Factorization of polynomials over finite fields
نویسندگان
چکیده
منابع مشابه
Polynomial-Time Factorization of Multivariate Polynomials over Finite Fields
We present a probabilistic algorithm that finds the irreducible factors of a bivariate polynomial with coefficients from a finite field in time polynomial in the input size, i.e. in the degree of the polynomial and log (cardinality of field). The algorithm generalizes to multivariate polynomials and has polynomial running time for densely encoded inputs. Also a deterministic version of the algo...
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A deterministic polynomial time algorithm is presented for finding the distinctdegree factorization of multivariate polynomials over finite fields. As a consequence, one can count the number of irreducible factors of polynomials over finite fields in deterministic polynomial time, thus resolving a theoretical open problem of Kaltofen from 1987.
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A new deterministic factorization algorithm for polynomials over finite fields was recently developed by the first author. The bottleneck in this algorithm is the last stage in which the irreducible factors of the polynomial are derived from the solutions of a system of linear equations. An efficient approach to the last stage was designed by the second author for the case of finite fields of c...
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As we will see, modular arithmetic aids in testing the irreducibility of polynomials and even in completely factoring polynomials in Z[x]. If we expect a polynomial f(x) is irreducible, for example, it is not unreasonable to try to find a prime p such that f(x) is irreducible modulo p. If we can find such a prime p and p does not divide the leading coefficient of f(x), then f(x) is irreducible ...
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We study the factorization into irreducibles of iterates of a quadratic polynomial f over a finite field. We call f settled when the factorization of its nth iterate for large n is dominated by “stable” polynomials, namely those that are irreducible under post-composition by any iterate of f . We prove that stable polynomials may be detected by their action on the critical orbit of f , and that...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1969
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1969-0257039-x