An upper bound for minimizing coefficients of dimension Kolchin polynomial

Authors:
M. V. Kondratieva
Affiliations:
Department of Mechanics and Mathematics, Moscow State University, Moscow, Russia 119992
Venue:
Programming and Computing Software
Year:
2010

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Abstract

In this paper, an upper bound for minimizing coefficients of the dimension Kolchin polynomial for a subset E 驴驴 0 m , which depends on the maximal order of elements in E, is obtained. The minimizing coefficients are always positive; some of them are invariant and play an important role in differential algebra. As an example of application of the result obtained, an estimate for a typical differential dimension of a system of partial differential equations is obtained in the case where the orders and degrees of the equations are bounded.