An algebraic formula for the intersection number of a polynomial immersion

TL;DR

This paper introduces an algebraic formula and an algorithm for computing the intersection number of polynomial immersions of algebraic manifolds into Euclidean space, facilitating topological and geometric analysis.

Contribution

It provides a new algebraic formula and an algorithm for calculating intersection numbers of polynomial immersions, advancing computational topology methods.

Findings

Effective algebraic formula for intersection number

Algorithm for computing topological degree of polynomial mappings

Application to polynomial immersions of algebraic manifolds

Abstract

There is presented an algorithm for computing the topological degree for a large class of polynomial mappings. As an application there is given an effective algebraic formula for the intersection number of a polynomial immersion M --> R^2m, where M is an m-dimensional algebraic manifold.