  A real symmetric n times n matrix is called copositive if the corresponding
quadratic form is non-negative on the closed first orthant. If the matrix fails
to be copositive there exists some non-negative certificate for which the
quadratic form is negative. Due to the scaling property, we can find such
certificates in every neighborhood of the origin but their properties depend on
the matrix of course and are hard to describe. If it is an integer matrix
however, we are guaranteed certificates of a complexity that is at most a
constant times the binary encoding length of the matrix raised to the power
3/2.
