This package tests containment of (irreducible) varieties and computes Segre classes, algebraic multiplicity, and Fulton-MacPherson intersection products. More generally, for subschemes of ℙ^{n1}x...xℙ^{nm}, this package tests if a top-dimensional irreducible component of the scheme associated to an ideal is contained in the scheme associated to another ideal. Specialized methods to test the containment of a variety in the singular locus of another are provided, these methods work without computing the ideal of the singular locus and can provide significant speed-ups relative to the standard methods when the singular locus has a complicated structure. The package works for subschemes of products of projective spaces. The package implements methods described in [1]. More details and relevant definitions can be found in [1].
References:
[1] Corey Harris and Martin Helmer. "Segre class computation and practical applications." arXiv preprint arXiv:1806.07408 (2018). Link: https://arxiv.org/abs/1806.07408.
This documentation describes version 1.02 of SegreClasses.
The source code from which this documentation is derived is in the file SegreClasses.m2.