Research Triangle Park, NC, USA
Oct. 30, 1989 to Nov. 1, 1989
S. Landau , Dept. of Math. Dept., Wesleyan Univ., Middletown, CT, USA
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 alpha 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 alpha over k.
minimal polynomial, radical simplification, nested radicals, decidable, equivalent expression, minimum nesting depth
S. Landau, "Simplification of nested radicals", FOCS, 1989, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science 1989, pp. 314-319, doi:10.1109/SFCS.1989.63496