Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Dual-Radix Modular Division Algorithm for Computing Periodic Orbits
  within Syracuse Dynamical Systems   This article analyzes the periodic orbits of Syracuse dynamical systems in a
novel algebraic setting: the commutative ring of graded $n$-adic integers.
Within this context, this article introduces a dual-radix modular division
algorithm for computing the graded canonical expansions and graded quotients
for a certain class of rational expressions that arise from periodic orbits
within these dynamical systems. This division algorithm yields two novel
methods for testing the integrality of the B\"{o}hm-Sontacchi numbers.

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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: eess