Numerical Computation of the Hilbert Function and Regularity of a Zero Dimensional Scheme

DOI10.1007/978-1-4939-0626-0_6zbMath1315.13032OpenAlexW1018558357MaRDI QIDQ5261424

Zachary A. Griffin, Chris Peterson, Jonathan D. Hauenstein, Andrew John Sommese

Publication date: 3 July 2015

Published in: Connections Between Algebra, Combinatorics, and Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-1-4939-0626-0_6

Mathematics Subject Classification ID

Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) (14M05) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40)

Related Items (6)

Binomiality testing and computing sparse polynomials via witness sets ⋮ Numerically deciding the arithmetically Cohen-Macaulayness of a projective scheme ⋮ Eliminating dual spaces ⋮ Learning algebraic varieties from samples ⋮ Numerical elimination and moduli space of vacua ⋮ Probabilistic Saturations and Alt’s Problem

Uses Software

• Algorithm 931

Cites Work

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• Isosingular sets and deflation
• Modified deflation algorithm for the solution of singular problems. I. A system of nonlinear algebraic equations
• Newton's method with deflation for isolated singularities of polynomial systems
• Algorithm 921
• A Numerical Local Dimension Test for Points on the Solution Set of a System of Polynomial Equations
• Algorithm 931
• Computing the multiplicity structure in solving polynomial systems

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