Fast computation of discrete invariants associated to a differential rational mapping

Guillermo Matera , Alexandre Sedoglavic (1, 2)

1 ALIEN - Algebra for Digital Identification and Estimation
2 LIFL - Laboratoire d'Informatique Fondamentale de Lille

We exhibit probabilistic algorithms which compute the differentiation index, the differential Hilbert function and a parametric set associated to a differential rational mapping. These algorithms are based on a process of linearization and specialization in a generic solution, and have polynomial time complexity.

Mots clés: Differential rational mapping; Discrete invariants; Kähler differentials; Probabilistic algorithm; Straight-line program; Differential algebra; Differential Hilbert function; Seminumerical algorithm

Domaines: Calcul formel [cs.SC]

Guillermo Matera, Alexandre Sedoglavic. Fast computation of discrete invariants associated to a differential rational mapping. Journal of Symbolic Computation, 2003, 36 (3--4), pp.473--499. ⟨10.1016/S0747-7171(03)00091-9⟩. ⟨hal-00129198⟩