Symbolic modeling of high energy beam optics

A classical problem of computational physics consists of finding the minimum of a chi /sup 2/ like function of many variables. Powerful optimization algorithms have been developed but do not guarantee convergence towards an absolute minimum. Analytical methods can improve the insight into a physical problem but calculations quickly exceed the power of a human brain. There comes the interest of optical design of high energy particle accelerators. The physics background is sketched and emphasis is put on the methodology. In practice, algebraic models may not be precise enough but they usually provide excellent initial conditions for a final numerical optimization. (4 refs).