Witness sets of projections

DOI10.1016/j.amc.2010.08.067zbMath1203.14072OpenAlexW2037402183MaRDI QIDQ613271

Jonathan D. Hauenstein, Andrew John Sommese

Publication date: 20 December 2010

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2010.08.067

zbMATH Keywords

projectionspolynomial systemnumerical algebraic geometryalgebraic setswitness sets

Mathematics Subject Classification ID

Computational aspects of higher-dimensional varieties (14Q15) Effectivity, complexity and computational aspects of algebraic geometry (14Q20)

Related Items (31)

Trace test ⋮ Evaluating and Differentiating a Polynomial Using a Pseudo-witness Set ⋮ Exceptional Stewart--Gough Platforms, Segre Embeddings, and the Special Euclidean Group ⋮ Isosingular sets and deflation ⋮ Tensor decomposition and homotopy continuation ⋮ Machine learning the real discriminant locus ⋮ Signatures of algebraic curves via numerical algebraic geometry ⋮ Landau discriminants ⋮ On the null spaces of the Macaulay matrix ⋮ Multiprojective witness sets and a trace test ⋮ \(u\)-generation: solving systems of polynomials equation-by-equation ⋮ Decomposing tensors into frames ⋮ Minimal Problems for the Calibrated Trifocal Variety ⋮ Numerical software to compute Newton polytopes and tropical membership ⋮ Newton polytopes and witness sets ⋮ Numerical computation of Galois groups ⋮ Unification and extension of intersection algorithms in numerical algebraic geometry ⋮ Numerically deciding the arithmetically Cohen-Macaulayness of a projective scheme ⋮ Foreword. What is numerical algebraic geometry? ⋮ Algebraic boundaries of Hilbert’s SOS cones ⋮ Equations for Lower Bounds on Border Rank ⋮ VSPs of cubic fourfolds and the Gorenstein locus of the Hilbert scheme of 14 points on \(\mathbb{A}^6\) ⋮ 96120 : The degree of the linear orbit of a cubic surface ⋮ Numerical elimination and moduli space of vacua ⋮ On identifiability of higher order block term tensor decompositions of rank L_r⊗ rank-1 ⋮ Decomposing Solution Sets of Polynomial Systems Using Derivatives ⋮ Noetherian operators and primary decomposition ⋮ Homotopy techniques for tensor decomposition and perfect identifiability ⋮ Numerical implicitization: a Macaulay2 package ⋮ Catastrophe in elastic tensegrity frameworks ⋮ Multilinear Compressive Sensing and an Application to Convolutional Linear Networks

Uses Software

• Bertini

Cites Work

• Unnamed Item
• Unnamed Item
• Modified deflation algorithm for the solution of singular problems. I. A system of nonlinear algebraic equations
• Deflation algorithm for the multiple roots of a system of nonlinear equations
• The adjunction theory of complex projective varieties
• Algebraic Geometry. I: Complex projective varieties.
• Newton's method with deflation for isolated singularities of polynomial systems
• The Convex Hull of a Variety
• Regeneration homotopies for solving systems of polynomials
• Numerical Decomposition of the Rank-Deficiency Set of a Matrix of Multivariate Polynomials
• Computing the multiplicity structure in solving polynomial systems
• The Numerical Solution of Systems of Polynomials Arising in Engineering and Science

This page was built for publication: Witness sets of projections