منابع مشابه
The Newton Polytope
This describes the map χ in the exact sequence. The map L in the sequence gives us a matrix such that ImL = kerχ. This matrix will generate a integer lattice Λ ⊆ Zm−n. Such an exact sequence gives rise to many different interpretations. The most familiar interpretation is that of a polytope in R which introduces geometry to the system. We can also view the exact sequence as defining a system of...
متن کاملOn the Newton Polytope of the Resultant
The study of Newton polytopes of resultants and discriminants has its orgin in the work of Gelfand, Kapranov, and Zelevinsky on generalized hypergeometric functions (see e.g., [8]). Central to this theory is the notion of the A-discriminant AA, which is the discriminant of a Laurent polynomial with specified support set A (see [6, 7]). Two main results of Gelfand, Kapranov, and Zelevinsky are c...
متن کاملThe Newton Polytope of the Implicit Equation
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.
متن کاملComputing the Newton Polytope of Specialized Resultants
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 polytopes so as to compute the extreme monomials of the Newton polytope of the resultant. We consider...
متن کاملRandom Polynomials with Prescribed Newton Polytope
The Newton polytope Pf of a polynomial f is well known to have a strong impact on its behavior. The Kouchnirenko-Bernstein theorem asserts that even the number of simultaneous zeros in (C∗)m of a system of m polynomials depends on their Newton polytopes. In this article, we show that Newton polytopes further have a strong impact on the distribution of mass and zeros of polynomials, the basic th...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1964
ISSN: 0002-9939
DOI: 10.2307/2034914