2016/05/19 by Alin Bostan, Xavier Caruso, Eric Schost · 1 citation
Computer Science · #cs.SC #msc:11Y16 #msc:68W30 #acm:11Y16 #acm:68W30
paper · pdf · doi:10.1145/2930889.2930897
Proceedings of ISSAC 2016, to appear
arxiv created 2016/05/19 · arxiv updated 2016/05/23
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 √ 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.