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1,161
The Newton polytope of the implicit equation
 MOSCOW MATH. J
, 2007
"... We apply tropical geometry to study the image of a map defined by Laurent polynomials with generic coefficients. If this image is a hypersurface then our approach gives a construction of its Newton polytope. ..."
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Cited by 23 (2 self)
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We apply tropical geometry to study the image of a map defined by Laurent polynomials with generic coefficients. If this image is a hypersurface then our approach gives a construction of its Newton polytope.
NEWTON POLYTOPES AND WITNESS SETS
, 2012
"... We present two algorithms that compute the Newton polytope of a polynomial defining a hypersurface H in C n using numerical computation. The first algorithm assumes that we may only compute values of f—this may occur if f is given as a straightline program, as a determinant, or as an oracle. The s ..."
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Cited by 2 (0 self)
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We present two algorithms that compute the Newton polytope of a polynomial defining a hypersurface H in C n using numerical computation. The first algorithm assumes that we may only compute values of f—this may occur if f is given as a straightline program, as a determinant, or as an oracle
Computing the Newton polytope of specialized resultants
 Proceeding of the MEGA 2007 conference
"... We consider sparse (or toric) elimination theory in order to describe, by combinatorial means, the monomials appearing in the (sparse) resultant of a given overconstrained algebraic system. A modification of reverse search allows us to enumerate all mixed cell configurations of the given Newton poly ..."
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Cited by 3 (1 self)
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polytopes so as to compute the extreme monomials of the Newton polytope of the resultant. We consider specializations of the resultant to a polynomial in a constant number of variables (typically up to 3) and propose a combinatorial algorithm for computing its Newton polytope; our algorithm need only
The dequantization transform and generalized Newton polytopes
 In [5
"... Abstract. For functions defined on Cn or Rn + we construct a dequantization transform f ↦ → ˆ f; this transform is closely related to the Maslov dequantization. If f is a polynomial, then the subdifferential ∂ ˆ f of ˆ f at the origin coincides with the Newton polytope of f. For the semiring of po ..."
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Cited by 6 (5 self)
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Abstract. For functions defined on Cn or Rn + we construct a dequantization transform f ↦ → ˆ f; this transform is closely related to the Maslov dequantization. If f is a polynomial, then the subdifferential ∂ ˆ f of ˆ f at the origin coincides with the Newton polytope of f. For the semiring
Newton Polytopes of Cluster Variables of Type An
"... Abstract. We study Newton polytopes of cluster variables in type An cluster algebras, whose cluster and coefficient variables are indexed by the diagonals and boundary segments of a polygon. Our main results include an explicit description of the affine hull and facets of the Newton polytope of the ..."
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Cited by 1 (0 self)
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Abstract. We study Newton polytopes of cluster variables in type An cluster algebras, whose cluster and coefficient variables are indexed by the diagonals and boundary segments of a polygon. Our main results include an explicit description of the affine hull and facets of the Newton polytope
Absolute Irreducibility Of Polynomials Via Newton Polytopes
, 1998
"... A multivariable polynomial is associated with a polytope, called its Newton polytope. A polynomial is absolutely irreducible if its Newton polytope is indecomposable in the sense of Minkowski sum of polytopes. Two general constructions of indecomposable polytopes are given, and they give many simple ..."
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Cited by 27 (9 self)
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A multivariable polynomial is associated with a polytope, called its Newton polytope. A polynomial is absolutely irreducible if its Newton polytope is indecomposable in the sense of Minkowski sum of polytopes. Two general constructions of indecomposable polytopes are given, and they give many
Random polynomials with prescribed Newton polytope
 J. Amer. Math. Soc
, 2002
"... 1.1. Statement of results 50 ..."
Results 1  10
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