A Fast Algorithm for Computing the p-Curvature
Résumé
We design an algorithm for computing the $p$-curvature of adifferential system in positive characteristic $p$. For a system ofdimension $r$ with coefficients of degree at most $d$, its complexityis $\tilde O (p d r^\omega)$ operations in the ground field (where$\omega$ denotes the exponent of matrix multiplication), whereas thesize of the output is about $p d r^2$. Our algorithm is thenquasi-optimal assuming that matrix multiplication is (\emph{i.e.}$\omega = 2$). The main theoretical input we are using is theexistence of a well-suited ring of series with divided powers forwhich an analogue of the Cauchy--Lipschitz Theorem holds.
Domaines
Calcul formel [cs.SC]| Origine | Fichiers produits par l'(les) auteur(s) |
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