Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Complexity of the Generalized MinRank Problem   We study the complexity of solving the \emph{generalized MinRank problem},
i.e. computing the set of points where the evaluation of a polynomial matrix
has rank at most $r$. A natural algebraic representation of this problem gives
rise to a \emph{determinantal ideal}: the ideal generated by all minors of size
$r+1$ of the matrix. We give new complexity bounds for solving this problem
using Gr\"obner bases algorithms under genericity assumptions on the input
matrix. In particular, these complexity bounds allow us to identify families of
generalized MinRank problems for which the arithmetic complexity of the solving
process is polynomial in the number of solutions. We also provide an algorithm
to compute a rational parametrization of the variety of a 0-dimensional and
radical system of bi-degree $(D,1)$. We show that its complexity can be bounded
by using the complexity bounds for the generalized MinRank problem.

30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph