Sparse rational function interpolation with finitely many values for the coefficients

Abstract

In this paper, we give new sparse interpolation algorithms for black box univariate and multivariate rational functions h= f/g whose coefficients are integers with an upper bound. The main idea is as follows: choose a proper integer β and let h(β) = a/ b with gcd (a, b) = 1. Then f and g can be computed by solving the polynomial interpolation problems f(β) = ka and g(β) = ka for some unique integer k. Experimental results show that the univariate interpolation algorithm is almost optimal.