source 2007 Hisil--Carter--Dawson
compute A = XX1^2
compute B = ZZ1^2
compute C = A+B
compute D = 2((XX1+ZZ1)^2-C)
compute E = A-B
compute F = 2 A
compute G = 2 B
compute J = a D+2 C
compute K = J+E
compute L = J-E
compute M = C E
compute N = G K
compute P = F L
compute X3 = X1(M-N)
compute Y3 = Y1((M+N)(P-M)+(D E)^2)
compute Z3 = Z1(P+M)
compute XX3 = X3^2
compute ZZ3 = Z3^2
compute R3 = (X3+Z3)^2-XX3-ZZ3