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-4*x^2-4*y^2-z^2+8*x*y-4*x*z+4*y*z canonical form

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   2      2      2                            
- z  - 4*x  - 4*y  - 4*x*z + 4*y*z + 8*x*y = 0
$$- 4 x^{2} + 8 x y - 4 x z - 4 y^{2} + 4 y z - z^{2} = 0$$
-4*x^2 + 8*x*y - 4*x*z - 4*y^2 + 4*y*z - z^2 = 0