Simplification of Nested Real Radicals Revisited

Abstract: 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 real radicals is known. However, this algorithm does not guarantee complete simplification for the case of radicals with nesting depth more than two. In the talk, we give a detailed presentation of the theory that provides an algorithm which simplifies triply nested reals radicals over the field of rationals. Some new examples of triply (or more) nested real radicals that cannot be simplified are also given.

symbolic computationclassical analysis and ODEs

Audience: researchers in the topic

Mathematical models and integration methods