Symbolic Algebra zone

Dr Darren says:

"I consider symbolic algebra languages and applications to be amongst the greatest technological achievements of humanity."

My interest in symbolic algebra started during my PhD research from 1989-1993 when I became interested in automating the tedious task of calculating Jacobians of numerical difference schemes for implicit gas/hydro dynamics solvers. I successfully used the REDUCE symbolic algebra system to generate FORTRAN code representing implicit integration methods, and I used it to model supernova shock waves.

Since then symbolic algebra has played a role in nearly all of my scientific activities, whether using the Maple, Mathematica, Mathcad, or MATLAB/Simulink symbolic application (thankfully the REDUCE command-line days are long gone).

My applications of symbolic algebra have included:

• Development of a symbolic algebra system for generating compilable code for implementing implicit 3D time-dependent PDE equation solvers. The system has been tested on an advanced gasdynamics solvers using adaptive gridding.
• Symbolic worksheets for modelling dust disruptions in electron particle accelerators (example: MapleV.3: HERA particle collider beam dynamics: Maple symbolic worksheet example.)
• Symbolic data analysis and visualisation of multi-dimensional datasets.

For more examples of some of my applications of symbolic algebra please visit the Maple zone.