Computer algebra for engineering and industry

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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.