Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classification of Conic Sections in $PE_2(\mathbb{R})$   This paper gives a complete classification of conics in $PE_2(\mathbb{R})$.
The classification has been made earlier (Reveruk [5]), but it showed to be
incomplete and not possible to cite and use in further studies of properties of
conics, pencil of conics, and of quadratic forms in pseudo-Euclidean spaces.
This paper provides that. A pseudo-orthogonal matrix, pseudo-Euclidean values
of a matrix, diagonalization of a matrix in a pseudo-Euclidean way are
introduced. Conics are divided in families and by types, giving both of them
geometrical meaning. The invariants of a conic with respect to the group of
motions in $PE_2(\mathbb{R})$ are determined, making it possible to determine a
conic without reducing its equation to canonical form. An overview table is
given.

35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol