Combinatorial Excess Intersection
Jose Rodriguez
TL;DR
This paper introduces formulas and algorithms for calculating excess intersection numbers of ideals, utilizing mixed volumes of polytopes for monomial ideals, and applies these results to design homotopies in numerical algebraic geometry.
Contribution
It provides new formulas and algorithms for excess intersection numbers, linking combinatorial geometry with algebraic computations and homotopy design.
Findings
Formulas for excess numbers of ideals.
Algorithms based on mixed volumes for monomial ideals.
Application to homotopy construction in numerical algebraic geometry.
Abstract
We provide formulas and algorithms for computing the excess numbers of certain ideals. The solution for monomial ideals is given by the mixed volumes of certain polytopes. These results enable us to design specific homotopies for numerical algebraic geometry.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Advanced Numerical Analysis Techniques