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On the Uniqueness of Simultaneous Rational Function Reconstruction

Eleonora Guerrini 1 Romain Lebreton 1 Ilaria Zappatore 1
1 ECO - Exact Computing
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
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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Submitted on : Friday, February 21, 2020 - 12:05:54 PM
Last modification on : Tuesday, January 19, 2021 - 1:01:12 PM
Long-term archiving on: : Friday, May 22, 2020 - 4:28:19 PM

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

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