# SegreClasses : Table of Contents

SegreClasses -- Tests containment of varieties and computes algebraic multiplicity of subvarieties and Fulton-MacPherson intersection products - via a very general Segre class computation. The package works for subschemes of products of projective spaces.
chowClass -- Finds the (fundamental) class of a subscheme in the Chow ring of the ambient space
containedInSingularLocus -- This method tests is an irreducible variety is contained in the singular locus of the reduced scheme of an irreducible scheme
intersectionProduct -- A class in the Chow ring of the ambient space representing the Fulton-MacPherson intersection product of two schemes inside a variety
isComponentContained -- This method tests containment of (irreducible) varieties; more generally it tests if a top-dimensional irreducible component of the scheme associated an ideal is contained in the scheme associated to another ideal
isMultiHom -- Tests if an ideal is multi-homogeneous with respect to the grading of its ring
makeChowRing -- Makes the Chow ring of a product of projective spaces.
makeProductRing -- Makes the coordinate ring of a product of projective spaces.
multiplicity -- This method computes the algebraic (Hilbert-Samuel) multiplicity
projectiveDegree -- This method computes a single projective degree of a scheme X inside a scheme Y, where X,Y are subschemes of some product of projective spaces
projectiveDegrees -- This method computes the projective degrees of a scheme X inside a scheme Y, where X,Y are subschemes of some product of projective spaces
segre -- This method computes the Segre class of a scheme X inside a scheme Y, where X,Y are subschemes of some product of projective spaces
segreDimX -- This method computes the dimension X part of the Segre class of a scheme X inside a scheme Y, where X,Y are subschemes of some product of projective spaces