Calculations with SCHOONSCHIP

An algebraic manipulation system is a program that allows one to do calculations with formulae, in the same way that the FORTRAN compiler allows one to do calculations with numbers. SCHOONSCHIP can handle any algebraic problem, at least if the programmer succeeds to present the method of solution in terms of elementary operations like: multiplying polynomials, substituting function, comparing terms, etc. It will be explained how SCHOONSCHIP works internally. In particular the use of memory, the representation of formulae and the overflow to disk will be sketched. A few examples of different types of calculations will be discussed.