Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computing Algebraic Matroids   An affine variety induces the structure of an algebraic matroid on the set of
coordinates of the ambient space. The matroid has two natural decorations: a
circuit polynomial attached to each circuit, and the degree of the projection
map to each base, called the base degree. Decorated algebraic matroids can be
computed via symbolic computation using Groebner bases, or through linear
algebra in the space of differentials (with decorations calculated using
numerical algebraic geometry). Both algorithms are developed here. Failure of
the second algorithm occurs on a subvariety called the non-matroidal or NM-
locus. Decorated algebraic matroids have widespread relevance anywhere that
coordinates have combinatorial significance. Examples are computed from applied
algebra, in algebraic statistics and chemical reaction network theory, as well
as more theoretical examples from algebraic geometry and matroid theory.

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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex