Irreducibility of polynomials modulo \(p\) via Newton polytopes.

DOI10.1016/S0022-314X(03)00044-1zbMath1108.13307OpenAlexW1982618205MaRDI QIDQ1399670

Shuhong Gao, Virgínia M. Rodrigues

Publication date: 30 July 2003

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0022-314x(03)00044-1

zbMATH Keywords

PDEgood reductionNewton polytopesabsolute irreducibility

Mathematics Subject Classification ID

Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Polynomials in general fields (irreducibility, etc.) (12E05) Polynomials, factorization in commutative rings (13P05) Polynomials (irreducibility, etc.) (11R09)

Related Items (11)

Zero-patterns of polynomials and Newton polytopes. ⋮ Reduction of bivariate polynomials from convex-dense to dense, with application to factorizations ⋮ Lifting and recombination techniques for absolute factorization ⋮ Families of polynomials and their specializations ⋮ Bivariate factorization using a critical fiber ⋮ On pseudopoints of algebraic curves ⋮ Arithmetic constraints of polynomial maps through discrete logarithms ⋮ Indecomposability of polynomials via Jacobian matrix ⋮ Nearly optimal algorithms for the decomposition of multivariate rational functions and the extended Lüroth theorem ⋮ On Functional Graphs of Quadratic Polynomials ⋮ Control of the non-geometrically integral reductions

Cites Work

• Fast parallel absolute irreducibility testing
• On multiplication and factorization of polynomials. I: Lexicographic orderings and extreme aggregates of terms
• Equations over finite fields. An elementary approach
• Reducibility of polynomials \(f(x,y)\) modulo \(p\)
• On the reduction modulo \(p\) of an absolutely irreducible polynomial \(f(x,y)\)
• Effective Noether irreducibility forms and applications
• Reduzibilität ebener Kurven.
• Factoring multivariate polynomials via partial differential equations
• Absolute irreducibility of polynomials via Newton polytopes
• Decomposition of polytopes and polynomials

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