Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Chordal networks of polynomial ideals   We introduce a novel representation of structured polynomial ideals, which we
refer to as chordal networks. The sparsity structure of a polynomial system is
often described by a graph that captures the interactions among the variables.
Chordal networks provide a computationally convenient decomposition into
simpler (triangular) polynomial sets, while preserving the underlying graphical
structure. We show that many interesting families of polynomial ideals admit
compact chordal network representations (of size linear in the number of
variables), even though the number of components is exponentially large.
Chordal networks can be computed for arbitrary polynomial systems using a
refinement of the chordal elimination algorithm from [Cifuentes-Parrilo-2016].
Furthermore, they can be effectively used to obtain several properties of the
variety, such as its dimension, cardinality, and equidimensional components, as
well as an efficient probabilistic test for radical ideal membership. We apply
our methods to examples from algebraic statistics and vector addition systems;
for these instances, algorithms based on chordal networks outperform existing
techniques by orders of magnitude.

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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas