Limits of quotients of real polynomial functions of three variables

An algorithm for computing the limit of a quotient of bivariate real analytic functions has been developed by one of the authors in (Limits of quotients of bivariate real analytic functions, Journal of Symbolic Computation, 50, 2013, 197 207). In this paper we provide a theoretical method based on the work developed in that article to determine the existence of the limit of a quotient of two polynomial functions of three variables. An algorithm to compute such limits, in the case where the polynomials have rational coefficients, or more generally, coefficients in a real finite extension of the rationals, is also described.