Computing a Gröbner basis of a polynomial ideal over a Euclidean domain

DOI10.1016/S0747-7171(88)80020-8zbMath0658.13016MaRDI QIDQ1111629

Deepak Kapur, Abdelilah Kandri Rody

Publication date: 1988

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

zbMATH Keywords

Buchberger's algorithmsGröbner basis algorithm for polynomial ideals over a Euclidean domain

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Software, source code, etc. for problems pertaining to commutative algebra (13-04) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Ideals and multiplicative ideal theory in commutative rings (13A15) Euclidean rings and generalizations (13F07)

Related Items (24)

Buchberger's algorithm: The term rewriter's point of view ⋮ Standard bases in mixed power series and polynomial rings over rings ⋮ Dynamical Gröbner bases ⋮ On the D-bases of polynomial ideals over principal ideal domains ⋮ Shirshov composition techniques in Lie superalgebras (noncommutative Gröbner bases) ⋮ Buchberger's algorithm: A constraint-based completion procedure ⋮ Signature Gröbner bases in free algebras over rings ⋮ GRÖBNER-SHIRSHOV BASIS FOR MONOMIALS SEMIRING OVER D-A RINGS ⋮ Modularity and Combination of Associative Commutative Congruence Closure Algorithms enriched with Semantic Properties ⋮ Standard bases over Euclidean domains ⋮ Efficient Gröbner bases computation over principal ideal rings ⋮ An extension of Gröbner basis theory to indexed polynomials without eliminations ⋮ A polynomial-time algorithm to compute generalized Hermite normal forms of matrices over \(\mathbb{Z} [x\)] ⋮ Semi-ring Based Gröbner–Shirshov Bases over a Noetherian Valuation Ring ⋮ Gröbner bases with coefficients in rings ⋮ A modular algorithm to compute the generalized Hermite normal form for \(\mathbb{Z}[x\)-lattices] ⋮ A general framework for Noetherian well ordered polynomial reductions ⋮ Standard Gröbner-Shirshov Bases of Free Algebras Over Rings, I ⋮ On lucky ideals for Gröbner basis computations ⋮ Toward involutive bases over effective rings ⋮ Non-commutative Gröbner bases in algebras of solvable type ⋮ Ideal membership in polynomial rings over the integers ⋮ A signature-based algorithm for computing Gröbner bases over principal ideal domains ⋮ On Gröbner bases under specialization

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Non-commutative Gröbner bases in algebras of solvable type
• On constructing bases for ideals in polynomial rings over the integers
• New constructive methods in classical ideal theory
• Lifting canonical algorithms from a ring R to the ring R[x]
• New decision algorithms for finitely presented commutative semigroups
• Über B. Buchbergers Verfahren, Systeme algebraischer Gleichungen zu lösen
• About the rewriting systems produced by the Knuth-Bendix completion algorithm
• Comments on the translation of my PhD thesis: ``An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal
• The Knuth-Bendix Completion Procedure and Thue Systems
• A simplified proof of the characterization theorem for Gröbner-bases
• Complete Sets of Reductions for Some Equational Theories
• Computer Algebra of Polynomials and Rational Functions
• Constructive Aspects of Noetherian Rings
• A Canonical Basis for the Ideals of a Polynomial Domain

This page was built for publication: Computing a Gröbner basis of a polynomial ideal over a Euclidean domain