source 2009 Hisil--Wong--Carter--Dawson, formula (9), plus substitutions U = XX, V = ZZ, W = R/2, plus R rotation
compute R1 = (X1+Z1)^2 - XX1 - ZZ1
compute YY1 = Y1^2
compute X3 = Y1 R1
compute Z3 = (ZZ1 - XX1)(ZZ1 + XX1)
compute XX3 = X3^2
compute ZZ3 = Z3^2
compute Y3 = 2 YY1^2 - a XX3 - ZZ3