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Algorithms for computing Gröbner bases of polynomial ideals over various Euclidean rings

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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1007/3-540-09519-5_52openalex-snapshot

A criterion for detecting unnecessary reductions in the construction of Gröbner-bases

inferredcites →https://doi.org/10.1007/978-3-642-81955-1_23openalex-snapshot

Simple Word Problems in Universal Algebras

inferredcites →https://doi.org/10.1007/978-3-7091-3406-1_2openalex-snapshot

Algebraic Simplification

inferredcites →https://doi.org/10.1016/0022-0000(81)90002-7openalex-snapshot

A complete proof of correctness of the Knuth-Bendix completion algorithm

inferredcites →https://doi.org/10.1016/b978-0-08-012975-4.50028-xopenalex-snapshot

Simple Word Problems in Universal Algebras††The work reported in this paper was supported in part by the U.S. Office of Naval Research.

inferredcites →https://doi.org/10.1016/s0924-6509(08)x7033-3openalex-snapshot

Algebra of Polynomials

inferredcites →https://doi.org/10.1080/00029890.1952.11988146openalex-snapshot

A Canonical Basis for the Ideals of a Polynomial Domain

inferredcites →https://doi.org/10.1137/0214073openalex-snapshot

The Knuth-Bendix Completion Procedure and Thue Systems

inferredcites →https://doi.org/10.1145/1088216.1088219openalex-snapshot

A theoretical basis for the reduction of polynomials to canonical forms

inferredcites →https://doi.org/10.1145/1089235.1089238openalex-snapshot

A simplified proof of the characterization theorem for Gröbner-bases

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Computer algebra symbolic and algebraic computation

inferredcites →https://doi.org/10.1145/322217.322230openalex-snapshot

Confluent Reductions: Abstract Properties and Applications to Term Rewriting Systems

inferredcites →https://doi.org/10.1145/800205.806353openalex-snapshot

Canonical representatives for residue classes of a polynomial ideal

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

inferred← citeshttps://doi.org/10.1006/jsco.1999.0262openalex-snapshot

A Categorical Critical-pair Completion Algorithm

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A path ordering for proving termination of term rewriting systems

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Basic features and development of the critical-pair/completion procedure

inferred← citeshttps://doi.org/10.1007/3-540-15976-2_17openalex-snapshot

An ideal-theoretic approach to word problems and unification problems over finitely presented commutative algebras

inferred← citeshttps://doi.org/10.1007/3-540-15983-5_1openalex-snapshot

Computer algebra: Past and future

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An overview of completion algorithms

inferred← citeshttps://doi.org/10.1007/3-540-51081-8_110openalex-snapshot

Generalized Gröbner bases: Theory and applications. A condensation

inferred← citeshttps://doi.org/10.1007/3-540-51517-8_137openalex-snapshot

Gröbner bases for polynomial ideals over commutative regular rings

inferred← citeshttps://doi.org/10.1007/978-0-585-33247-5_10openalex-snapshot

Gröbner Bases for Polynomial Ideals

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Theorem Proving for Verification (Invited Tutorial)

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Automating Elementary Number-Theoretic Proofs Using Gröbner Bases

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A solution to Kronecker's problem

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On Gr�bner bases under specialization

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Shirshov composition techniques in Lie superalgebras (noncommutative Gröbner bases)

inferred← citeshttps://doi.org/10.1007/bfb0039183openalex-snapshot

Standard bases and non-noetherianity: Non-commutative polynomial rings

inferred← citeshttps://doi.org/10.1007/bfb0039192openalex-snapshot

Some bounds for the construction of Gröbner bases

inferred← citeshttps://doi.org/10.1016/0021-8693(91)90166-6openalex-snapshot

The reduction ring property is hereditary

inferred← citeshttps://doi.org/10.1016/j.jsc.2016.08.009openalex-snapshot

Standard bases in mixed power series and polynomial rings over rings

inferred← citeshttps://doi.org/10.1016/j.jsc.2019.10.020openalex-snapshot

Efficient Gröbner bases computation over principal ideal rings

inferred← citeshttps://doi.org/10.1016/s0304-3975(00)00172-9openalex-snapshot

Computational ideal theory in finitely generated extension rings

inferred← citeshttps://doi.org/10.1016/s0747-7171(86)80025-6openalex-snapshot

Computer Algebra: Past and Future

inferred← citeshttps://doi.org/10.1016/s0747-7171(87)80020-2openalex-snapshot

History and basic features of the critical-pair/completion procedure

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On the construction of Gröbner bases using syzygies

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A Tutte Polynomial for Coloured Graphs

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Standard Gröbner-Shirshov Bases of Free Algebras Over Rings, I

inferred← citeshttps://doi.org/10.1145/134342.134344openalex-snapshot

Nonexistence of degree bounds of various bases for ideals of polynomials over the integers

inferred← citeshttps://doi.org/10.1145/164081.164144openalex-snapshot

Geometry theorem proving in vector spaces by means of Gröbner bases

inferred← citeshttps://doi.org/10.1145/174130.174133openalex-snapshot

Unification in commutative theories, Hilbert's basis theorem, and Gröbner bases

inferred← citeshttps://doi.org/10.1145/32439.32479openalex-snapshot

Geometry theorem proving using Hilbert's Nullstellensatz

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Effective computation of strong Gröbner bases over Euclidean domains

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