A Scheme for Manipulative Algebra on a Computer

This paper describes a scheme of programs that have been written to perform elementary manipulation of multiple Fourier series. These are represented in their literal form in the computer and a wide variety of operations may be performed upon them. The paper describes the principles adopted while programming the scheme, lists a number of the principal operations that may be performed, and presents two examples to demonstrate how the scheme may be employed to solve certain types of equations.