Book Chapter10.1007/978-3-7091-7551-4_8
Factorization of Polynomials
E. Kaltofen
- 01 Jan 1983
- pp 95-113
74
TL;DR: Algorithms for factoring polynomials in one or more variables over various coefficient domains are discussed and an attempt is made to establish a complete historic trace for today’s methods.
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Abstract: Algorithms for factoring polynomials in one or more variables over various coefficient domains are discussed. Special emphasis is given to finite fields, the integers, or algebraic extensions of the rationals, and to multivariate polynomials with integral coefficients. In particular, various squarefree decomposition algorithms and Hensel lifting techniques are analyzed. An attempt is made to establish a complete historic trace for today’s methods. The exponential worst case complexity nature of these algorithms receives attention.
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References
Probabilistic algorithms for sparse polynomials
Richard Zippel
- 01 Jun 1979
TL;DR: This work has tried to demonstrate how sparse techniques can be used to increase the effectiveness of the modular algorithms of Brown and Collins and believes this work has finally laid to rest the bad zero problem.
•Book
Elementary and analytic theory of algebraic numbers
Władysław Narkiewicz
- 01 Jan 1990
TL;DR: In this paper, Dedekind Domains and Valuations have been used to define the theory of P-adic fields and to define a local compact Abelian group. But they do not consider the relation between the two types of fields.
1.1K
Factoring polynomials over large finite fields
TL;DR: In this paper, the authors present a deterministic procedure for factoring polynomials over finite fields, which reduces the problem of factoring an arbitrary polynomial over the Galois field GF(p m) to finding the roots in GF(m) of certain other polynomorphisms over GF (m).
Probabilistic Algorithms in Finite Fields
TL;DR: Probabilistic algorithms for the problems of finding an irreducible polynomial of degree n over a finite field, finding roots of a polynometric, and factoring aPolynomial into its irredUCible factors over a infinite field are presented.
A new algorithm for factoring polynomials over finite fields
David G. Cantor,Hans Zassenhaus +1 more
TL;DR: A new probabilistic method is presented which, when combined with the above algorithms, avoids the need for both resultants and linear equations and leads to algorithms which are conceptually simpler than previous methods.