Noether normalization guided by monomial cone decompositions

DOI10.1016/j.jsc.2009.02.004zbMath1190.13026OpenAlexW1984152394MaRDI QIDQ840706

Daniel Robertz

Publication date: 14 September 2009

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

Full work available at URL: https://doi.org/10.1016/j.jsc.2009.02.004

zbMATH Keywords

involutive basesJanet basesNoether normalizationStanley decompositionssparse coordinate change

Mathematics Subject Classification ID

Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes (13F55) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Computational aspects and applications of commutative rings (13Pxx)

Related Items (7)

Deterministic genericity for polynomial ideals ⋮ Recursive structures in involutive bases theory ⋮ Effective Genericity, δ-Regularity and Strong Noether Position ⋮ An \(L_2\)-quotient algorithm for finitely presented groups. ⋮ A combinatorial approach to involution and \(\delta \)-regularity. II: Structure analysis of polynomial modules with Pommaret bases ⋮ Nœther bases and their applications ⋮ Complementary decompositions of monomial ideals and involutive bases

Uses Software

• Macaulay2
• Magma
• SINGULAR
• Janet
• noether.lib

Cites Work

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• Computing combinatorial decompositions of rings
• The theory of involutive divisions and an application to Hilbert function computations
• Finding sparse systems of parameters
• The Magma algebra system. I: The user language
• Involutive bases of polynomial ideals
• Janet's approach to presentations and resolutions for polynomials and linear PDEs
• Gröbner bases and Stanley decompositions of determinantal ideals
• An efficient algebraic algorithm for the geometric completion to involution
• Combinatorics and commutative algebra.
• Bruno Buchberger's PhD thesis 1965: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal. Translation from the German
• Saturation and Castelnuovo-Mumford regularity
• Characteristic-free bounds for the Castelnuovo–Mumford regularity
• Efficient Algorithms for Computing Nœther Normalization
• SINGULAR
• Computational methods of commutative algebra and algebraic geometry. With chapters by David Eisenbud, Daniel R. Grayson, Jürgen Herzog and Michael Stillman

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