On continuity of the roots of a parametric zero dimensional multivariate polynomial ideal

Yosuke Sato, Ryoya Fukasaku, Hiroshi Sekigawa

研究成果: 著書/レポートタイプへの貢献会議での発言

1 引用 (Scopus)

抄録

Let F = ( f1 (Ā,X¯ ), . . ., fl (Ā,X¯ )) be a finite set of polynomials in Q[Ā,X¯ ] with variables Ā = A1, . . .,Am and X¯ = X1, . . .,Xn . We study the continuity of the map θ from an element ā of Cm to a subset of Cn defined by θ (ā) = “the zeros of the polynomial ideal hf1 (ā,X¯ ), . . ., fl (ā,X¯ )i”. Let G = ((G1, S1), . . ., (Gk , Sk )) be a comprehensive Gröbner system of hF i regarding Ā as parameters. By a basic property of a comprehensive Gröbner system, when the ideal hf1 (ā,X¯ ), . . ., fl (ā,X¯ )i is zero dimensional for some ā ∈ Si , it is also zero dimensional for any ā ∈ Si and the cardinality of θ (ā) is identical on Si counting their multiplicities. In this paper, we prove that θ is also continuous on Si . Our result ensures the correctness of an algorithm for real quantifier elimination one of the authors has recently developed.

元の言語英語
ホスト出版物のタイトルISSAC 2018 - Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation
出版者Association for Computing Machinery
ページ359-365
ページ数7
ISBN(電子版)9781450355506
DOI
出版物ステータス出版済み - 7 11 2018
外部発表Yes
イベント43rd ACM International Symposium on Symbolic and Algebraic Computation, ISSAC 2018 - New York, 米国
継続期間: 7 16 20187 19 2018

出版物シリーズ

名前Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC

会議

会議43rd ACM International Symposium on Symbolic and Algebraic Computation, ISSAC 2018
米国
New York
期間7/16/187/19/18

Fingerprint

Polynomial Ideals
Zero-dimensional
Multivariate Polynomials
Roots
Quantifier Elimination
Finite Set
Cardinality
Counting
Correctness
Multiplicity
Polynomial
Subset
Zero

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

これを引用

Sato, Y., Fukasaku, R., & Sekigawa, H. (2018). On continuity of the roots of a parametric zero dimensional multivariate polynomial ideal. : ISSAC 2018 - Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation (pp. 359-365). (Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC). Association for Computing Machinery. https://doi.org/10.1145/3208976.3209004

On continuity of the roots of a parametric zero dimensional multivariate polynomial ideal. / Sato, Yosuke; Fukasaku, Ryoya; Sekigawa, Hiroshi.

ISSAC 2018 - Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation. Association for Computing Machinery, 2018. p. 359-365 (Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC).

研究成果: 著書/レポートタイプへの貢献会議での発言

Sato, Y, Fukasaku, R & Sekigawa, H 2018, On continuity of the roots of a parametric zero dimensional multivariate polynomial ideal. : ISSAC 2018 - Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation. Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC, Association for Computing Machinery, pp. 359-365, 43rd ACM International Symposium on Symbolic and Algebraic Computation, ISSAC 2018, New York, 米国, 7/16/18. https://doi.org/10.1145/3208976.3209004
Sato Y, Fukasaku R, Sekigawa H. On continuity of the roots of a parametric zero dimensional multivariate polynomial ideal. : ISSAC 2018 - Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation. Association for Computing Machinery. 2018. p. 359-365. (Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC). https://doi.org/10.1145/3208976.3209004
Sato, Yosuke ; Fukasaku, Ryoya ; Sekigawa, Hiroshi. / On continuity of the roots of a parametric zero dimensional multivariate polynomial ideal. ISSAC 2018 - Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation. Association for Computing Machinery, 2018. pp. 359-365 (Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC).
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