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 r Z1^2/Y1^2, intermediate x'/y' replaced by W/V, output X/Y replaced by sqrt(r) Z3/Y3; plus common-subexpression elimination parameter s assume s = (1+r)/(1-r) compute YY = Y1^2 compute ZZ = r Z1^2 compute V = s(ZZ-YY)^2 compute W = (ZZ+YY)^2 compute Y3 = W-V compute Z3 = W+V