How does symbolic math figure in?
Symbolic math is really a higher form of compilationsymbol solving. It is a way of converting one symbol system into anothertranslation. The whole pre-computer fields of mathematical analysis and symbolic logic fit into this scenario. It is reductionistic. But as most numerical analysts will tell you, the way to solve PDEs by computer is to reduce them to ODEs, or to algebraic equations with finite-element or finite-difference approximations. The way to do this metaphorically is to use systems like Maple or Macsyma to transform the abstract PDE formulations into meta-calculus programs.
