Absolute irreducibility of polynomials via newton polytopes

[摘要] 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. (C) 2001 Academic Press

[发布日期] 2001-03-15

[效力级别]  Proceedings Paper

[关键词] fields;multivariable polynomials;absolute irreducibility;Newton polytopes;Newton polygons;indecomposable polytopes;Eisenstein criterion;Minkowski sums