Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Algebraic Construction of Hyperbolic Planes over a Euclidean Ordered
  Field   Using concepts and techniques of bilinear algebra, we construct hyperbolic
planes over a euclidean ordered field that satisfy all the Hilbert axioms of
incidence, order and congruence for a basic plane geometry, but for which the
hyperbolic version of the parallel axiom holds rather than the classical
Euclidean parallel postulate.

21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin