Ideals Modulo a Prime

DOI10.1142/S0219498821500420zbMath1472.13043arXiv1801.06112OpenAlexW2995901691WikidataQ126587676 ScholiaQ126587676MaRDI QIDQ4988232

Anna Maria Bigatti, John Abbott, Lorenzo Robbiano

Publication date: 12 May 2021

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.06112

zbMATH Keywords

Gröbner basesmodularidealsterm orderings

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Computational aspects of algebraic surfaces (14Q10) Software, source code, etc. for problems pertaining to commutative algebra (13-04) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) (13P25)

Related Items

Modular computations of standard bases for subalgebras, \textsc{Sagbi} combinatorics of maximal minors and a \textsc{Sagbi} algorithm

Uses Software

• CoCoA
• CoCoALib
• gmp
• SINGULAR

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Implicitization of hypersurfaces
• The Gröbner fan of an ideal
• A p-adic approach to the computation of Gröbner bases
• Modular algorithms for computing Gröbner bases.
• Fault-tolerant modular reconstruction of rational numbers
• A modular method to compute the rational univariate representation of zero-dimensional ideals
• Usage of modular techniques for efficient computation of ideal operations
• Computing and using minimal polynomials
• Parallelization of modular algorithms
• Gröbner bases with coefficients in rings
• Implementation of prime decomposition of polynomial ideals over small finite fields
• Computational Linear and Commutative Algebra
• Bad Primes in Computational Algebraic Geometry
• Maximal quotient rational reconstruction
• Modular Algorithms for Computing Minimal Associated Primes and Radicals of Polynomial Ideals
• SINGULAR