source 2006 Doche--Icart--Kohel "Efficient scalar multiplication by isogeny decompositions", page 199, top display, plus reversal of roles of 1 and 2
parameter a3
assume a3 = 3 a
assume Z2 = 1
compute A = X2 ZZ1
compute B = Y2 ZZ1 Z1
compute C = X1-A
compute D = Y1-B
compute Z3 = Z1 C
compute E = Z3^2
compute F = C^2
compute G = C F
compute H = A F
compute X3 = D^2-G-a3 E-2 H
compute Y3 = D(H-X3)-B G
compute ZZ3 = E