Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Fast Algorithm for Computing the p-Curvature   We design an algorithm for computing the $p$-curvature of a differential
system in positive characteristic $p$. For a system of dimension $r$ with
coefficients of degree at most $d$, its complexity is $\softO (p d r^\omega)$
operations in the ground field (where $\omega$ denotes the exponent of matrix
multiplication), whereas the size of the output is about $p d r^2$. Our
algorithm is then quasi-optimal assuming that matrix multiplication is
(\emph{i.e.} $\omega = 2$). The main theoretical input we are using is the
existence of a well-suited ring of series with divided powers for which an
analogue of the Cauchy--Lipschitz Theorem holds.

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The categories of this paper are: astro-ph
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin