Invariant \(\mathrm G^2\mathrm V\) algorithm for computing SAGBI-Gröbner bases

DOI10.1007/s11425-012-4506-8zbMath1281.13018OpenAlexW2040590588MaRDI QIDQ382761

Benyamin M.-Alizadeh, Amir Hashemi, Monireh Riahi

Publication date: 22 November 2013

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-012-4506-8

zbMATH Keywords

\(\mathrm G^2\mathrm V\) algorithminvariant \(\mathrm F_5\) algorithminvariant \(\mathrm G^2\mathrm V\) algorithmSAGBI-Gröbner bases

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) Actions of groups on commutative rings; invariant theory (13A50)

Related Items

InvariantG2V.mpl

Uses Software

• Maple
• F5C
• Isrewritten.mpl

Cites Work

• The F5 algorithm in Buchberger's style
• Extended \(F_5\) criteria
• F5C: A variant of Faugère's F5 algorithm with reduced Gröbner bases
• Applying IsRewritten criterion on Buchberger algorithm
• On an installation of Buchberger's algorithm
• A constructive description of SAGBI bases for polynomial invariants of permutation groups
• SAGBI and SAGBI-Gröbner bases over principal ideal domains
• An algorithm to calculate optimal homogeneous systems of parameters
• A new efficient algorithm for computing Gröbner bases \((F_4)\)
• Computational invariant theory
• Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay
• The infiniteness of the SAGBI bases for certain invariant rings.
• Analogs of Gröbner bases in polynomial rings over a ring
• Calculating invariant rings of finite groups over arbitrary fields
• Solving systems of polynomial equations with symmetries using SAGBI-Gröbner bases
• A new incremental algorithm for computing Groebner bases
• A new framework for computing Gröbner bases
• A generalized criterion for signature related Gröbner basis algorithms
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