Probabilistic Saturations and Alt’s Problem

DOI10.1080/10586458.2020.1740835zbMath1502.14146arXiv1908.06020OpenAlexW3013251704MaRDI QIDQ5866512

Martin Helmer, Jonathan D. Hauenstein

Publication date: 22 September 2022

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.06020

zbMATH Keywords

homotopy continuationcomputational algebraic geometryfour-bar linkagemodular Gröbner basis

Mathematics Subject Classification ID

Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Geometric aspects of numerical algebraic geometry (14Q65)

Related Items (2)

On the equations defining some Hilbert schemes ⋮ Segre-driven radicality testing

Uses Software

• Magma
• Bertini
• alphaCertified
• CSM-A
• CharacteristicClasses

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Newton-Okounkov bodies, semigroups of integral points, graded algebras and intersection theory
• Algorithms to compute the topological Euler characteristic, Chern-Schwartz-MacPherson class and Segre class of projective varieties
• Hilbert functions and the Buchberger algorithm
• A constrained homotopy technique for excluding unwanted solutions from polynomial equations arising in kinematics problems
• Coefficient-parameter polynomial continuation
• On lucky ideals for Gröbner basis computations
• Efficient computation of zero-dimensional Gröbner bases by change of ordering
• The Magma algebra system. I: The user language
• Modular algorithms for computing Gröbner bases.
• Comparison of probabilistic algorithms for analyzing the components of an affine algebraic variety
• Computing characteristic classes of projective schemes.
• Brunn-Minkowski inequality for multiplicities
• Beyond polyhedral homotopies
• Multiprojective witness sets and a trace test
• A direct algorithm to compute the topological Euler characteristic and Chern-Schwartz-MacPherson class of projective complete intersection varieties
• Algorithm 921
• Regeneration homotopies for solving systems of polynomials
• Convex bodies associated to linear series
• Fast Probabilistic Algorithms for Verification of Polynomial Identities
• A Product-Decomposition Bound for Bezout Numbers
• A polynomial generalization of the Euler characteristic for algebraic sets
• Segre class computation and practical applications
• Numerical Computation of the Hilbert Function and Regularity of a Zero Dimensional Scheme

This page was built for publication: Probabilistic Saturations and Alt’s Problem