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Integrating Symbolic Computation Tools into
Scientific Problem Solving Environments

Bruce Char, Tom Hewett, Jeremy Johnson, Lakshman Yagati, Ron Perline,
Raji Venkatesan, Michael Miller, Hoi Man Chang, Clint Hepner

Presented at the 1997 CRPC Annual Meeting Poster Session

After three decades' work, the computer algebra community has implemented many routines that can aid in problem analysis and coding development phases of scientific problem solving. Our multi-university research group (PSEware) aims to facilitate the development of PSE building tools by leveraging multiplatform commercially supported software and languages. The goal of the subgroup group at Drexel is to draw symbolic computation (computer algebra, or CA) out of the "self-contained system" ghetto, into the larger domain of (primarily numeric) problem solving. While some of this work involves the development of new algorithms, systems, or language interfaces, we believe that there's a lot that can be accomplished through the use of existing tools integrated into larger frameworks.

We see several immediate opportunities, including code generation for modelling, or for visualization, and "groupware" with mathematical capabilities. We develop such opportunities through the development of "glue" software for existing systems, and by more thoroughly understanding how to support the nature of the work, from a HCI point of view.

We have developed a few testbed examples to illustrate our approach:

  1. The "Soliton Explorer". Ron Perline, a research mathematician wishes to look at the geometry of solutions to differential equations that corresponds to certain soliton. CA is used to derive parameteric formulas from a mathematical starting point, that become function modules for a numeric ODE or PDE solver. Perline is interested in comparing and contrasting solutions for various values of the parameters. Features of the environment such as response time, easy manipulation of parameters and of the computation, animation, history, and session management are as important as the basic mathmatical computation. By developing a "Maple module" for the NAG Explorer visualization system we can get much of the desired functionality without the mathematician having to do direct Maple or Fortran programming. We are currently planning HCI experiments to assess the effectiveness of the current interface in supporting Perline's working methods.
  2. "Techtalk". Integration of interactive computer mathematics systems with Web services is area of activity. Techtalk 1.0 is a system that allows multiple users to access one or more Maple and/or Matlab sessions (or both) through a Web site. A user, after logging into Techtalk at the site, is able to see a chat window with conversation with the other participants, and windows with Maple/Matlab input and output. The software framework can be adapted to extend to other interactive systems. While Techtalk was originally motivated by the need to hold a distributed real-time conversation between computer science researchers to discussing mathematical formulae, the current version of Techtalk was used for "virtual office hours" involving a numerical analysis instructor and a few students at Drexel in Winter Quarter 1997. Subsequent versions of Techtalk will be used in larger scale experiments, including classes, in Fall 1997. Anyone with a Web browser can access Techtalk; Techtalk sites can be established by those who can run a Web server, Java, and the appropriate interactive math systems.