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On the Coprimeness Property of Discrete Systems without the Irreducibility Condition
Symmetry, integrability and geometry: methods and applications, Tome 14 (2018) Cet article a éte moissonné depuis la source Math-Net.Ru

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In this article we investigate the coprimeness properties of one and two-dimensional discrete equations, in a situation where the equations are decomposable into several factors of polynomials. After experimenting on a simple equation, we shall focus on some higher power extensions of the Somos-4 equation and the (1-dimensional) discrete Toda equation. Our previous results are that all of the equations satisfy the irreducibility and the coprimeness properties if the r.h.s. is not factorizable. In this paper we shall prove that the coprimeness property still holds for all of these equations even if the r.h.s. is factorizable, although the irreducibility property is no longer satisfied.
Keywords: integrability detector; coprimeness; singularity confinement; discrete Toda equation. 
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     author = {Masataka Kanki and Takafumi Mase and Tetsuji Tokihiro},
     title = {On the {Coprimeness} {Property} of {Discrete} {Systems} without the {Irreducibility} {Condition}},
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}
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Masataka Kanki; Takafumi Mase; Tetsuji Tokihiro. On the Coprimeness Property of Discrete Systems without the Irreducibility Condition. Symmetry, integrability and geometry: methods and applications, Tome 14 (2018). http://geodesic.mathdoc.fr/item/SIGMA_2018_14_a64/

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