Derivatives without tears in Algol 68

Abstract

Algol 68 is a very suitable language for tackling problems which lie somewhere between numerical calculation and algebraic manipulation. An algorithm is presented which evaluates a function of n variables and its n partial derivatives using at most C.m operations, where m is the number of operations required to evaluate the function and C is a constant independent of n. By altering mode declarations, an ordinary piece of program text written to evaluate the function can be made instead to generate the expression tree required for calculation of derivatives.