Euclid Meets Bézout: Intersecting Algebraic Plane Curves with the Euclidean Algorithm

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

[1]  H. O. Foulkes.  Abstract Algebra , 1967, Nature.

[2]  Anthony W. Knapp.  Advanced Algebra , 1938, Nature.

[3]  C. Hoffmann.  Algebraic curves , 1988 .

[4]  R. J. Walker.  Algebraic curves , 1950 .