Speeding up polynomial GCD, a crucial operation in Maple

Abstract

Given two multivariate polynomials A and B with integer coefficientswe present a new GCD algorithm which computes G = gcd(A,B).Our algorithm is based on the Hu/Monagan GCD algorithm.If A = G A̅ and B = G B̅ we have modified the Hu/Monaganso that it can interpolate the smaller of G and A̅.
 We have implemented the new GCD algorithm in Maple withseveral subroutines coded in C for efficiency.Maple currently uses Zippel's sparse modular GCD algorithm.We present timing results comparing Maple's implementation of Zippel's algorithm

Упрощение Рациональных Функций Для Редукции С Использованием Соотношений Интегрирования По Частям И Не Только

“…High-performance algorithms relevant for polynomials and rational functions are continually and actively developed in Maple (see e.g. [44,48,49]). To simplify rational functions, Maple utilizes the normal function with the option expanded to prevent storing polynomials in factorized form.…”