Lazy Hermite Reduction and Creative Telescoping for Algebraic Functions

We present criteria on the existence of telescopers for trivariate rational functions in four mixed cases, in which discrete and continuous variables appear simultaneously. We reduce the existence problem in the trivariate case to the exactness testing problem, the separation problem and the existence problem in the bivariate case. The existence criteria we present help us determine the termination of Zeilberger's algorithm for the input functions studied in this paper.