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arXiv · 1605.06126

Computation of the Similarity Class of the p-Curvature

Alin Bostan·Xavier Caruso·Eric Schost
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Abstract

The $p$-curvature of a system of linear differential equations in positive characteristic $p$ is a matrix that measures how far the system is from having a basis of polynomial solutions. We show that the similarity class of the $p$-curvature can be determined without computing the $p$-curvature itself. More precisely, we design an algorithm that computes the invariant factors of the $p$-curvature in time quasi-linear in $\sqrt p$. This is much less than the size of the $p$-curvature, which is generally linear in $p$. The new algorithm allows to answer a question originating from the study of the Ising model in statistical physics.

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Alin Bostan, Xavier Caruso, Eric Schost. 2016-05-19. Computation of the Similarity Class of the p-Curvature. https://doi.org/10.1145/2930889.2930897

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