###
chern.lib: a library for symbolic computations with Chern classes

### Overview

This library is a toolbox for symbolic computations with Chern classes.
The Aluffi's algorithms for computation of characteristic classes of algebraic varieties
(Segre, Fulton, Chern-Schwartz-MacPherson classes) are implemented as well
(cf. doi:10.1016/S0747-7171(02)00089-5).

The current version of the library chern.lib is available
here.

An informal discussion of the algorithms implemented in the library:
ps-file
,
pdf-file
.

### On different approaches to compute the Chern classes of a tensor product of two vector bundles

A comparison of different algorithms implemented in the library to compute the Chern classes of a tensor product of two vector bundles:
ps-file
,
pdf-file
.

Times
needed to obtain all the formulas for the Chern classes of tensor products E⊗F with rank(E⊗F)=N.

The Singular code
used for testing the four different implementations.

###
Some examples

The
total Chern class and the Hilbert polynomial of the Horrocks-Mumford bundle
(cf. doi:10.1016/0040-9383(73)90022-0).
####
Things that can be computed with the help of the library in around 1 second.

(Laptop 2 x Intel Celeron 2957U @ 1.4 GHz with 8.3 GB of RAM)

The
first 38 terms of the Chern character.

The
first 16 terms of the Todd class.

The
first 12 Chern classes of a tensor product of two bundles.

The
Chern classes of all exterior powers of a rank 11 vector bundle of a 3-fold.

The
Chern classes of 9 first symmetric powers of a rank 5 vector bundle of a 4-fold.