  This paper focuses on the problem of reconstructing a vector of rational
functions given some evaluations, or more generally given their remainders
modulo different polynomials. The special case of rational functions sharing
the same denominator, a.k.a.Simultaneous Rational Function Reconstruction
(SRFR), has many applications from linear system solving to coding theory,
provided that SRFR has a unique solution. The number of unknowns in SRFR is
smaller than for a general vector of rational function. This allows to reduce
the number of evaluation points needed to guarantee the existence of a
solution, but we may lose its uniqueness. In this work, we prove that
uniqueness is guaranteed for a generic instance.
