Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Novel Approach for Computing Hilbert Functions   One standard approach to compute the Hilbert function of any graded module
over a field is to come up with a free-resolution for the graded module and
another is via a Hilbert power series which serves as a generating function.
The proposed approaches enable generating the values of a Hilbert function when
the graded module is a quotient ring over a field by using combinatorics and
homological algebra. Two of these approaches named the lcm-Lattice method and
the Syzygy method, are conceptually combinatorial and work for any polynomial
quotient ring over a field. The third approach named Hilbert function table
method, also uses syzygies but the approach is better described in terms of
homological algebra.

11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc