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Conference Papers Year : 2020

On the Uniqueness of Simultaneous Rational Function Reconstruction

Eleonora Guerrini
Romain Lebreton
Ilaria Zappatore
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Abstract

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.
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Dates and versions

lirmm-02486922 , version 1 (21-02-2020)

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Eleonora Guerrini, Romain Lebreton, Ilaria Zappatore. On the Uniqueness of Simultaneous Rational Function Reconstruction. ISSAC 2020 - 45th International Symposium on Symbolic and Algebraic Computation, Jul 2020, Kalamata, Greece. pp.226-233, ⟨10.1145/3373207.3404051⟩. ⟨lirmm-02486922⟩
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