source 1986 Chudnovsky--Chudnovsky "Sequences of numbers generated by addition in formal groups and new primality and factorization tests", formula 4.9ii
compute S3 = 2 C1 Z1 D1 S1
compute C3 = (C1 Z1)^2-(D1 Z1)^2+(C1 D1)^2
compute D3 = (D1 Z1)^2-(C1 Z1)^2+(C1 D1)^2
compute Z3 = (D1 Z1)^2+(C1 Z1)^2-(C1 D1)^2