source 2015 Kohel "The geometry of efficient arithmetic on elliptic curves"
parameter 2overd
assume 2overd d = 2
parameter aoverddd
assume aoverddd d^3 = a
compute R = a X1 X1^2
compute V = Y1 Y1^2
compute S = Z1 Z1^2
compute T = R+S
compute N = T(S+V)(V+R)
compute M = (R-S)(S-V)(V-R)
compute C = (T+V) (T+V)^2
compute D = aoverddd C
compute E = N - 8 D
compute X3 = 2overd (C - 3(D + N))
compute Y3 = E + M
compute Z3 = E - M