source 2007 Bernstein--Lange; derived from 2006 Doche--Icart--Kohel "Efficient scalar multiplication by isogeny decompositions", page 197, middle display, by substitution Z2=1, simplification, projectification, clearing denominators, common-subexpression elimination compute A = Y1 ZZ2-Y2 ZZ1 compute AA = A^2 compute X2Z1 = X2 Z1 compute B = X1 Z2-X2Z1 compute C = B Z2 compute E = C Z1 compute EE = E^2 compute F = E C compute D = F X1 compute U = AA-a EE-D-X2Z1 E B compute X3 = 2 U compute Y3 = 2 ((E+A)^2-EE-AA) (D-U)-Y1 (2 F)^2 compute Z3 = 2 EE compute ZZ3 = Z3^2