Characteristic classes of coincident root loci
==============================================

Coincident root loci (or discriminant strata) are subsets 
of the space of homogeneous polynomials in two variables defined by
root multiplicities: A nonzero degree _n_ polynomial has _n_ roots in the
complex projective line P^1, but some of these can coincide, which gives us a
partition of _n_. Hence for each partition _lambda_ we get a set of polynomials
(those with root multiplicities given by _lambda_), 
which  together stratify the space of these polynomials, which (modulo multiplying by scalars) 
is P^n. These are quasi-projective varieties, invariant under the action of GL(2);
their closures are highly singular projective varieties, making them a good
example for studying invariants of singular varieties.

This package contains a number of different algorithms to compute invariants
and characteristic classes of these varieties:

- degree
- Euler characteristic
- the fundamental class in equivariant cohomology
- Chern-Schwartz-MacPherson (CSM) class, Segre-SM class
- equivariant CSM class
- Hirzebruch Chi-y genus
- Todd class, motivic Hirzebruch class
- motivic Chern class
- equivariant motivic Chern class

Some of the algorithms are implemented in Mathematica 
instead of (or in addition to) Haskell.

Another (better organized) Mathematica implementation is available at
<https://github.com/bkomuves/mathematica-packages>.


Example usage
=============

For example if you want to know what is the equivariant CSM class of the
(open) loci corresponding to the partition [2,2,1,1], you can use the following
piece of code:

    {-# LANGUAGE TypeApplications #-}

    import Math.Combinat.Partitions
    import Math.RootLoci.Algebra.SymmPoly ( AB )
    import Math.Algebra.Polynomial.Pretty ( pretty )
    import Math.RootLoci.CSM.Equivariant.Umbral

    csm ps = umbralOpenCSM @AB (mkPartition ps)

    main = do
      putStrLn $ pretty $ csm [2,2,1,1]