In this note we consider hyperelliptic-M-symmetric Riemann surfaces, that is, hyperelliptic Riemann surfaces with a symmetry with maximal number of components of fixed points. These surfaces can be represented either by real algebraic curves or by real Schottky groups. To obtain one of these in terms of the other is difficult. In this note we proceed to describe explicit transcendental relations between the different sets of parameters these representations give. This can be used to obtain a computer program which permits obtain numerical approximations of the algebraic curve in terms of real Schottky group and viceversa