Yves Papegay, Sophia, INRIA, France  (Yves.Papegay@sophia.inria.fr)

Title: "Design and Performance Analysis of Optical Instruments with 
        Computer Algebra"

Abstract:  This talk describes a computer algebra package to help the design 
           and performance analysis of optical instruments. 
           The design of a complex optical instrument, such as an 
           interferometer, leads to the study of a very large model 
           represented as a set of equations that relate the parameters of 
           the instrument. The problem is then to find some optimal values 
           of these parameters with respect to some performances.
           Due to the complexity of the models involved, there is no 
           completely automatic method to solve this optimal design problem. 
           We show how computer algebra can be an invaluable tool in the 
           design process: 
           - to generate the model from a physical description of the 
             instrument (by applying suitable physical relations)
           - to show how some parameters or performances can be expressed as
             functions of other parameters, insuring the validity of each
             physical relation (that comes with a set of inequations that
             describe its domain of validity) 
           - to generate some specialized numerical code when a 
             symbolic treatment is no more possible.