New Polynomial GCD and Factorization Algorithms and Software for Maple

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Maplesoft is a Candian company based in Waterloo, Ontario. Maplesoft's primary product, Maple, is a mathematical software system. Maple is used by scientists, engineers and researchers who work in academia and industry to perform mathematical computations and explorations.One of the main capabilities that Maple provides is the ability to represent and compute with formulas, such as polynomials in one or more variables and formulas involving functions like ln(x), sin(y), etc. Maple can differentiate and integrate formulas and solve systems of polynomial equations and differential equations.This research and development proposal aims to design and implement new algorithms for factoring polynomials and computing greatest common divisors of polynomials. These are two core operations. The overall speed of Maple depends substantially on how fast Maple can do these operations.We aim to speed up these two operations by a factor of 100 or more using new sparse polynomial interpolation methods. We also aim to further speed up these two operations by parallelizing the algorithms for multi-core computers.These improvements will give Maple a huge advantage over Maplesoft's main competitor Mathematica. Also, for the students who work on this project, the mathematics skills, computing skills and parallel programming skills that they learn will equip them with practical skills which are desired by industry.