Computing Limits of Real Multivariate Rational Functions

Computing Limits of Quotients of Multivariate Real Analytic Functions

“…In the univariate case computing limits of rational functions is easy, and the state of the art limit computation algorithms [3,6] are applicable to large classes of functions. In the multivariate case computing limits of real rational functions is a nontrivial problem that has been a subject of recent research [1,2,8,9,10]. In [7] we compared five methods for computation of limits of real rational functions based on the Cylindrical Algebraic Decomposition (CAD) algorithm.…”

“…The algorithm uses Wu's elimination method, rational univariate representations, and requires adjoining two infinitesimal elements to the field. The algorithm presented in [1] (which generalizes algorithms of [2,8]) solves Problem 1 under the additional assumption that c is an isolated zero of h. The authors use the theory of Lagrange multipliers to reduce the problem to computing the limit along a real algebraic set, and solve the reduced problem using regular chains methods.…”