On the implementation of CGS real QE

Ryoya Fukasaku; Hidenao Iwane; Yosuke Sato

doi:10.1007/978-3-319-42432-3_21

On the implementation of CGS real QE

Ryoya Fukasaku, Hidenao Iwane, Yosuke Sato

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

5 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 language	English
Title of host publication	Mathematical Software - 5th International Conference, ICMS 2016, Proceedings
Editors	Gert-Martin Greuel, Andrew Sommese, Thorsten Koch, Peter Paule
Publisher	Springer Verlag
Pages	165-172
Number of pages	8
ISBN (Print)	9783319424316
DOIs	https://doi.org/10.1007/978-3-319-42432-3_21
Publication status	Published - Jan 1 2016
Externally published	Yes
Event	5th International Conference on Mathematical Software, ICMS 2016 - Berlin, Germany Duration: Jul 11 2016 → Jul 14 2016

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9725
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	5th International Conference on Mathematical Software, ICMS 2016
Country/Territory	Germany
City	Berlin
Period	7/11/16 → 7/14/16

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

Access to Document

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

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 proceeding › Conference 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)). doi: 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)).

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On the implementation of CGS real QE

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