The differential Hilbert function of a differential rational mapping can be computed in polynomial time

Guillermo Matera	Alexandre Sedoglavic
Departamento de Computacion, Univ. Favaloro	Projet Algorithmes
Belgrano 1723, (1093) Buenos Aires, Argentina	INRIA -- Rocquencourt
and	F-78153 Le Chesnay Cedex, France
IDH, Univ. Nacional de General Sarmiento	Alexandre.Sedoglavic@inria.fr
Campus Universitario, J.M. Gutiérrez 1150
(1613) Los Polvorines, Buenos Aires, Argentina
gmatera@favaloro.edu.ar

Abstract: We present a probabilistic seminumerical algorithm that computes the differential Hilbert function associated to a differential rational mapping. This algorithm explicitly determines the set of variables and derivatives which can be arbitrarily fixed in order to locally invert the differential mapping under consideration. The arithmetic complexity of this algorithm is polynomial in the input size.

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