Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multihomogeneous Resultant Formulae for Systems with Scaled Support   Constructive methods for matrices of multihomogeneous (or multigraded)
resultants for unmixed systems have been studied by Weyman, Zelevinsky,
Sturmfels, Dickenstein and Emiris. We generalize these constructions to mixed
systems, whose Newton polytopes are scaled copies of one polytope, thus taking
a step towards systems with arbitrary supports. First, we specify matrices
whose determinant equals the resultant and characterize the systems that admit
such formulae. Bezout-type determinantal formulae do not exist, but we describe
all possible Sylvester-type and hybrid formulae. We establish tight bounds for
all corresponding degree vectors, and specify domains that will surely contain
such vectors; the latter are new even for the unmixed case. Second, we make use
of multiplication tables and strong duality theory to specify resultant
matrices explicitly, for a general scaled system, thus including unmixed
systems. The encountered matrices are classified; these include a new type of
Sylvester-type matrix as well as Bezout-type matrices, known as partial
Bezoutians. Our public-domain Maple implementation includes efficient storage
of complexes in memory, and construction of resultant matrices.

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The categories of this paper are: adap-org
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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: funct-an
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The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas