source 2007 Hisil--Carter--Dawson parameter b assume b = a^2-1 compute UU = XX1^2 compute WW = ZZ1^2 compute RR = R1^2 compute A = 4(UU - WW) compute AA = A^2 compute B = 2(UU + WW)+ a RR compute BB = B^2 compute AB = (A+B)^2-AA-BB compute C = b RR^2 compute Q = 2(BB-C) compute X3 = X1(AB - Q) compute Z3 = Z1(AB + Q) compute Y3 = Y1(Q^2 - 4 AA C) compute XX3 = X3^2 compute ZZ3 = Z3^2 compute R3 = (X3+Z3)^2-XX3-ZZ3