Polynomial Homotopies for Dense, Sparse and Determinantal Systems

Abstract

Numerical homotopy continuation methods for three classes of polynomial systems are presented. For a generic instance of the class, every path leads to a solution and the homotopy is optimal. The counting of the roots mirrors the resolution of a generic system that is used to start up the deformations. Software and applications are discussed.

References in corpus (2)

• Degree of the generalized Plücker embedding of a Quot scheme and Quantum cohomology
• Numerical homotopies to compute generic points on positive dimensional algebraic sets

Cited by in corpus (2)

• On the Complexity of the Generalized MinRank Problem
• An excursion from enumerative goemetry to solving systems of polynomial equations with Macaulay 2