source 2009 Bernstein--Kohel--Lange
parameter i
assume i^2 = -1
parameter minustwo
assume minustwo = -2
parameter 2d
assume 2d = 2 d
compute iZ = i Z1
compute A = (Y1 - iZ)(Y1 + iZ)
compute B = Y1 Z1
compute C = (A - B)(Y1 + Z1)
compute D = (A + B)(Z1 - Y1)
compute E = 3 C - 2d X1 B
compute X3 = minustwo X1 D
compute Y3 = (D - E)Z1
compute Z3 = (D + E)Y1