Improved dense multivariate polynomial factorization algorithms
نویسندگان
چکیده
منابع مشابه
Improved dense multivariate polynomial factorization algorithms
We present new deterministic and probabilistic algorithms that reduce the factorization of dense polynomials from several to one variable. The deterministic algorithm runs in sub-quadratic time in the dense size of the input polynomial, and the probabilistic algorithm is softly optimal when the number of variables is at least three. We also investigate the reduction from several to two variable...
متن کاملImproved Sparse Multivariate Polynomial Interpolation Algorithms
We consider the problem of interpolating sparse multivariate polynomials from their values. We discuss two algorithms for sparse interpolation, one due to Ben-Or and Tiwari (1988) and the other due to Zippel (1988). We present efficient algorithms for finding the rank of certain special Toeplitz systems arising in the Ben-Or and Tiwari algorithm and for solving transposed Vandermonde systems of...
متن کاملPolynomial factorization algorithms over number fields
Factorization algorithms over Q[X] and Fp[X] are key tools of computational number theory. Many algorithms over number fields rely on the possibility of factoring polynomials in those fields. Because of the recent development of relative methods in computational number theory, see for example (Cohen et al. 1998, Daberkow and Pohst 1995), efficient generalizations of factorization algorithms to ...
متن کاملPolynomial Factorization Sharp Bounds, Efficient Algorithms
A new coeÆcient bound is established for factoring univariate polynomials over the integers. Unlike an overall bound, the new bound limits the size of the coeÆcients of at least one irreducible factor of the given polynomial. The single-factor bound is derived from the weighted norm introduced in Beauzamy et al. (1990) and is almost optimal. E ective use of this bound in p-adic lifting results ...
متن کاملAn Improved Multivariate Polynomial Factoring Algorithm
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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2007
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2007.01.003