Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $k$-Equivalence Relations and Associated Algorithms   Lines and circles pose significant scalability challenges in synthetic
geometry. A line with $n$ points implies ${n \choose 3}$ collinearity atoms, or
alternatively, when lines are represented as functions, equality among ${n
\choose 2}$ different lines. Similarly, a circle with $n$ points implies ${n
\choose 4}$ cocyclicity atoms or equality among ${n \choose 3}$ circumcircles.
We introduce a new mathematical concept of $k$-equivalence relations, which
generalizes equality ($k=1$) and includes both lines ($k=2$) and circles
($k=3$), and present an efficient proof-producing procedure to compute the
closure of a $k$-equivalence relation.

23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
2
The categories of this paper are: math
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga