Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computing Multi-Homogeneous Bezout Numbers is Hard   The multi-homogeneous Bezout number is a bound for the number of solutions of
a system of multi-homogeneous polynomial equations, in a suitable product of
projective spaces.
  Given an arbitrary, not necessarily multi-homogeneous system, one can ask for
the optimal multi-homogenization that would minimize the Bezout number.
  In this paper, it is proved that the problem of computing, or even estimating
the optimal multi-homogeneous Bezout number is actually NP-hard.
  In terms of approximation theory for combinatorial optimization, the problem
of computing the best multi-homogeneous structure does not belong to APX,
unless P = NP.
  Moreover, polynomial time algorithms for estimating the minimal
multi-homogeneous Bezout number up to a fixed factor cannot exist even in a
randomized setting, unless BPP contains NP.

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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys