Approximate computation of zero-dimensional polynomial ideals

DOI10.1016/j.jsc.2008.11.010zbMath1176.13003OpenAlexW1963730962MaRDI QIDQ731932

Hennie Poulisse, Martin Kreuzer, Sebastian Pokutta, Daniel Heldt

Publication date: 9 October 2009

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

Full work available at URL: https://doi.org/10.1016/j.jsc.2008.11.010

zbMATH Keywords

ideal membershipborder basisBuchberger-Möller algorithm

Mathematics Subject Classification ID

Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Computational aspects in algebraic geometry (14Q99)

Related Items

Subideal border bases ⋮ Deformations of border bases ⋮ Noise-tolerant algebraic method for reconstruction of nonlinear dynamical systems ⋮ Inverse multivariate polynomial root-finding: numerical implementations of the affine and projective Buchberger-Möller algorithm ⋮ Verification of a low-degree polynomial vanishing at empirical points ⋮ Computing border bases using mutant strategies ⋮ Simple varieties for limited precision points ⋮ Computing the state difference equations for discrete overdetermined linear \(m \operatorname{D}\) systems ⋮ Computing border bases without using a term ordering ⋮ Stable monomial basis for multivariate Birkhoff interpolation problems ⋮ Computing all border bases for ideals of points ⋮ Numerical computation of H-bases ⋮ Prony's method in several variables ⋮ From Oil Fields to Hilbert Schemes ⋮ A Polyhedral Characterization of Border Bases ⋮ Stable border bases for ideals of points ⋮ Multivariate polynomial interpolation with perturbed data ⋮ Almost vanishing polynomials for sets of limited precision points

Uses Software

• ApCoCoA

Cites Work

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• Computing border bases
• Deformations of border bases
• Remarks on automatic algorithm stabilization
• Computing ideals of points
• Characterizations of border bases
• H-bases for polynomial interpolation and system solving
• Gröbner bases of ideals defined by functionals with an application to ideals of projective points
• Gröbner bases, H–bases and interpolation
• On determining the structure of a non-linear system
• Pseudozeros of multivariate polynomials
• Numerical Polynomial Algebra

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