Upper bound for effective differential elimination

10/13/2016

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by   Alexey Ovchinnikov, et al.

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We present an upper bound for the number of differentiations in differential elimination for systems of polynomial ODEs, the first such bound as far as we are aware. Elimination of unknowns from systems of equations, starting with Gaussian elimination, is a problem of general interest. In this paper, we study elimination of unknowns from systems of polynomial ODEs, that is, how to derive consequences of a system that do not depend on a selected set of unknowns. This is called differential elimination. One way to do this is to find a uniform (independent of the coefficients of the system) upper bound N so that, after differentiating the system N times, the remaining computation becomes polynomial elimination.