The C-library cddlib is a C implementation of the Double Description
Method of Motzkin et al. for generating all vertices (i.e. extreme points)
and extreme rays of a general convex polyhedron in R^d given by a system
of linear inequalities:

P = { x=(x1, ..., xd)^T : b - A x >= 0 }

where A is a given m x d real matrix, b is a given m-vector
and 0 is the m-vector of all zeros.

The program can be used for the reverse operation (i.e. convex hull
computation). This means that one can move back and forth between
an inequality representation and a generator (i.e. vertex and ray)
representation of a polyhedron with cdd. Also, cdd can solve a linear
programming problem, i.e. a problem of maximizing and minimizing
a linear function over P.