Computing Intersection Multiplicities with Regular Chains

We extend a generalization of Fulton’s intersection multiplicity algorithm to handle zero-dimensional regular chains as input, allowing the generalization of Fulton’s algorithm to compute intersection multiplicities at points containing non-rational coordinates. Moreover, we describe the implementation of this extension in Maple, and show that the range of input systems for which intersection multiplicities can be computed has increased substantially from existing standard basis free intersection multiplicity algorithm available in Maple. Lastly, we show our implementation of the generalization of Fulton’s algorithm often outperforms the existing standard basis free intersection multiplicity algorithm, typically by one to two orders of magnitude.