Border bases for lattice ideals

DOI10.1016/j.jsc.2016.08.005zbMath1356.13034arXiv1608.08004OpenAlexW2514557457MaRDI QIDQ321275

Alessandro Logar, Giandomenico Boffi

Publication date: 13 October 2016

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

Full work available at URL: https://arxiv.org/abs/1608.08004

zbMATH Keywords

Gröbner basisborder basislattice ideals

Mathematics Subject Classification ID

Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Combinatorial aspects of commutative algebra (05E40)

Uses Software

• CoCoA
• Normaliz
• SageMath
• 4ti2
• Algorithm 457

Cites Work

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• Computing Gröbner bases of pure binomial ideals via submodules of \(\mathbb Z^n\)
• Constructions and complexity of secondary polytopes
• Computing border bases
• A note on the problem of reporting maximal cliques
• Stable border bases for ideals of points
• The Gröbner fan of an ideal
• Computing toric ideals
• Characterizations of border bases
• Gröbner bases of toric varieties
• Gröbner bases of lattices, corner polyhedra, and integer programming
• Gröbner bases of ideals defined by functionals with an application to ideals of projective points
• Stable normal forms for polynomial system solving
• Toric border basis
• Algorithm 457: finding all cliques of an undirected graph

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