Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the computation of the HNF of a module over the ring of integers of a
  number field   We present a variation of the modular algorithm for computing the Hermite
normal form of an $\mathcal O_K$-module presented by Cohen, where $\mathcal
O_K$ is the ring of integers of a number field $K$. An approach presented in
(Cohen 1996) based on reductions modulo ideals was conjectured to run in
polynomial time by Cohen, but so far, no such proof was available in the
literature. In this paper, we present a modification of the approach of Cohen
to prevent the coefficient swell and we rigorously assess its complexity with
respect to the size of the input and the invariants of the field $K$.

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The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys