Section: New Results
Computation of the similarity class of the -curvature
The -curvature of a system of linear differential equations in positive characteristic is a matrix that measures how far the system is from having a basis of polynomial solutions. Alin Bostan, together with Xavier Caruso (CNRS and Univ. Rennes) and Éric Schost (Univ. Waterloo), have showed in [10] that the similarity class of the -curvature can be determined without computing the -curvature itself. More precisely, we have designed an algorithm that computes the invariant factors of the -curvature in time quasi-linear in . This is much less than the size of the -curvature, which is generally linear in . The new algorithm allowed to answer a question originating from the study of the Ising model in statistical physics.