Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An algorithm for canonical forms of finite subsets of $\mathbb{Z}^d$ up
  to affinities   In this paper we describe an algorithm for the computation of canonical forms
of finite subsets of $\mathbb{Z}^d$, up to affinities over $\mathbb{Z}$. For
fixed dimension $d$, this algorithm has worst-case asymptotic complexity $O(n
\log^2 n \, s\,\mu(s))$, where $n$ is the number of points in the given subset,
$s$ is an upper bound to the size of the binary representation of any of the
$n$ points, and $\mu(s)$ is an upper bound to the number of operations required
to multiply two $s$-bit numbers. In particular, the problem is fixed-parameter
tractable with respect to the dimension $d$. This problem arises e.g. in the
context of computation of invariants of finitely presented groups with
abelianized group isomorphic to $\mathbb{Z}^d$. In that context one needs to
decide whether two Laurent polynomials in $d$ indeterminates, considered as
elements of the group ring over the abelianized group, are equivalent with
respect to a change of basis.

16
The categories of this paper are: stat
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph