Symbolic Linear Algebra Computation

这个项目的目标是改进已实现的和可用的软件，用于解决各种矩阵计算问题，包括参数化线性方程组的解，多项式函数域上线性方程组的解，矩阵范式计算，以及矩阵相似性和等价性的确定。这些工具是计算机代数包（如Maple、Mathematica和Magma）中大量使用的一部分。此外，它们与定制的大规模应用程序相关。研究将集中在(1)算法设计，(2)并行和分布式实现，以及(3)启发式的使用。这项工作的一个明确目标是提供可直接被科学界使用的实现。这样的实现将包括独立的可移植代码和将包含在一个或多个通常可用的计算机代数系统的库中的代码。从这个意义上说，这项工作将增强科学和工程计算的问题解决环境。

The goal of this project is the improvement of the implemented and available software for solution of a variety of matrix computation problems, including solution of systems of parameterized linear equations, solution of systems of linear equations over a polynomial function domain, matrix normal form computations, and determination of matrix similarity and equivalence. Such tools are a heavily used portion of computer algebra packages such as Maple, Mathematica, and Magma. Also they are relevant to custom large scale applications. The research will focus on (1) algorithm design, (2) parallel and distributed implementation, and (3) use of heuristics. An explicit goal of this work is to provide implementations that are directly usable by the scientific community. Such implementations will include stand-alone portable codes and code to be included in the libraries of one or more of the generally available computer algebra systems. In this sense this work will enhance the problem solving environments available for scientific and engineering computation.