On QE algorithms over an algebraically closed field based on comprehensive Gröbner systems

DOI10.1007/s11786-015-0237-xzbMath1341.68311OpenAlexW2116273190MaRDI QIDQ748755

Yosuke Sato, Shutaro Inoue, Ryoya Fukasaku

Publication date: 30 October 2015

Published in: Mathematics in Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11786-015-0237-x

zbMATH Keywords

quantifier eliminationalgebraically closed fieldcomprehensive Gröbner system

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30)

Related Items (3)

Generic Gröbner basis of a parametric ideal and its application to a comprehensive Gröbner system ⋮ A survey on algorithms for computing comprehensive Gröbner systems and comprehensive Gröbner bases ⋮ Complexity bounds on Semaev's naive index calculus method for ECDLP

Uses Software

• Maple
• Mathematica
• PGB
• Risa/Asir
• HOL Light

Cites Work

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• Comprehensive Gröbner bases
• On the stability of Gröbner bases under specializations
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• A new algorithm for computing comprehensive Gröbner systems
• A simple algorithm to compute comprehensive Gröbner bases using Gröbner bases
• 55th International Mathematical Olympiad
• Comprehensive Triangular Decomposition
• ZERO DECOMPOSITION THEOREMS FOR COUNTING THE NUMBER OF SOLUTIONS FOR PARAMETRIC EQUATION SYSTEMS
• Algorithms in real algebraic geometry
• Degree reduction under specialization

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