source 2009.03.11 Hisil--Wong--Carter--Dawson, after formula (17), plus denominator elimination parameter k assume k c = 1 compute R1 = X2 Y2 compute R2 = Z2^2 compute A = X1 Y1 compute B = Z1^2 compute C = R2 A compute D = R1 B compute E = (X1-X2)(Y1+Y2)-A+R1 compute F = (X1+Y2)(Y1+X2)-A-R1 compute G = (Z1+Z2)^2-B-R2 compute X3 = 2 E(C+D) compute Y3 = 2 F(C-D) compute Z3 = k E F G