Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Singular degree of a rational matrix pseudodifferential operator   In our previous work we studied minimal fractional decompositions of a
rational matrix pseudodifferential operator: H=A/B, where A and B are matrix
differential operators, and B is non-degenerate of minimal possible degree
deg(B). In the present paper we introduce the singular degree sdeg(H)=deg(B),
and show that for an arbitrary rational expression H=sum_a
(A^a_1)/(B^a_1)...(A^a_n)/(B^a_n), we have that sdeg(H) is less than or equal
to sum_{a,i} deg(B^a_i). If the equality holds, we call such an expression
minimal. We study the properties of the singular degree and of minimal rational
expressions. These results are important for the computations involved in the
Lenard-Magri scheme of integrability.

1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph