source 2007 Bernstein--Birkner--Lange--Peters
parameter a3
assume a3 = 3 a
assume Z2 = 1
compute A = X2 ZZ1
compute B = Y2 ZZ1 Z1
compute C = X1-A
compute D = 2(Y1-B)
compute F = C^2
compute F4 = 4 F
compute Z3 = (Z1+C)^2-ZZ1-F
compute E = Z3^2
compute G = C F4
compute H = A F4
compute X3 = D^2-G-2 H-a3 E
compute Y3 = D(H-X3)-2 B G
compute ZZ3 = E