Simplification of Nested Real Radicals Revisited.

The problem of simplification of nested radicals over arbitrary number fields was studied by many authors. The case of real radicals over real number fields is somewhat easier to study (at least, from theoretical point of view). In particular, an efficient (i.e., a polynomial-time) algorithm of simplification of at most doubly nested radicals is known. However, this algorithm does not guarantee complete simplification for the case of radicals with nesting depth more than two. In the paper, we give a detailed presentation of the theory that provides an algorithm which simplifies triply nested reals radicals over Q . Some examples of triply nested real radicals that cannot be simplified are also given.