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

Guillermo Matera (1) , Alexandre Sedoglavic (2, 3)

1 IDH - Instituto de Desarrollo Humano [Los Polvorines]
2 ALIEN - Algebra for Digital Identification and Estimation
3 LIFL - Laboratoire d'Informatique Fondamentale de Lille

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.

Domaines: Calcul formel [cs.SC]; Optimisation et contrôle [math.OC]

Guillermo Matera, Alexandre Sedoglavic. The differential Hilbert function of a differential rational mapping can be computed in polynomial time. International Symposium on Symbolic and Algebraic Computation, Jul 2002, lille, France. pp.184-191. ⟨hal-00129689⟩