Abstract
Our aim in this and in the following chapter is to study the Newton polytope of the A-discriminant Δ A . This will be done through an intermediary object, the so-called principal A-determinant E A . Like the A-discriminant, E A = E A (f) is a polynomial function in coefficients a ω of an indeterminate polynomial f ∈ CA. We shall do the following:
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(1)
give a complete description of the Newton polytope of E A . It turns out to coincide with the secondary polytope Σ(A) (see Chapter 7);
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(2)
give a formula (prime factorization) expressing E A as a product of Δ A and discriminants corresponding to some subsets of A;
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(3)
give a formula for the product of values of a polynomial at its critical points in terms of the principal A-determinants.
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© 1994 Springer Science+Business Media New York
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Gelfand, I.M., Kapranov, M.M., Zelevinsky, A.V. (1994). Principal A-Determinants. In: Discriminants, Resultants, and Multidimensional Determinants. Mathematics: Theory & Applications. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4771-1_11
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DOI: https://doi.org/10.1007/978-0-8176-4771-1_11
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-0-8176-4770-4
Online ISBN: 978-0-8176-4771-1
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