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Absolute Irreducibility of Polynomials via Newton Polytopes

โœ Scribed by Shuhong Gao

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
139 KB
Volume
237
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

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 irreducibility criteria including the well-known Eisenstein criterion. Polynomials from these criteria are over any field and have the property of remaining absolutely irreducible when their coefficients are modified arbitrarily in the field, but keeping a certain collection of them nonzero.

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