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Title: The Canny-Emiris conjecture for the sparse resultant
Author: D'Andrea, Carlos, 1973-
Jeronimo, Gabriela
Sombra, Martín
Keywords: Politops
Geometria algebraica
Àlgebra commutativa
Algebraic Geometry
Commutative Algebra
Issue Date: 30-Mar-2022
Publisher: Springer Verlag
Abstract: We present a product formula for the initial parts of the sparse resultant associated with an arbitrary family of supports, generalizing a previous result by Sturmfels. This allows to compute the homogeneities and degrees of this sparse resultant, and its evaluation at systems of Laurent polynomials with smaller supports. We obtain an analogous product formula for some of the initial parts of the principal minors of the Sylvester-type square matrix associated with a mixed subdivision of a polytope. Applying these results, we prove that under suitable hypothesis, the sparse resultant can be computed as the quotient of the determinant of such a square matrix by one of its principal minors. This generalizes the classical Macaulay formula for the homogeneous resultant and confirms a conjecture of Canny and Emiris.
Note: Versió postprint del document publicat a:
It is part of: Foundations of Computational Mathematics, 2022
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ISSN: 1615-3375
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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