Improving the DISPGB algorithm using the discriminant ideal

DOI10.1016/j.jsc.2005.09.013zbMath1121.13031arXivmath/0601763OpenAlexW2168553897MaRDI QIDQ2457398

Montserrat Manubens, Antonio Montes

Publication date: 23 October 2007

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0601763

zbMATH Keywords

parametric polynomial systemcomprehensive Gröbner basesdiscriminant ideal

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10)

Related Items (20)

Gröbner systems conversion ⋮ Computing comprehensive Gröbner systems: a comparison of two methods ⋮ Comprehensive Gröbner basis theory for a parametric polynomial ideal and the associated completion algorithm ⋮ Gröbner bases for polynomial systems with parameters ⋮ On the computation of parametric Gröbner bases for modules and syzygies ⋮ An efficient method of finding new symplectic schemes for Hamiltonian mechanics problems with the aid of parametric Gröbner bases ⋮ Generic Gröbner basis of a parametric ideal and its application to a comprehensive Gröbner system ⋮ Boolean Gröbner bases ⋮ A survey on algorithms for computing comprehensive Gröbner systems and comprehensive Gröbner bases ⋮ Solving parametric polynomial systems ⋮ Minimal polynomial systems for parametric matrices ⋮ Parametric FGLM algorithm ⋮ Properties of regular systems and algorithmic improvements for regular decomposition ⋮ On the Computation of Elimination Ideals of Boolean Polynomial Rings ⋮ Erratum to ``A new algorithm for discussing Gröbner bases with parameters [J. Symbolic Comput. 33 (1-2) (2002) 183-208] ⋮ Comprehensive Gröbner Bases in a Java Computer Algebra System ⋮ Cylinders Through Five Points: Complex and Real Enumerative Geometry ⋮ Automatic Discovery of Geometry Theorems Using Minimal Canonical Comprehensive Gröbner Systems ⋮ Minimal canonical comprehensive Gröbner systems ⋮ On the Computation of Comprehensive Boolean Gröbner Bases

Uses Software

• dpgb

Cites Work

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• An algorithm for solving parametric linear systems
• Comprehensive Gröbner bases
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• A new algorithm for discussing Gröbner bases with parameters.
• An alternative approach to comprehensive Gröbner bases
• Canonical comprehensive Gröbner bases
• Dynamic evaluation and algebraic closure in Axiom
• Solving Polynomial Systems Using a Branch and Prune Approach
• Solving the load flow problem using Gröbner basis
• Gröbner bases specialization through Hilbert functions
• Properties of Gröbner bases under specializations
• Degree reduction under specialization

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