An example of a problem in the physical sciences is discussed where application of various symbolic computation facilities available in many algebraic computing systems leads to a significant expansion of the range problems that can be solved. Since most interesting problems in the physical sciences eventually require the numerical solution of systems of equations, of various types, we will introduce an example and describe an approach to a solution, beginning at the development of relevant differential equations, using, for example REDUCE, and leading eventually to the generation of highly efficient and stable numerical code for the solution, using, in our case, the C language. The use of SCOPE and GENTRAN, as well as series packages in REDUCE will be discussed.In many areas of interest, a considerable amount of work has to be performed to arrive at the symbolic equations to solve, and this is particularly true in General Relativity and related gravitation theories. Some packages, such as REDTEN [1], for calculation in this field will be discussed.