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 ..."
appliesto jacobian-3
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