source 2006 Gaudry "Variants of the Montgomery form based on Theta functions", page 22/52, with A^2/B^2 = (a^2+b^2)/(a^2-b^2) as on page 20/52, replacing incorrect B^2/A^2 and b/a on page 22/52 with correct A^2/B^2 and a/b; or 2009 Gaudry--Lubicz "The arithmetic of characteristic 2 Kummer surfaces and of elliptic Kummer lines", Section 6.2, replacing incorrect A'/B' = (a^2+b^2)/(a^2-b^2) with correct A'^2/B'^2 = (a^2+b^2)/(a^2-b^2), replacing A'^2/B'^2 with A^2/B^2, and replacing z... with y...; plus notation changes: a/b and A^2/B^2 defined as 1/sqrt(r) and (1+r)/(1-r), input x^2/y^2 replaced by Z1/Y1, intermediate x'/y' replaced by W/V, output X^2/Y^2 replaced by Z3/Y3; plus assumption Z1=1; plus standard simplification assume Z1 = 1 parameter s assume s = (1+r)/(1-r) compute W = (1+Y1)^2 compute V = s(W-4 Y1) compute Y3 = (W-V)^2 compute Z3 = r(W+V)^2