A Generalized Class of Polynomials that are Hard to Factor
Copyright policy )A Generalized Class of Polynomials that are Hard to Factor
A class of univariate polynomials is defined which make the Berlekamp-Hensel factorization algorithm take an exponential amount of time. The class contains as subclasses the Swinnerton-Dyer polynomials discussed by Berlekamp and a subset of the cyclotomic polynomials. Aside from shedding light on the complexity of polynomial factorization this class is also useful in testing implementations of the Berlekamp-Hensel and related algorithms.
exponential time, Galois groups, Analysis of algorithms and problem complexity, Cyclotomic extensions, polynomial factorization, Berlekamp-Hensel algorithm, Symbolic computation and algebraic computation, computer algebra, Polynomials (irreducibility, etc.)
exponential time, Galois groups, Analysis of algorithms and problem complexity, Cyclotomic extensions, polynomial factorization, Berlekamp-Hensel algorithm, Symbolic computation and algebraic computation, computer algebra, Polynomials (irreducibility, etc.)
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