Macaulay2 package SegreClasses - Tests containment of varieties and computes algebraic multiplicity of subvarieties and Fulton-MacPherson intersection products - via a very general Segre class computation. This package tests containment of (irreducible) varieties and computes Segre classes, algebraic multiplicity, and Fulton-MacPherson intersection products. More generally, for subschemes of PP^{n_1}x...xPP^{n_m}, 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].

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