source 2007 Bernstein--Lange
compute XX = X1^2
compute YY = Y1^2
compute ZZ = Z1^2
compute YYYY = YY^2
compute M = 3 XX+a ZZ^2
compute MM = M^2
compute E = 6 ((X1+YY)^2-XX-YYYY)-MM
compute EE = E^2
compute T = 16 YYYY
compute U = (M+E)^2-MM-EE-T
compute X3 = 4 (X1 EE-4 YY U)
compute Y3 = 8 Y1 (U (T-U)-E EE)
compute Z3 = (Z1+E)^2-ZZ-EE
