source 2006 Doche--Icart--Kohel "Efficient scalar multiplication by isogeny decompositions", page 199, top display, plus Z2=1, plus simplification, plus projectification, plus denominator clearing, plus common-subexpression elimination parameter a3 assume a3 = 3 a compute A = X2 ZZ1-X1 ZZ2 compute B = Y2 Z1 ZZ1-Y1 Z2 ZZ2 compute C = Z2 A compute CC = C^2 compute D = X1 CC compute Z3 = Z1 C compute E = Z3^2 compute X3 = B^2-A A^2-a3 E-2 D compute Y3 = B(D-X3)-Y1 C CC compute ZZ3 = E