Symbolic Computation Techniques for Large Expressions from Math. and Engineering

This thesis studies the use of computer algebra methods to solve some large expression problems from mathematics and engineering. We give several strategies for solving problems from symbolic linear algebra and dynamic systems.
First, we describe new forms for fraction-free LU factoring and QR factoring. Secondly, we propose a general method, hierarchical representation and signature computing for zero testing, to deal with problems with intermediate or inherent expression swell. Besides large expression problems from linear algebra, we also explore large expression problems from engineering, especially those arising from analyzing and solving multibody dynamic systems and limit cycle computations.
The techniques we develop in this thesis are quite general and can be easily applied to other similar areas, such as computing determinants and solving more general DAE models.