Digit Recurrence for Algebraic Functions

An algebraic function is defined as the solution to a multivariate polynomial equation. This definition can often be combined with the equation of a radix-β representation to obtain a digit-recurrence algorithm evaluating the function. This is a generalization of a technique described in detail in Chap. 9 for division (another algebraic function). It is first demonstrated on square and cube roots, then on 2D and 3D Euclidean norms, and finally on the evaluation of an arbitrary rational function.