  In this paper, the spectrum and the decomposability of a multivariate
rational function are studied by means of the effective Noether's
irreducibility theorem given by Ruppert. With this approach, some new effective
results are obtained. In particular, we show that the reduction modulo p of the
spectrum of a given integer multivariate rational function r coincides with the
spectrum of the reduction of r modulo p for p a prime integer greater or equal
to an explicit bound. This bound is given in terms of the degree, the height
and the number of variables of r. With the same strategy, we also study the
decomposability of r modulo p. Some similar explicit results are also provided
for the case of polynomials with coefficients in a polynomial ring.
