Involutive bases algorithm incorporating F\(_5\) criterion

DOI10.1016/j.jsc.2013.08.002zbMath1435.68391arXiv1306.6811OpenAlexW2964031943MaRDI QIDQ2437322

Benyamin M.-Alizadeh, Vladimir P. Gerdt, Amir Hashemi

Publication date: 3 March 2014

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

Full work available at URL: https://arxiv.org/abs/1306.6811

zbMATH Keywords

Gröbner basesinvolutive basesinvolutive divisionBuchberger's criteriaF\(_5\) criterionG\(^2\)V algorithm

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

A survey on signature-based algorithms for computing Gröbner bases ⋮ Combinatorial decompositions for monomial ideals ⋮ Improved Computation of Involutive Bases

Uses Software

• Ginv
• Maple
• PoSSo
• Janet
• F5C
• G2V.mpl

Cites Work

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• The F5 algorithm in Buchberger's style
• Extended \(F_5\) criteria
• F5C: A variant of Faugère's F5 algorithm with reduced Gröbner bases
• Specialized computer algebra system GINV
• On selection of nonmultiplicative prolongations in computation of Janet bases
• Involution. The formal theory of differential equations and its applications in computer algebra
• On an installation of Buchberger's algorithm
• The theory of involutive divisions and an application to Hilbert function computations
• A new efficient algorithm for computing Gröbner bases \((F_4)\)
• On an algorithmic optimization in computation of involutive bases
• Involutive bases of polynomial ideals
• Effectiveness of involutive criteria in computation of polynomial Janet bases
• Detecting unnecessary reductions in an involutive basis computation
• A new incremental algorithm for computing Groebner bases
• Involutive Division Generated by an Antigraded Monomial Ordering
• Using Algebraic Geometry
• Signature-based algorithms to compute Gröbner bases
• A generalized criterion for signature related Gröbner basis algorithms