On the implementation of CGS real QE

Ryoya Fukasaku, Hidenao Iwane, Yosuke Sato

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

4 Citations (Scopus)

Abstract

A CGS real QE method is a real quantifier elimination (QE) method which is composed of the computation of comprehensive Gröbner systems (CGSs) based on the theory of real root counting. Its fundamental algorithm was first introduced by Weispfenning in 1998. We further improved the algorithm in 2015 so that we can make a satisfactorily practical implementation. For its efficient implementation, there are several key issues we have to take into account. In this extended abstract we introduce them together with some important techniques for making an efficient CGS real QE implementation.

Original languageEnglish
Title of host publicationMathematical Software - 5th International Conference, ICMS 2016, Proceedings
EditorsGert-Martin Greuel, Andrew Sommese, Thorsten Koch, Peter Paule
PublisherSpringer Verlag
Pages165-172
Number of pages8
ISBN (Print)9783319424316
DOIs
Publication statusPublished - Jan 1 2016
Externally publishedYes
Event5th International Conference on Mathematical Software, ICMS 2016 - Berlin, Germany
Duration: Jul 11 2016Jul 14 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9725
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other5th International Conference on Mathematical Software, ICMS 2016
CountryGermany
CityBerlin
Period7/11/167/14/16

Fingerprint

Quantifier Elimination
Real Roots
Efficient Implementation
Counting

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Fukasaku, R., Iwane, H., & Sato, Y. (2016). On the implementation of CGS real QE. In G-M. Greuel, A. Sommese, T. Koch, & P. Paule (Eds.), Mathematical Software - 5th International Conference, ICMS 2016, Proceedings (pp. 165-172). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9725). Springer Verlag. https://doi.org/10.1007/978-3-319-42432-3_21

On the implementation of CGS real QE. / Fukasaku, Ryoya; Iwane, Hidenao; Sato, Yosuke.

Mathematical Software - 5th International Conference, ICMS 2016, Proceedings. ed. / Gert-Martin Greuel; Andrew Sommese; Thorsten Koch; Peter Paule. Springer Verlag, 2016. p. 165-172 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9725).

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

Fukasaku, R, Iwane, H & Sato, Y 2016, On the implementation of CGS real QE. in G-M Greuel, A Sommese, T Koch & P Paule (eds), Mathematical Software - 5th International Conference, ICMS 2016, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9725, Springer Verlag, pp. 165-172, 5th International Conference on Mathematical Software, ICMS 2016, Berlin, Germany, 7/11/16. https://doi.org/10.1007/978-3-319-42432-3_21
Fukasaku R, Iwane H, Sato Y. On the implementation of CGS real QE. In Greuel G-M, Sommese A, Koch T, Paule P, editors, Mathematical Software - 5th International Conference, ICMS 2016, Proceedings. Springer Verlag. 2016. p. 165-172. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-42432-3_21
Fukasaku, Ryoya ; Iwane, Hidenao ; Sato, Yosuke. / On the implementation of CGS real QE. Mathematical Software - 5th International Conference, ICMS 2016, Proceedings. editor / Gert-Martin Greuel ; Andrew Sommese ; Thorsten Koch ; Peter Paule. Springer Verlag, 2016. pp. 165-172 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
@inproceedings{6327679b42fa4b918b7d12eb5ef51dbf,
title = "On the implementation of CGS real QE",
abstract = "A CGS real QE method is a real quantifier elimination (QE) method which is composed of the computation of comprehensive Gr{\"o}bner systems (CGSs) based on the theory of real root counting. Its fundamental algorithm was first introduced by Weispfenning in 1998. We further improved the algorithm in 2015 so that we can make a satisfactorily practical implementation. For its efficient implementation, there are several key issues we have to take into account. In this extended abstract we introduce them together with some important techniques for making an efficient CGS real QE implementation.",
author = "Ryoya Fukasaku and Hidenao Iwane and Yosuke Sato",
year = "2016",
month = "1",
day = "1",
doi = "10.1007/978-3-319-42432-3_21",
language = "English",
isbn = "9783319424316",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "165--172",
editor = "Gert-Martin Greuel and Andrew Sommese and Thorsten Koch and Peter Paule",
booktitle = "Mathematical Software - 5th International Conference, ICMS 2016, Proceedings",
address = "Germany",

}

TY - GEN

T1 - On the implementation of CGS real QE

AU - Fukasaku, Ryoya

AU - Iwane, Hidenao

AU - Sato, Yosuke

PY - 2016/1/1

Y1 - 2016/1/1

N2 - A CGS real QE method is a real quantifier elimination (QE) method which is composed of the computation of comprehensive Gröbner systems (CGSs) based on the theory of real root counting. Its fundamental algorithm was first introduced by Weispfenning in 1998. We further improved the algorithm in 2015 so that we can make a satisfactorily practical implementation. For its efficient implementation, there are several key issues we have to take into account. In this extended abstract we introduce them together with some important techniques for making an efficient CGS real QE implementation.

AB - A CGS real QE method is a real quantifier elimination (QE) method which is composed of the computation of comprehensive Gröbner systems (CGSs) based on the theory of real root counting. Its fundamental algorithm was first introduced by Weispfenning in 1998. We further improved the algorithm in 2015 so that we can make a satisfactorily practical implementation. For its efficient implementation, there are several key issues we have to take into account. In this extended abstract we introduce them together with some important techniques for making an efficient CGS real QE implementation.

UR - http://www.scopus.com/inward/record.url?scp=84978791363&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84978791363&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-42432-3_21

DO - 10.1007/978-3-319-42432-3_21

M3 - Conference contribution

AN - SCOPUS:84978791363

SN - 9783319424316

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

SP - 165

EP - 172

BT - Mathematical Software - 5th International Conference, ICMS 2016, Proceedings

A2 - Greuel, Gert-Martin

A2 - Sommese, Andrew

A2 - Koch, Thorsten

A2 - Paule, Peter

PB - Springer Verlag

ER -