arXiv Open Access 2016

Computation of the Similarity Class of the p-Curvature

Alin Bostan Xavier Caruso Eric Schost

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Abstrak

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.

Topik & Kata Kunci

cs.SC

Penulis (3)

Alin Bostan

Xavier Caruso

Eric Schost

Format Sitasi

APA MLA BibTeX

Bostan, A., Caruso, X., Schost, E. (2016). Computation of the Similarity Class of the p-Curvature. https://arxiv.org/abs/1605.06126

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Informasi Jurnal

Tahun Terbit: 2016
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓