Euclid meets Bezout: Intersecting algebraic plane curves with the Euclidean algorithm

TL;DR

This paper introduces a novel method leveraging the Euclidean algorithm to compute intersection points, including multiplicities, of two algebraic plane curves, bridging algebraic geometry and algorithmic techniques.

Contribution

It presents a new approach using the Euclidean algorithm for polynomials to determine curve intersections with multiplicities.

Findings

Effective computation of intersection points including multiplicities.

Bridging algebraic geometry with polynomial algorithms.

Potential applications in computational algebraic geometry.

Abstract

We show how the Eulcidean algorithm for polynomials can be used to find the intersection points, with multiplicities, of two plane algebraic curves.