… An important question in this context is how to represent the solutions of 0-dimensional … a
rational function evaluated at the roots of a univariate polynomial. We find this representation …

… of a τ-sparse, n-variate rational function f , where τ is the … The complexity of our sparse rational
interpolation algorithm … we densely interpolate univariate auxiliary rational functions of the …

… rationality of a t-sparse shift for f(x) and provide an efficient algorithm for computing a sparse
… our result to the problem of constructing sparse decompositions of univariate polynomials. …

To give an efficiently computable representation of the zeros of a zero-dimensional ideal I,
Rouillier (1996) introduced the rational univariate representation (RUR) as an extension of …

… of a t-sparse univariate rational function f(X), we proceed as follows: We consider representations
of f(… Such a function is called a real quasi-rational function. Furthermore, we call such a …

… However, for our purpose the univariate case is sufficient. Consider the polynomial (1) f ( z
) = ∑ i = 1 T c α i z α i with T nonzero terms. The c α i are the coefficients of the monomials of …

… To address this problem, we describe here a method, based on the rational univariate
reduction (RUR), for computing roots of systems of multivariate polynomials with rational …

… rational function can be combined with sparse multivariate polynomial interpolation algorithms
to interpolate a sparse rational … The algorithm makes use of a univariate rational function …

… In the context of computing a Rational Univariate Representation (RUR) of its solutions, we
address the problem of certifying a separating linear form and, once certified, calculating the …

… The total cost of computing Pj is therefore an O(δ2dNl(Pj)) where l(Pj) is the number of
monomials of Pj (assumed to be represented as a sparse distributed polynomial), δ the total …