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

Authors:
Guillermo Matera;Alexandre Sedoglavic
Affiliations:
IDH, Univ. Nacional de General Sarmiento, Campus Universitario, (1613) Los Polvorines, Buenos Aires, Argentina;INRIA - Rocquencourt, F-78153 Le Chesnay Cedex, France
Venue:
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Year:
2002

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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.