Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tabulation of cubic function fields via polynomial binary cubic forms   We present a method for tabulating all cubic function fields over
$\mathbb{F}_q(t)$ whose discriminant $D$ has either odd degree or even degree
and the leading coefficient of $-3D$ is a non-square in $\mathbb{F}_{q}^*$, up
to a given bound $B$ on the degree of $D$. Our method is based on a
generalization of Belabas' method for tabulating cubic number fields. The main
theoretical ingredient is a generalization of a theorem of Davenport and
Heilbronn to cubic function fields, along with a reduction theory for binary
cubic forms that provides an efficient way to compute equivalence classes of
binary cubic forms. The algorithm requires $O(B^4 q^B)$ field operations as $B
\rightarrow \infty$. The algorithm, examples and numerical data for
$q=5,7,11,13$ are included.

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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas