The basis of a computer system for modern algebra

So-called general purpose systems for algebraic computation such as ALTRAN, MACSYMA, SAC, SCRATCHPAD and REDUCE are almost exclusively concerned with what is usually known as “classical algebra”, that is, rings of real or complex polynomials and rings of real or complex functions. These systems have been designed to compute with elements in a fixed algebraic structure (usually the ring of real functions). Typical of the facilities provided are: the arithmetic operations of the ring, the calculation of polynomial gcd's, the location of the zeros of a polynomial; and some operations from calculus: differentiation, integration, the calculation of limits, and the analytic solution of certain classes of differential equations. For brevity, we shall refer to these systems as CA systems.