  In this paper we use the method of discrete Darboux polynomials to calculate
preserved measures and integrals of rational maps. The approach is based on the
use of cofactors and Darboux polynomials and relies on the use of symbolic
algebra tools. Given sufficient computing power, most, if not all, rational
preserved integrals can be found (and even some non-rational ones).
  We show, in a number of examples, how it is possible to use this method to
both determine and detect preserved measures and integrals of the considered
rational maps. Many of the examples arise from the Kahan-Hirota-Kimura
discretization of completely integrable systems of ordinary differential
equations.
