Open Access
Sparse Hensel Lifting
Eric hK altofen
- 01 Jan 1985
51
TL;DR: In this article, the multivariate leading coefficients of polynomial factors from their univariate images are computed using sparse Hensel lifting and the content of the input polynomials in the main variable is provided as a byproduct.
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Abstract: An ew a lgorithm is introduced which computes the multivariate leading coefficients of polynomial factors from their univariate images. This algorithm is incorporated into a sparse Hensel lifting scheme and only requires the factorization of a single univariate image. The algorithm also provides the content of the input polynomial in the main variable as a by-product. We sho wh ow w ec an tak ea dvantage of this property when computing the GCD of multivariate polynomials by sparse Hensel lifting.
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Handbook of Finite Fields
Gary L. Mullen,Daniel Panario +1 more
- 17 Jun 2013
TL;DR: The Handbook of Finite Fields describes various mathematical and practical applications of finite fields in combinatorics, algebraic coding theory, cryptographic systems, biology, quantum information theory, engineering, and other areas.
351
Complexity issues in bivariate polynomial factorization
Alin Bostan,Grégoire Lecerf,Bruno Salvy,Éric Schost,B. Wiebelt +4 more
- 04 Jul 2004
TL;DR: This work proposes an algorithm based on a faster multi-moduli computation for univariate polynomials and shows that it saves a constant factor compared to the classical multifactor lifting algorithm.
Effective Hilbert irreducibility
TL;DR: A probabilistic irreducibility test for sparse multivariate polynomials over arbitrary perfect fields is constructed by means of a very effective version of the Hilbert irreduceibility theorem.
40
Dagwood: a system for manipulating polynomials given by straight-line programs
TL;DR: This work discusses the design, implementation, and benchmarking of a system that can manipulate symbolic expressions represented by their straight-line computations capable of performing rational arithmetic on, evaluating, differentiating, taking greatest common divisors of, and factoring polynomials instraight-line format.
39
Computing with polynomials given by straight-line programs II sparse factorization
Erich Kaltofen
- 21 Oct 1985
TL;DR: An algorithm for the factorization of a multivariate polynomial represented by a straight-line program into its irreducible factors represented as sparse polynomials is developed with controllably high probability the correct factorization.
37
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•Book
The Hensel lemma in algebraic manipulation
David Y. Y. Yun
- 01 Jan 1980
TL;DR: The EZGCD Algorithm is given special emphasis and demonstrates promising efficiencies by taking advantage of the sparseness of multivariate polynomials.
63
Using basis computation to determine pseudo-multiplicative independence
H. I. Epstein
- 10 Aug 1976
TL;DR: Algorithms which find a basis for a set of Gaussian rational functions and the corresponding linear equations are presented in detail and bounds on their theoretical computing times are derived.
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