On QE Algorithms over an Algebraically Closed Field Based on Comprehensive Gröbner Systems

Ryoya Fukasaku, Shutaro Inoue, Yosuke Sato

研究成果: ジャーナルへの寄稿記事

1 引用 (Scopus)

抄録

We introduce new algorithms for quantifier eliminations (QE) in the domain of an algebraically closed field. Our algorithms are based on the computation of comprehensive Gröbner systems (CGS). We study Suzuki–Sato’s CGS computation algorithm and its successors in more detail and modify them into an optimal form for applying to QE. Based on this modified algorithm, we introduce two QE algorithms. One is pursuing the simplest output quantifier free formula which employs only the computations of CGS. The other consists of parallel computations of CGS and GCD of parametric unary polynomials. It achieves faster computation time with reasonably simple output quantifier free formulas. Our implementation shows that in many examples our algorithms are superior to other existing algorithms such as a QE algorithm adopted in the Mathematica package Reduce and Resolve or a QE algorithm adopted in the Maple package Projection which are the most efficient existing implementations as far as we know.

元の言語英語
ページ(範囲)267-281
ページ数15
ジャーナルMathematics in Computer Science
9
発行部数3
DOI
出版物ステータス出版済み - 10 1 2015

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Quantifier Elimination
Algebraically closed
Quantifiers
Output
Maple
Unary
Mathematica
Parallel Computation
Efficient Implementation
Resolve
Polynomials
Projection
Polynomial

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

これを引用

On QE Algorithms over an Algebraically Closed Field Based on Comprehensive Gröbner Systems. / Fukasaku, Ryoya; Inoue, Shutaro; Sato, Yosuke.

:: Mathematics in Computer Science, 巻 9, 番号 3, 01.10.2015, p. 267-281.

研究成果: ジャーナルへの寄稿記事

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