Canonical comprehensive Gröbner bases

DOI10.1016/S0747-7171(03)00099-3zbMath1054.13015OpenAlexW3086943959MaRDI QIDQ1878493

Volker Weispfenning

Publication date: 20 August 2004

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

Full work available at URL: https://doi.org/10.1016/s0747-7171(03)00099-3

zbMATH Keywords

comprehensive Gröbner basesGröbner systemsuniformity in parameters

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 (15)

Gröbner systems conversion ⋮ Testing binomiality of chemical reaction networks using comprehensive Gröbner systems ⋮ Comprehensive Gröbner basis theory for a parametric polynomial ideal and the associated completion algorithm ⋮ Gröbner bases for polynomial systems with parameters ⋮ Generic Gröbner basis of a parametric ideal and its application to a comprehensive Gröbner system ⋮ Algorithms for computing greatest common divisors of parametric multivariate polynomials ⋮ Automated reducible geometric theorem proving and discovery by Gröbner basis method ⋮ A survey on algorithms for computing comprehensive Gröbner systems and comprehensive Gröbner bases ⋮ Improving the DISPGB algorithm using the discriminant ideal ⋮ Generalizing the Steiner-Lehmus theorem using the Gröbner cover ⋮ Gröbner bases for families of affine or projective schemes ⋮ Minimal polynomial systems for parametric matrices ⋮ Parametric FGLM algorithm ⋮ Minimal canonical comprehensive Gröbner systems ⋮ A Study on Gröbner Basis with Inexact Input

Uses Software

• Maple

Cites Work

• Formally \(p\)-adic fields
• Comprehensive Gröbner bases
• Direct methods for primary decomposition
• On Gröbner bases under specialization
• On the stability of Gröbner bases under specializations
• Algebraic solution of the load-flow problem for a 4-nodes electrical network
• A new algorithm for discussing Gröbner bases with parameters.
• Solving the load flow problem using Gröbner basis
• Degree reduction under specialization
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