source 1986 Chudnovsky--Chudnovsky "Sequences of numbers generated by addition in formal groups and new primality and factorization tests", page 414, formula (4.2ii) modified as indicated after "It is even smarter ..."
compute S = 4 X1 Y1^2
compute M = 3(X1-Z1^2)(X1+Z1^2)
compute T = M^2-2 S
compute X3 = T
compute Y3 = M(S-T)-8 Y1^4
compute Z3 = 2 Y1 Z1
