source 2007 Bernstein--Lange
compute XX = X1^2
compute YY = Y1^2
compute YYYY = YY^2
compute ZZ = Z1^2
compute S = 2 ((X1+YY)^2-XX-YYYY)
compute M = 3 XX+a ZZ^2
compute T = M^2-2 S
compute X3 = T
compute Y3 = M (S-T)-8 YYYY
compute Z3 = (Y1+Z1)^2-YY-ZZ
