  We consider the algorithmic problem of computing a primitive idempotent of a
central simple algebra over the field of rational functions over a finite
field. The algebra is given by a set of structure constants. The problem is
reduced to the computation of a division algebra Brauer equivalent to the
central simple algebra. This division algebra is constructed as a cyclic
algebra, once the Hasse invariants have been computed. We give an application
to skew constacyclic convolutional codes.
