Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Canny-Emiris conjecture for the sparse resultant   We present a product formula for the initial parts of the sparse resultant
associated to an arbitrary family of supports, generalising a previous result
by Sturmfels. This allows to compute the homogeneities and degrees of the
sparse resultant, and its evaluation at systems of Laurent polynomials with
smaller supports. We obtain a similar product formula for some of the initial
parts of the principal minors of the Sylvester-type square matrix associated to
a mixed subdivision of a polytope. Applying these results, we prove that the
sparse resultant can be computed as the quotient of the determinant of such a
square matrix by a certain principal minor, under suitable hypothesis. This
generalises the classical Macaulay formula for the homogeneous resultant, and
confirms a conjecture of Canny and Emiris.

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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph