A survey on algorithms for computing comprehensive Gröbner systems and comprehensive Gröbner bases
DOI10.1007/s11424-019-8357-zzbMath1417.68295OpenAlexW2913333968MaRDI QIDQ1730311
Dong Lu, Yao Sun, Ding-Kang Wang
Publication date: 6 March 2019
Published in: Journal of Systems Science and Complexity (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11424-019-8357-z
quantifier eliminationcomprehensive Gröbner systemparametric polynomial systemcomprehensive Gröbner basisdiscovering geometric theorems mechanically
Symbolic computation and algebraic computation (68W30) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Research exposition (monographs, survey articles) pertaining to computer science (68-02)
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- Gröbner bases for polynomial systems with parameters
- On QE algorithms over an algebraically closed field based on comprehensive Gröbner systems
- A quantifier-elimination based heuristic for automatically generating inductive assertions for programs
- Generic regular decompositions for parametric polynomial systems
- Minimal canonical comprehensive Gröbner systems
- Basic principles of mechanical theorem proving in elementary geometries
- An algorithm for solving parametric linear systems
- Comprehensive Gröbner bases
- On the stability of Gröbner bases under specializations
- A new algorithm for discussing Gröbner bases with parameters.
- Universal Gröbner basis for parametric polynomial ideals
- Solving the perspective-three-point problem using comprehensive Gröbner systems
- Automated reducible geometric theorem proving and discovery by Gröbner basis method
- An alternative approach to comprehensive Gröbner bases
- Canonical comprehensive Gröbner bases
- An efficient algorithm for computing a comprehensive Gröbner system of a parametric polynomial system
- An efficient method for computing comprehensive Gröbner bases
- Gröbner systems conversion
- Comprehensive Gröbner basis theory for a parametric polynomial ideal and the associated completion algorithm
- Parametric equation solving and quantifier elimination in finite fields with the characteristic set method
- Solving parametric polynomial systems
- Improving the DISPGB algorithm using the discriminant ideal
- The generic Gröbner walk
- Gröbner bases for families of affine or projective schemes
- Improving a CGS-QE Algorithm
- On the Implementation of CGS Real QE
- Real Quantifier Elimination by Computation of Comprehensive Gröbner Systems
- An Algorithm to Check Whether a Basis of a Parametric Polynomial System is a Comprehensive Gröbner Basis and the Associated Completion Algorithm
- A new algorithm for computing comprehensive Gröbner systems
- A simple algorithm to compute comprehensive Gröbner bases using Gröbner bases
- Comprehensive Triangular Decomposition
- A simple proof of the Beijing theorem
- Parametric Greatest Common Divisors using Comprehensive Gröbner Systems
- An Efficient Algorithm for Computing Parametric Multivariate Polynomial GCD
- Computing comprehensive Gröbner systems and comprehensive Gröbner bases simultaneously
- Automatic Discovery of Geometry Theorems Using Minimal Canonical Comprehensive Gröbner Systems
- Automated Deduction in Geometry
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