The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Subresultants and Reduced Polynomial Remainder Sequences
Journal of the ACM (JACM)
On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors
Journal of the ACM (JACM)
ACM '73 Proceedings of the ACM annual conference
The computing time of the Euclidean algorithm.
The computing time of the Euclidean algorithm.
Algorithms for polynomial factorization.
Algorithms for polynomial factorization.
Factoring multivariate polynomials over the integers
ACM SIGSAM Bulletin
A fast implementation of polynomial factorization
SYMSAC '86 Proceedings of the fifth ACM symposium on Symbolic and algebraic computation
A p-adic approach to the computation ofGröbner bases
Journal of Symbolic Computation
Constructive lifting in graded structures: A unified view of Buchberger and Hensel methods
Journal of Symbolic Computation
ACM SIGSAM Bulletin
A p-adic division with remainder algorithm
ACM SIGSAM Bulletin
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Two Hensel-type univariate polynomial Greatest Common Divisor (GCD) algorithms are presented and compared. The regular linear Hensel construction is shown to be generally more efficient than the Zassenhaus quadratic construction. The UNIGCD algorithm for UNIvariate polynomial GCD computations, based on the regular Hensel construction is then presented and compared with the Modular algorithm based on the Chinese Remainder Algorithm. From both an analytical and an experimental point of view, the UNIGCD algorithm is shown to be preferable for many common univariate GCD computations. This is true even for dense polynomials, which was considered to be the most suitable case for the application of the Modular algorithm.