Matrix product multi-variable polynomials from quantum algebras

量子代数的矩阵积多变量多项式

• 批准号: DP190102897
• 负责人: Prof Jan de Gier
• 金额: $ 21.06万
• 依托单位: The University of Melbourne
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2019
• 资助国家: 澳大利亚
• 起止时间: 2019-06-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP190102897
• 关键词: Matrix; product; multi; variable; polynomials

This project aims to expand the theory of polynomials and develop generalised polynomial families using connections to affine and toroidal algebras. Many combinatorial and computational problems in pure and applied mathematics as well as mathematical physics can be solved using polynomials in many variables, such as Macdonald polynomials. This project is anticipated to address the current difficulty of implementing symmetric and non-symmetric polynomials in symbolic algebra packages by developing completely new algorithms. New understanding from the project is expected to facilitate challenging computational problems of measurable quantities in quantum systems.

该项目旨在扩大多项式理论，并使用与仿射和环形代数的联系发展广义的多项式家庭。纯数学和应用数学以及数学物理学中的许多组合和计算问题都可以使用许多变量（例如麦克唐纳多项式）中的多项式解决。预计该项目将通过开发全新的算法来解决当前在符号代数软件包中实施对称和非对称多项式的困难。预计该项目的新理解将促进量子系统中可测量数量的挑战计算问题。