Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A fast, deterministic algorithm for computing a Hermite Normal Form of a
  polynomial matrix   Given a square, nonsingular matrix of univariate polynomials $\mathbf{F} \in
\mathbb{K}[x]^{n \times n}$ over a field $\mathbb{K}$, we give a fast,
deterministic algorithm for finding the Hermite normal form of $\mathbf{F}$
with complexity $O^{\sim}\left(n^{\omega}d\right)$ where $d$ is the degree of
$\mathbf{F}$. Here soft-$O$ notation is Big-$O$ with log factors removed and
$\omega$ is the exponent of matrix multiplication. The method relies of a fast
algorithm for determining the diagonal entries of its Hermite normal form,
having as cost $O^{\sim}\left(n^{\omega}s\right)$ operations with $s$ the
average of the column degrees of $\mathbf{F}$.

5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
19
The categories of this paper are: eess