Physical Sciences and Mathematics Commons^™

Towards A Generalization Of Fulton's Intersection Multiplicity Algorithm, Ryan Sandford

Electronic Thesis and Dissertation Repository

In this manuscript we generalize Fulton's bivariate intersection multiplicity algorithm to a partial intersection multiplicity algorithm in the n-variate setting. We extend this generalization of Fulton's algorithm to work at any point, rational or not, using the theory of regular chains. We implement these algorithms in Maple and provide experimental testing. The results indicate the proposed algorithm often outperforms the existing standard basis-free intersection multiplicity algorithm in Maple, typically by one to two orders of magnitude. Moreover, we also provide some examples where the proposed algorithm outperforms intersection multiplicity algorithms which rely on standard bases, indicating the proposed algorithm is …

Computing Intersection Multiplicity Via Triangular Decomposition, Paul Vrbik

Electronic Thesis and Dissertation Repository

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.