A fast parallel sparse polynomial GCD algorithm. (July 2021)

• Record Type: Journal Article
• Authors: Hu, Jiaxiong; Monagan, Michael
• Is Part Of: Journal of symbolic computation. Volume 105(2021)
• Page Start: 28
• Page End: 63
• Publication Date: 2021-07
• Subjects: Polynomial GCD computation -- Sparse polynomial interpolation -- Modular algorithms; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2020.06.001
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We present a parallel GCD algorithm for sparse multivariate polynomials with integer coefficients. The algorithm combines a Kronecker substitution with a Ben-Or/Tiwari sparse interpolation modulo a smooth prime to determine the support of the GCD. We have implemented our algorithm in C for primes of various sizes and have parallelized it using Cilk C. We compare our implementation with Maple and Magma's serial implementations of Zippel's GCD algorithm.