Computation of the Similarity Class of the p-Curvature

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.

Proceedings of ISSAC 2016, to appear

References in corpus (3)

• A fast algorithm for computing the characteristic polynomial of the p-curvature
• Globally nilpotent differential operators and the square Ising model
• A Fast Algorithm for Computing the p-Curvature

Cited by in corpus (2)

• Guessing with Little Data
• Fast Computation of the $N$-th Term of a $q$-Holonomic Sequence and Applications