A symbolic-numerical algorithm for isolating real roots of certain radical expressions

We propose a symbolic-numerical algorithm for isolating the real roots of certain non-nested radical expressions in a given interval. The algorithm uses numerical techniques to isolate the simple roots of the radical expression and symbolic techniques to isolate the (potential) multiple roots of the radical expression and the critical roots of the radical expression at the boundary of the domain in which the radical expression is defined. In the case when the associated polynomial of the radical expression constructed in the paper does not vanish, our algorithm succeeds to isolate all the desired roots. Experimental comparisons are provided to show the efficiency of the algorithm on test examples.