Simple polynomials are known to most of us from basic school algebra. They can be used to express geometrical identities such as the Pythagorean Theorem a2 + b2 = c2. Algebraic manipulations can even mimic geometrical reasoning. Here is a proof of the Pythagorean Theorem based on some areal equations:
In higher mathematics polynomials can be viewed as algebraic extensions of rings. An interesting operation is the evaluation of an algebraic expression in a polynomial ring. This is exactly what the following Prolog text does. The original Prolog text is an adaption of a Lisp program and can be found in the Aquarius test suite .
One test iteration computes (1-x+y-z)10.