Electronic Thesis and Dissertation Repository

Degree

Doctor of Philosophy

Program

Computer Science

Supervisor

Dr. Marc Moreno Maza

2nd Supervisor

Dr. Eric Schost

Joint Supervisor

Abstract

Fulton’s algorithm is used to calculate the intersection multiplicity of two plane curves about a rational point. This work extends Fulton’s algorithm first to algebraic points (encoded by triangular sets) and then, with some generic assumptions, to l many hypersurfaces.

Out of necessity, we give a standard-basis free method (i.e. practically efficient method) for calculating tangent cones at points on curves.


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