Simplification of nested radicals

Radical simplification is a fundamental mathematical question, as well as an important part of symbolic computation systems. The general denesting problem had not been known to be decidable. Necessary and sufficient conditions for a radical α over a field k to be denested, as well as the first algorithm to decide whether the expression can be denested, are given. The algorithm computes an equivalent expression of minimum nesting depth. It has running time polynomial in the size of the splitting field of the minimal polynomial of α over k