Bezoutian and quotient ring structure

DOI10.1016/j.jsc.2004.11.010zbMath1120.13035OpenAlexW2015821533MaRDI QIDQ2456551

Mourrain, Bernard

Publication date: 19 October 2007

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

Full work available at URL: https://doi.org/10.1016/j.jsc.2004.11.010

zbMATH Keywords

normal formlinear algebraresultantBezoutianpolynomial system solvingmultiplication matrixquotient ring structure

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Computational aspects and applications of commutative rings (13P99)

Related Items (7)

An FGLM-like algorithm for computing the radical of a zero-dimensional ideal ⋮ Further perspectives on elimination ⋮ On the computation of matrices of traces and radicals of ideals ⋮ A general framework for Noetherian well ordered polynomial reductions ⋮ HELP: a sparse error locator polynomial for BCH codes ⋮ Degröbnerization: a political manifesto ⋮ Effective algorithm for computing Noetherian operators of zero-dimensional ideals

Cites Work

• Le formalisme du résultant. (The formalism of resultant)
• Computing the isolated roots by matrix methods
• Residue currents and Bezout identities
• Bounds for the degrees and heights in the division problem
• Inertia forms and resultant: A formulary
• Implicitization of parametric curves and surfaces by using multidimensional Newton formulae
• Isolated points, duality and residues
• Straight-line programs in geometric elimination theory
• Generalized resultants over unirational algebraic varieties
• Algorithms for residues and Łojasiewicz exponents
• Sharp estimates for the arithmetic Nullstellensatz
• Bounds of traces in complete intersections and degrees in the Nullstellensatz
• Effective Bezout identities in \({\mathbb{Q}}[z_ 1,\dots ,z_ n\)]
• Computing Multidimensional Residues
• Resultant over the residual of a complete intersection.
• Explicit formulas for the multivariate resultant.
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