Aspects of Computer and Information Sciences - 7th International Conference, MACIS 2017, Proceedings. ed. / Ilias S. Kotsireas; Johannes Blomer; Dimitris E. Simos; Temur Kutsia. Springer Verlag, 2017. p. 258-263 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10693 LNCS).

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

Fukasaku, R & Sato, Y 2017, On real roots counting for non-radical parametric ideals. in IS Kotsireas, J Blomer, DE Simos & T Kutsia (eds), 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

Fukasaku R, Sato Y. On real roots counting for non-radical parametric ideals. In Kotsireas IS, Blomer J, Simos DE, Kutsia T, editors, Mathematical Aspects of Computer and Information Sciences - 7th International Conference, MACIS 2017, Proceedings. Springer Verlag. 2017. p. 258-263. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-72453-9_18

Fukasaku, Ryoya ; Sato, Yosuke. / On real roots counting for non-radical parametric ideals. Mathematical Aspects of Computer and Information Sciences - 7th International Conference, MACIS 2017, Proceedings. editor / Ilias S. Kotsireas ; Johannes Blomer ; Dimitris E. Simos ; Temur Kutsia. Springer Verlag, 2017. pp. 258-263 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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