source 2008 Hisil--Wong--Carter--Dawson, http://eprint.iacr.org/2008/522, Section 3.3, plus assumption Z1=1, plus standard simplification
assume Z1 = 1
compute A = X1^2
compute B = Y1^2
compute D = a A
compute E = (X1+Y1)^2-A-B
compute G = D + B
compute H = D - B
compute X3 = E (G - 2)
compute Y3 = G H
compute T3 = E H
compute Z3 = G^2 - 2 G