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This example uses Weyl to perform a simple computation. The functions f_{n} satisfy the recurrence relation shown at the top. To begin the computation, we must first create the algebraic domain in which the f_{n} lie. This is done by the assignment statement.

Next the symbolic variables are mu, eps and sigma are created as polynomials in the ring to represent the expressions mu, epsilon and sigma respectively. Finally the program is written as a recurrence in the standard fashion. Notice that standard Lisp programming is used, with the usual control structures and operators.