SymPy Gamma

diophantine (3*x**2+4*y**2-5*z**2+4*x*y-7*y*z+7*z*x)

$$\begin{align}&\mathrm{Solve~the~diophantine~equation~}3 x^{2} + 4 x y + 7 x z + 4 y^{2} - 7 y z - 5 z^{2} = 0\\&\mathrm{where~}(x, z, y)\mathrm{~are~integers}\end{align}$$

diophantine (3*x**2+4*y**2-5*z**2+4*x*y-7*y*z+7*z*x)

x	y	z
$$- 16 p^{2} + 28 p q + 20 q^{2}$$	$$3 p^{2} + 38 p q - 25 q^{2}$$	$$4 p^{2} - 24 p q + 68 q^{2}$$