Excerpts from a proposal to the National Science

1 Summary We propose to concentrate on investigations of technology in support of advanced scientiic computation, based on a higher-level view of the relationship of mathematical modeling to computation. This is based on the following considerations: 1. Symbolic mathematical manipulation and computer algebra systems: These are tools and techniques that support problem solving, code development, comprehension, debugging and partial evaluation (the principle behind many optimization techniques). 2. Data modeling: in particular, the use of IEEE oating-point number representations and operations. 3. Closed form or exact solutions: For some sub-problems of scientiic interest, numerical solutions are not the only paradigm. The availability of exact solutions, or symbolic-approximation solutions has advanced along with computing technology too. 4. The use of scripting languages: the linkage of high-performance library routines to graphical interfaces for data analysis and model setup can be enhanced by symbolic support and high-level scripting languages. 5. Extending the use of remote computation. We are now using standard network connections for the acquisition of complex data (in this case, symbolic solution of deenite integrals). 2 New Experiments In this section we discuss a variety of topics of of current interest. The (by now) traditional approach to mathematical modeling is to formulate \by hand" mathematical models whose consequences can be simulated by running computer programs. These programs are typically written in Fortran, but are increasingly being written in C, C++, or other languages that have better tools for abstraction and data structures. In part, the computational approach we advocate involves the use of computers in that earlier \by hand" stage of model formulation, using symbolic mathematics. The blossoming of this area via commercial programs typiied by Mathematica and Maple, as well as some less widely used but still viable competitors (Axiom, Macsyma, MuPAD) might suggests that this approach is (a) successful and (b) needs no more academic research. Actually, the relatively higher level of activity (and funding) in Europe has demonstrated that important results remain to be found in advancement of algorithms and building systems. Work at RISC-Linz (Austria), ETH (Zurich), CAN (Netherlands), INRIA (France) and the multinational POSSO project are just a few sample programs. Their activities overshadow the limited work in US universities, and point to the fact 1