Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On two algebraic parametrizations for rational solutions of the cuboid
  equations   A rational perfect cuboid is a rectangular parallelepiped whose edges and
face diagonals are given by rational numbers and whose space diagonal is equal
to unity. Its existence is equivalent to the existence of a perfect cuboid with
all integer edges and diagonals. Finding such a cuboid or proving its
non-existence is an old unsolved problem. Recently, based on a symmetry
approach, the equations of a perfect cuboid were transformed to factor
equations. The factor equations turned out to be solvable and, being solved,
have led to a pair of inverse problems. Our efforts in the present paper are
toward solving these inverse problems. Algebraic parametrizations for their
solutions using algebraic functions of two rational arguments are found.

27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
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The categories of this paper are: supr-con
1
The categories of this paper are: cs
16
The categories of this paper are: stat
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org