source 2015 Bernstein--Chuengsatiansup--Kohel--Lange "Twisted Hessian curves"
parameter w
assume w^2+w+1 = 0
parameter f
assume f d^3 = 27 a
parameter 3overd
assume d 3overd = 3
compute R = a X1 X1^2
compute V = Y1 Y1^2
compute S = Z1 Z1^2
compute wS = w S
compute wV = w V
compute wSV = wS - wV
compute F = R + S + V
compute G = R + wSV - V
compute H = R - S - wSV
compute A = F F^2
compute B = A - f A
compute C = G G^2
compute D = H H^2
compute wC = w C
compute wD = w D
compute wCD = wC - wD
compute X3 = 3overd (B + C + D)
compute Y3 = B + wCD - D
compute Z3 = B - C - wCD