source 2007 Bernstein--Birkner--Lange--Peters
parameter a3
assume a3 = 3 a
compute ZZZ2 = Z2 ZZ2
compute ZZZ1 = Z1 ZZ1
compute A = X2 ZZ1-X1 ZZ2
compute B = Y2 ZZZ1-Y1 ZZZ2
compute AA = A^2
compute C = (Z2+A)^2-ZZ2-AA
compute CC = C^2
compute CC8 = 8 CC
compute D = X1 CC8
compute Z3 = (Z1+C)^2-ZZ1-CC
compute E = Z3^2
compute X3 = 16(B^2-A AA)-D-a3 E
compute Y3 = 2 B(D-2 X3)-Y1 C CC8
compute ZZ3 = E