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An algorithm for the decomposition of differential polynomials in the general case

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Abstract

The theory of decomposition of differential polynomials (DPs) is considered. For a given differential algebraic equation

$P(x,y(x), y'(x), \ldots ,y^{(n)} (x)) = 0,$

the possibility to represent the differential polynomial P as the composition P = Q(x, R, R′, ..., R (q)), R = R(x, y(x), ..., y(r)(x)) of DPs Q and R is studied. It is shown that the decomposition problem is reduced to the factorization of linear ordinary differential operators (LODOs). A generic decomposition algorithm for DPs is described based on the Vandermonde differential theorem.

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Correspondence to M. V. Sosnin.

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Original Russian Text © M.V. Sosnin, 2011, published in Programmirovanie, 2011, Vol. 37, No. 4.

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Sosnin, M.V. An algorithm for the decomposition of differential polynomials in the general case. Program Comput Soft 37, 181–186 (2011). https://doi.org/10.1134/S0361768811020101

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  • DOI: https://doi.org/10.1134/S0361768811020101

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