Computational complexity in algebraic function fields

Abstract

The problem solved in this paper is the following. Let x I' xn be indeterminates; let [I' ... , rk be simple radicals, by which is meant let rl' ... , rk be the square roots of rational functions of x I' ... , xn ; and let f I' , fm be simple algebraic Junctions, by which is meant let f I' , fm be rational functions of rl' ... , rk and xI' ... , x(l" What is the minimum possible cost of computing f I' ... , fm from x I' ... , xn ' if rational operations have cost zero and square root extractions (the only irrational operations allowed) have cost one?