Computer algebra for engineering and industry

该项目开发算法，使计算机代数系统可以更有效地用于解决数学问题。所开发的算法将在广泛可用的计算平台上实现，并分发给科学和工程界。所考虑的数学问题将来自工程和科学的重要领域。工业制造过程和工程设计是科学计算的重要领域。定量建模是分析工程设备性能的最佳方法。然而，定量和数值是不一样的；出于设计目的，包含符号的分析可能更好。一个例子可能对非科学家有所帮助。假设你正在设计一个使用活塞的东西，你的工作是选择活塞杆的长度。这样做的一种方法是选择一个确定的初始长度，为了一个例子，让我们说10厘米，并计算行为。然后您可以使用9.5 cm的长度重复计算。而不是每次有变化时都重新计算，您可以尝试将长度称为L，并只推导一次建模方程。帮助完成这种任务的软件产品通常被称为计算机代数系统。该项目将通过加速数值计算，增加可能的代数操作类型的数量和控制表达式膨胀来加强计算系统，特别是在应用中。最后一项涉及这样一个事实，即符号表达式在整个计算过程中往往不断增长，甚至中等大小的问题也可能生成完全填满计算机内存的表达式，从而有效地停止计算。这个建议建立在早期工作的基础上，开发了在工业重要计算中控制非常大的表达式的技术。

This project develops algorithms so that computer algebra systems can be used more effectively for the solution of mathematical problems. The algorithms developed  will be implemented in widely available computational platforms and distributed to the scientific and engineering communities. The mathematical problems considered will be drawn from important areas of engineering and science. Industrial manufacturing processes and engineering design are important areas of scientific computation. The performance of a piece of engineering equipment is best analysed using quantitative modelling. Quantitative is not the same as numerical, however; for design purposes, an analysis containing symbols might be better. An example might help non-scientists. Suppose you are designing something that uses a piston, and your job is to select the length of the piston rod. One way to do this would be to select a definite initial length, for the sake of an example let us say 10 cm, and calculate the behaviour. Then you might repeat the calculation using a length of 9.5 cm. Instead of recalculating every time that there is a change, you might try instead to call the length L and derive the modelling equations just once. The software products that help perform such a task are often called computer algebra systems. This project will strengthen computational systems, especially in applications, by speeding numerical calculations, increasing the number of types of algebraic manipulation possible and controlling expression swell. This last item refers to the fact that symbolic expressions tend to grow constantly throughout a calculation, and even moderate-sized problems can generate expressions that completely fill computer memory, thereby effectively stopping the calculation. This proposal builds on earlier work to develop techniques for controlling very large expressions in industrially significant calculations.