@Carl Love From the referenced text by Brannan et. al.;
(The procedure rho) is the hyperbolic reflection (of point z) in the hyperbolic line that is part of a Euclidean circle with centre alpha.
How can the Mobius transformation in rho calculate a hyperbolic reflection of a point without requiring input of a radius of the circle referred to? Are not both a centre and a radius required to define the hyperbolic line of reflection?
My procedure InversePtMobius does require both of these inputs and only reproduces the output of procedure rho when InversePtMobius a centre of alpha and a radius of 1. This is why it seems to me that procedure rho assumes a radius of 1.
*** I just realized that any given centre of the circle mentioned above implies its radius under the condition that the circle meets the Poincare disk at right angles. ***
I therefore withdraw my Maple Primes question