source 2007 Feng--Wu, first JQN2 doubling formula, plus correction of obvious typos, plus epsilon=1, plus delta=-a
parameter a2
assume a2 = 2 a
compute A1 = (X1 Z1+Y1)^2
compute A2 = Y1^2
compute Q1 = (X1^2)^2
compute S1 = (X1 Z1)^2
compute T = A2-Q1-2 a S1
compute X3 = A1-A2-S1
compute Y3 = (T+Q1)(A2+a2 S1)+4 S1^2
compute Z3 = T-Q1
compute XX3 = X3^2
compute ZZ3 = Z3^2
compute T3 = XX3+ZZ3