Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $3$-dimensional Continued Fraction Algorithms Cheat Sheets   Multidimensional Continued Fraction Algorithms are generalizations of the
Euclid algorithm and find iteratively the gcd of two or more numbers. They are
defined as linear applications on some subcone of $\mathbb{R}^d$. We consider
multidimensional continued fraction algorithms that acts symmetrically on the
positive cone $\mathbb{R}^d_+$ for $d=3$. We include well-known and old ones
(Poincar\'e, Brun, Selmer, Fully Subtractive) and new ones
(Arnoux-Rauzy-Poincar\'e, Reverse, Cassaigne).
  For each algorithm, one page (called cheat sheet) gathers a handful of
informations most of them generated with the open source software Sage with the
optional Sage package \texttt{slabbe-0.2.spkg}. The information includes the
$n$-cylinders, density function of an absolutely continuous invariant measure,
domain of the natural extension, lyapunov exponents as well as data regarding
combinatorics on words, symbolic dynamics and digital geometry, that is,
associated substitutions, generated $S$-adic systems, factor complexity,
discrepancy, dual substitutions and generation of digital planes.
  The document ends with a table of comparison of Lyapunov exponents and gives
the code allowing to reproduce any of the results or figures appearing in these
cheat sheets.

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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: astro-ph