Real quantifier elimination by computation of comprehensive Gröbner systems

Ryoya Fukasaku, Hidenao Iwane, Yosuke Sato

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

9 Citations (Scopus)

Abstract

A real quantifier elimination method based on the theory of real root counting and the computation of comprehensive Gröbner systems introduced by V. Weispfenning is studied in more detail. We introduce a simpler and more intuitive algorithm which is shown to be an improvement of the original algorithm. Our algorithm is implemented on the computer algebra system Maple using a recent algorithm to compute comprehensive Gröbner systems together with several simplification techniques. According to our computation experiments, our program is superior to other existing implementations for many examples which contain many equalities.

Original languageEnglish
Title of host publicationISSAC 2015 - Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation
PublisherAssociation for Computing Machinery
Pages173-180
Number of pages8
ISBN (Electronic)9781450334358
DOIs
Publication statusPublished - Jun 24 2015
Event40th ACM International Symposium on Symbolic and Algebraic Computation, ISSAC 2015 - Bath, United Kingdom
Duration: Jul 6 2015Jul 9 2015

Publication series

NameProceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC
Volume2015-June

Conference

Conference40th ACM International Symposium on Symbolic and Algebraic Computation, ISSAC 2015
CountryUnited Kingdom
CityBath
Period7/6/157/9/15

Fingerprint

Quantifier Elimination
Real Roots
Computer algebra system
Maple
Simplification
Intuitive
Counting
Equality
Experiment

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Fukasaku, R., Iwane, H., & Sato, Y. (2015). Real quantifier elimination by computation of comprehensive Gröbner systems. In ISSAC 2015 - Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation (pp. 173-180). (Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC; Vol. 2015-June). Association for Computing Machinery. https://doi.org/10.1145/2755996.2756646

Real quantifier elimination by computation of comprehensive Gröbner systems. / Fukasaku, Ryoya; Iwane, Hidenao; Sato, Yosuke.

ISSAC 2015 - Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation. Association for Computing Machinery, 2015. p. 173-180 (Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC; Vol. 2015-June).

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

Fukasaku, R, Iwane, H & Sato, Y 2015, Real quantifier elimination by computation of comprehensive Gröbner systems. in ISSAC 2015 - Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation. Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC, vol. 2015-June, Association for Computing Machinery, pp. 173-180, 40th ACM International Symposium on Symbolic and Algebraic Computation, ISSAC 2015, Bath, United Kingdom, 7/6/15. https://doi.org/10.1145/2755996.2756646
Fukasaku R, Iwane H, Sato Y. Real quantifier elimination by computation of comprehensive Gröbner systems. In ISSAC 2015 - Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation. Association for Computing Machinery. 2015. p. 173-180. (Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC). https://doi.org/10.1145/2755996.2756646
Fukasaku, Ryoya ; Iwane, Hidenao ; Sato, Yosuke. / Real quantifier elimination by computation of comprehensive Gröbner systems. ISSAC 2015 - Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation. Association for Computing Machinery, 2015. pp. 173-180 (Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC).
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