source 2007 Bernstein--Birkner--Lange--Peters
assume c = 1
compute XX = X1^2
compute YY = Y1^2
compute ZZ = Z1^2
compute ZZ4 = 4 ZZ
compute D = XX+YY
compute DD = D^2
compute H = 2 D(XX-YY)
compute P = DD-YY ZZ4
compute Q = DD-XX ZZ4
compute T = H+Q
compute TT = T^2
compute U = H-P
compute X3 = 2 P U X1
compute Y3 = Q((T+Y1)^2-TT-YY)
compute Z3 = U((T+Z1)^2-TT-ZZ)
