source 2007 Bernstein--Birkner--Lange--Peters
parameter c2
assume c2 = 2*c
compute XX = X1^2
compute YY = Y1^2
compute ZZ = (c2 Z1)^2
compute D = XX+YY
compute DD = D^2
compute H = 2 D (XX-YY)
compute P = DD-YY ZZ
compute Q = DD-XX ZZ
compute T = H+Q
compute U = H-P
compute X3 = P U X1
compute Y3 = Q T Y1
compute Z3 = T U Z1
