  We present a computer algebra package based on Magma for performing
computations in rational Cherednik algebras at arbitrary parameters and in
Verma modules for restricted rational Cherednik algebras. Part of this package
is a new general Las Vegas algorithm for computing the head and the
constituents of a module with simple head in characteristic zero which we
develop here theoretically. This algorithm is very successful when applied to
Verma modules for restricted rational Cherednik algebras and it allows us to
answer several questions posed by Gordon in some specific cases. We could
determine the decomposition matrices of the Verma modules, the graded G-module
structure of the simple modules, and the Calogero-Moser families of the generic
restricted rational Cherednik algebra for around half of the exceptional
complex reflection groups. In this way we could also confirm Martino's
conjecture for several exceptional complex reflection groups.
