On real roots counting for non-radical parametric ideals

Ryoya Fukasaku, Yosuke Sato

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish
Title of host publicationMathematical Aspects of Computer and Information Sciences - 7th International Conference, MACIS 2017, Proceedings
EditorsIlias S. Kotsireas, Johannes Blomer, Dimitris E. Simos, Temur Kutsia
PublisherSpringer Verlag
Pages258-263
Number of pages6
ISBN (Print)9783319724522
DOIs
Publication statusPublished - Jan 1 2017
Externally publishedYes
Event7th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2017 - Vienna, Austria
Duration: Nov 15 2017Nov 17 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10693 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference7th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2017
CountryAustria
CityVienna
Period11/15/1711/17/17

Fingerprint

Real Roots
Counting
Equality
Quantifier Elimination
Quadratic form
Tend
First-order

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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 proceedingConference 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)).
@inproceedings{d57451ce3fad44bca81ef594d3eab5c7,
title = "On real roots counting for non-radical parametric ideals",
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.",
author = "Ryoya Fukasaku and Yosuke Sato",
year = "2017",
month = "1",
day = "1",
doi = "10.1007/978-3-319-72453-9_18",
language = "English",
isbn = "9783319724522",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "258--263",
editor = "Kotsireas, {Ilias S.} and Johannes Blomer and Simos, {Dimitris E.} and Temur Kutsia",
booktitle = "Mathematical Aspects of Computer and Information Sciences - 7th International Conference, MACIS 2017, Proceedings",
address = "Germany",

}

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

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 -