New Polynomial GCD and Factorization Algorithms and Software for Maple

Maple 的新多项式 GCD 和因式分解算法和软件

• 批准号: 576162-2022
• 负责人: Monagan, MichaelMB
• 金额: $ 1.75万
• 依托单位: Simon Fraser University
• 依托单位国家: 加拿大
• 项目类别: Alliance Grants
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=758442
• 关键词: New; Polynomial; GCD; Factorization; Algorithms

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.

Maplesoft是一家加拿大公司，总部位于安大略滑铁卢。Maplesoft的主要产品Maple是一个数学软件系统。Maple被学术界和工业界的科学家、工程师和研究人员用来进行数学计算和探索。Maple提供的主要功能之一是用公式表示和计算的能力，例如一个或多个变量的多项式和涉及ln（x），sin（y），Maple可以对公式进行微分和积分，并可以求解多项式方程和微分方程组。本研究和开发计划旨在设计和实现多项式因式分解和计算的新算法多项式的最大公因子这是两个核心业务。Maple的整体速度在很大程度上取决于Maple执行这些操作的速度。我们的目标是使用新的稀疏多项式插值方法将这两个操作的速度提高100倍或更多。我们还打算通过并行化多核计算机的算法来进一步加快这两个操作。这些改进将使Maple相对于Maplesoft的主要竞争对手Mathematica具有巨大的优势。此外，对于从事该项目的学生来说，他们所学的数学技能、计算技能和并行编程技能将使他们具备行业所需的实用技能。