An improved multivariate polynomial factoring algorithm
TL;DR: A new algorithm for factoring multivariate polynomials over the integers based on an algorithm by Wang and Rothschild is described, which is generally faster and requires less store then the original algorithm.
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Abstract: A new algorithm for factoring multivariate polynomials over the integers based on an algorithm by Wang and Rothschild is described. The new algorithm has improved strategies for dealing with the known problems of the original algorithm, namely, the leading coefficient problem, the bad-zero problem and the occurrence of extraneous factors. It has an algorithm for correctly predetermining leading coefficients of the factors. A new and efficient p-adic algorithm named EEZ is described. Bascially it is a linearly convergent variable-by-variable parallel construction. The improved algorithm is generally faster and requires less store then the original algorithm. Machine examples with comparative timing are included.
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Citations
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.
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A Singular Introduction to Commutative Algebra
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References
•Book
The Art of Computer Programming, Volume 2: Seminumerical Algorithms
Donald E. Knuth
- 01 Jan 1981
4.4K
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).
Factoring polynomials over finite fields
TL;DR: The method reduces the factorization of a polynomial of degree m over GF(q) to the solution of about m(q − 1)/q linear equations in as many unknowns over GF (q).
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