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