Computer Algebra Domains and Interfaces

计算机代数领域和接口

• 批准号: 203419-2012
• 负责人: Watt, Stephen
• 金额: $ 2.48万
• 依托单位: University of Western Ontario
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2014
• 资助国家: 加拿大
• 起止时间: 2014-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=546341
• 关键词: Computer; Algebra; Domains; Interfaces

Much of the current work in computer algebra examines algorithmic questions in algebraic geometry, linear algebra and differential algebra. Current algorithms are excellent at computing with particular polynomials, matrices or differential equations, but little attention has been paid to computing with symbolic objects. By this we mean objects such as polynomials of unknown degree, e.g. x^(n^2 +n) - 81y^(2m), matrices of unknown dimension, elements of an unspecified finite field, etc. Our earlier work has found several algorithms for these sorts of symbolic objects, including polynomial GCD, factorization and functional decomposition.

目前计算机代数的大部分工作都在研究代数几何、线性代数和微分代数中的算法问题。目前的算法在计算特定的多项式、矩阵或微分方程方面表现出色，但很少关注符号对象的计算。我们的意思是对象，如多项式的未知次数，例如x^（n^2 +n）-81 y ^（2 m），矩阵的未知维数，元素的一个未指定的有限域，等等。我们早期的工作已经发现了几个算法，这些种类的符号对象，包括多项式GCD，因式分解和功能分解。