  Creative telescoping algorithms compute linear differential equations
satisfied by multiple integrals with parameters. We describe a precise and
elementary algorithmic version of the Griffiths-Dwork method for the creative
telescoping of rational functions. This leads to bounds on the order and degree
of the coefficients of the differential equation, and to the first complexity
result which is simply exponential in the number of variables. One of the
important features of the algorithm is that it does not need to compute
certificates. The approach is vindicated by a prototype implementation.
