Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Polynomial-time Algorithm to Compute Generalized Hermite Normal Form
  of Matrices over Z[x]   In this paper, a polynomial-time algorithm is given to compute the
generalized Hermite normal form for a matrix F over Z[x], or equivalently, the
reduced Groebner basis of the Z[x]-module generated by the column vectors of F.
The algorithm is also shown to be practically more efficient than existing
algorithms. The algorithm is based on three key ingredients. First, an F4 style
algorithm to compute the Groebner basis is adopted, where a novel prolongation
is designed such that the coefficient matrices under consideration have
polynomial sizes. Second, fast algorithms to compute Hermite normal forms of
matrices over Z are used. Third, the complexity of the algorithm are guaranteed
by a nice estimation for the degree and height bounds of the polynomials in the
generalized Hermite normal form.

6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom