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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2015, Number 6, Pages 9–14
(Mi vmumm276)
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This article is cited in 1 scientific paper (total in 1 paper)
Mathematics
Generalized separants of differential polynomials
M. A. Limonov Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Abstract:
Let $f\in K\{y\}$ be an element of the ring of differential polynomials in one differential variable $y$ with one differential operator $\delta$. For any variable $y_k$, the polynomial $g=\delta^n(f)$ can be represented in the form $g=A_ky_k+g_0$, where $g_0$ does not depend on $y_k$. If $y_k$ is the leader of $g$, then $A_k$ is a separant of the polynomial $f$. A formula for $A_k$ is obtained for sufficiently large numbers $n$ and $k$ and some applications of this formula are presented.
Key words:
differential polynomial, separant, generalized separant, quasilinear polynomial.
Received: 23.06.2014
Citation:
M. A. Limonov, “Generalized separants of differential polynomials”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2015, no. 6, 9–14; Moscow University Mathematics Bulletin, 70:6 (2015), 248–252
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https://www.mathnet.ru/eng/vmumm276 https://www.mathnet.ru/eng/vmumm/y2015/i6/p9
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