Radical sums

Luís Fernando Schultz Xavier da Silveira

University of Ottawa

We look at the problem of deciding whether a sum of square roots of non-negative rational numbers is smaller, equal or greater than another one. The connections of this problem to computational geometry are explored and the state of the art is surveyed. A polynomial time algorithm adapted from a work of Blömer to decide for equality is presented, but to decide which one is smaller when they differ is still a very important open problem.