Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counting Isolated Roots of Trinomial Systems in the Plane and Beyond   We prove that any pair of bivariate trinomials has at most 5 isolated roots
in the positive quadrant. The best previous upper bounds independent of the
polynomial degrees counted only non-degenerate roots and even then gave much
larger bounds, e.g., 248832 via a famous general result of Khovanski. Our bound
is sharp, allows real exponents, and extends to certain systems of n-variate
fewnomials, giving improvements over earlier bounds by a factor exponential in
the number of monomials. We also derive new bounds on the number of real
connected components of fewnomial hypersurfaces.

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The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
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The categories of this paper are: econ
8
The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin