El lugar geométrico del ortocentro del triángulo pedal de un punto P que varía en la cuártica Q023 es una séptica.

Ecuación obtenida por Bernard Gibert (mensaje personal 13-12-2014)


a^6 b^6 c^6 x^6 y-a^4 b^8 c^6 x^6 y-a^2 b^10 c^6 x^6 y+b^12 c^6 x^6 y-a^6 b^4 c^8 x^6 y-2 a^4 b^6 c^8 x^6 y-a^2 b^8 c^8 x^6 y-4 b^10 c^8 x^6 y+3 a^4 b^4 c^10 x^6 y+5 a^2 b^6 c^10 x^6 y+6 b^8 c^10 x^6 y-3 a^2 b^4 c^12 x^6 y-4 b^6 c^12 x^6 y+b^4 c^14 x^6 y+3 a^8 b^4 c^6 x^5 y^2-5 a^6 b^6 c^6 x^5 y^2-a^4 b^8 c^6 x^5 y^2+5 a^2 b^10 c^6 x^5 y^2-2 b^12 c^6 x^5 y^2-a^8 b^2 c^8 x^5 y^2-6 a^6 b^4 c^8 x^5 y^2-a^4 b^6 c^8 x^5 y^2-8 a^2 b^8 c^8 x^5 y^2+8 b^10 c^8 x^5 y^2+5 a^6 b^2 c^10 x^5 y^2+9 a^4 b^4 c^10 x^5 y^2+4 a^2 b^6 c^10 x^5 y^2-12 b^8 c^10 x^5 y^2-7 a^4 b^2 c^12 x^5 y^2-4 a^2 b^4 c^12 x^5 y^2+8 b^6 c^12 x^5 y^2+3 a^2 b^2 c^14 x^5 y^2-2 b^4 c^14 x^5 y^2+3 a^10 b^2 c^6 x^4 y^3-9 a^8 b^4 c^6 x^4 y^3+4 a^6 b^6 c^6 x^4 y^3+8 a^4 b^8 c^6 x^4 y^3-7 a^2 b^10 c^6 x^4 y^3+b^12 c^6 x^4 y^3-8 a^8 b^2 c^8 x^4 y^3+10 a^6 b^4 c^8 x^4 y^3+18 a^2 b^8 c^8 x^4 y^3-4 b^10 c^8 x^4 y^3+4 a^6 b^2 c^10 x^4 y^3-12 a^4 b^4 c^10 x^4 y^3-18 a^2 b^6 c^10 x^4 y^3+6 b^8 c^10 x^4 y^3+4 a^4 b^2 c^12 x^4 y^3+10 a^2 b^4 c^12 x^4 y^3-4 b^6 c^12 x^4 y^3-3 a^2 b^2 c^14 x^4 y^3+b^4 c^14 x^4 y^3+a^12 c^6 x^3 y^4-7 a^10 b^2 c^6 x^3 y^4+8 a^8 b^4 c^6 x^3 y^4+4 a^6 b^6 c^6 x^3 y^4-9 a^4 b^8 c^6 x^3 y^4+3 a^2 b^10 c^6 x^3 y^4-4 a^10 c^8 x^3 y^4+18 a^8 b^2 c^8 x^3 y^4+10 a^4 b^6 c^8 x^3 y^4-8 a^2 b^8 c^8 x^3 y^4+6 a^8 c^10 x^3 y^4-18 a^6 b^2 c^10 x^3 y^4-12 a^4 b^4 c^10 x^3 y^4+4 a^2 b^6 c^10 x^3 y^4-4 a^6 c^12 x^3 y^4+10 a^4 b^2 c^12 x^3 y^4+4 a^2 b^4 c^12 x^3 y^4+a^4 c^14 x^3 y^4-3 a^2 b^2 c^14 x^3 y^4-2 a^12 c^6 x^2 y^5+5 a^10 b^2 c^6 x^2 y^5-a^8 b^4 c^6 x^2 y^5-5 a^6 b^6 c^6 x^2 y^5+3 a^4 b^8 c^6 x^2 y^5+8 a^10 c^8 x^2 y^5-8 a^8 b^2 c^8 x^2 y^5-a^6 b^4 c^8 x^2 y^5-6 a^4 b^6 c^8 x^2 y^5-a^2 b^8 c^8 x^2 y^5-12 a^8 c^10 x^2 y^5+4 a^6 b^2 c^10 x^2 y^5+9 a^4 b^4 c^10 x^2 y^5+5 a^2 b^6 c^10 x^2 y^5+8 a^6 c^12 x^2 y^5-4 a^4 b^2 c^12 x^2 y^5-7 a^2 b^4 c^12 x^2 y^5-2 a^4 c^14 x^2 y^5+3 a^2 b^2 c^14 x^2 y^5+a^12 c^6 x y^6-a^10 b^2 c^6 x y^6-a^8 b^4 c^6 x y^6+a^6 b^6 c^6 x y^6-4 a^10 c^8 x y^6-a^8 b^2 c^8 x y^6-2 a^6 b^4 c^8 x y^6-a^4 b^6 c^8 x y^6+6 a^8 c^10 x y^6+5 a^6 b^2 c^10 x y^6+3 a^4 b^4 c^10 x y^6-4 a^6 c^12 x y^6-3 a^4 b^2 c^12 x y^6+a^4 c^14 x y^6-a^6 b^8 c^4 x^6 z+3 a^4 b^10 c^4 x^6 z-3 a^2 b^12 c^4 x^6 z+b^14 c^4 x^6 z+a^6 b^6 c^6 x^6 z-2 a^4 b^8 c^6 x^6 z+5 a^2 b^10 c^6 x^6 z-4 b^12 c^6 x^6 z-a^4 b^6 c^8 x^6 z-a^2 b^8 c^8 x^6 z+6 b^10 c^8 x^6 z-a^2 b^6 c^10 x^6 z-4 b^8 c^10 x^6 z+b^6 c^12 x^6 z-2 a^8 b^6 c^4 x^5 y z+8 a^6 b^8 c^4 x^5 y z-12 a^4 b^10 c^4 x^5 y z+8 a^2 b^12 c^4 x^5 y z-2 b^14 c^4 x^5 y z-2 a^8 b^4 c^6 x^5 y z-4 a^6 b^6 c^6 x^5 y z+12 a^4 b^8 c^6 x^5 y z-12 a^2 b^10 c^6 x^5 y z+6 b^12 c^6 x^5 y z+8 a^6 b^4 c^8 x^5 y z+12 a^4 b^6 c^8 x^5 y z+8 a^2 b^8 c^8 x^5 y z-4 b^10 c^8 x^5 y z-12 a^4 b^4 c^10 x^5 y z-12 a^2 b^6 c^10 x^5 y z-4 b^8 c^10 x^5 y z+8 a^2 b^4 c^12 x^5 y z+6 b^6 c^12 x^5 y z-2 b^4 c^14 x^5 y z+4 a^8 b^6 c^4 x^4 y^2 z-13 a^6 b^8 c^4 x^4 y^2 z+15 a^4 b^10 c^4 x^4 y^2 z-7 a^2 b^12 c^4 x^4 y^2 z+b^14 c^4 x^4 y^2 z-3 a^10 b^2 c^6 x^4 y^2 z-4 a^8 b^4 c^6 x^4 y^2 z-a^6 b^6 c^6 x^4 y^2 z-4 a^4 b^8 c^6 x^4 y^2 z+14 a^2 b^10 c^6 x^4 y^2 z-2 b^12 c^6 x^4 y^2 z+17 a^8 b^2 c^8 x^4 y^2 z+19 a^6 b^4 c^8 x^4 y^2 z-18 a^4 b^6 c^8 x^4 y^2 z-20 a^2 b^8 c^8 x^4 y^2 z-2 b^10 c^8 x^4 y^2 z-23 a^6 b^2 c^10 x^4 y^2 z+28 a^2 b^6 c^10 x^4 y^2 z+8 b^8 c^10 x^4 y^2 z+7 a^4 b^2 c^12 x^4 y^2 z-17 a^2 b^4 c^12 x^4 y^2 z-7 b^6 c^12 x^4 y^2 z+2 a^2 b^2 c^14 x^4 y^2 z+2 b^4 c^14 x^4 y^2 z+2 a^12 b^2 c^4 x^3 y^3 z-6 a^10 b^4 c^4 x^3 y^3 z+4 a^8 b^6 c^4 x^3 y^3 z+4 a^6 b^8 c^4 x^3 y^3 z-6 a^4 b^10 c^4 x^3 y^3 z+2 a^2 b^12 c^4 x^3 y^3 z-4 a^10 b^2 c^6 x^3 y^3 z+8 a^6 b^6 c^6 x^3 y^3 z-4 a^2 b^10 c^6 x^3 y^3 z-4 a^8 b^2 c^8 x^3 y^3 z-20 a^6 b^4 c^8 x^3 y^3 z-20 a^4 b^6 c^8 x^3 y^3 z-4 a^2 b^8 c^8 x^3 y^3 z+8 a^6 b^2 c^10 x^3 y^3 z+24 a^4 b^4 c^10 x^3 y^3 z+8 a^2 b^6 c^10 x^3 y^3 z+2 a^4 b^2 c^12 x^3 y^3 z+2 a^2 b^4 c^12 x^3 y^3 z-4 a^2 b^2 c^14 x^3 y^3 z+a^14 c^4 x^2 y^4 z-7 a^12 b^2 c^4 x^2 y^4 z+15 a^10 b^4 c^4 x^2 y^4 z-13 a^8 b^6 c^4 x^2 y^4 z+4 a^6 b^8 c^4 x^2 y^4 z-2 a^12 c^6 x^2 y^4 z+14 a^10 b^2 c^6 x^2 y^4 z-4 a^8 b^4 c^6 x^2 y^4 z-a^6 b^6 c^6 x^2 y^4 z-4 a^4 b^8 c^6 x^2 y^4 z-3 a^2 b^10 c^6 x^2 y^4 z-2 a^10 c^8 x^2 y^4 z-20 a^8 b^2 c^8 x^2 y^4 z-18 a^6 b^4 c^8 x^2 y^4 z+19 a^4 b^6 c^8 x^2 y^4 z+17 a^2 b^8 c^8 x^2 y^4 z+8 a^8 c^10 x^2 y^4 z+28 a^6 b^2 c^10 x^2 y^4 z-23 a^2 b^6 c^10 x^2 y^4 z-7 a^6 c^12 x^2 y^4 z-17 a^4 b^2 c^12 x^2 y^4 z+7 a^2 b^4 c^12 x^2 y^4 z+2 a^4 c^14 x^2 y^4 z+2 a^2 b^2 c^14 x^2 y^4 z-2 a^14 c^4 x y^5 z+8 a^12 b^2 c^4 x y^5 z-12 a^10 b^4 c^4 x y^5 z+8 a^8 b^6 c^4 x y^5 z-2 a^6 b^8 c^4 x y^5 z+6 a^12 c^6 x y^5 z-12 a^10 b^2 c^6 x y^5 z+12 a^8 b^4 c^6 x y^5 z-4 a^6 b^6 c^6 x y^5 z-2 a^4 b^8 c^6 x y^5 z-4 a^10 c^8 x y^5 z+8 a^8 b^2 c^8 x y^5 z+12 a^6 b^4 c^8 x y^5 z+8 a^4 b^6 c^8 x y^5 z-4 a^8 c^10 x y^5 z-12 a^6 b^2 c^10 x y^5 z-12 a^4 b^4 c^10 x y^5 z+6 a^6 c^12 x y^5 z+8 a^4 b^2 c^12 x y^5 z-2 a^4 c^14 x y^5 z+a^14 c^4 y^6 z-3 a^12 b^2 c^4 y^6 z+3 a^10 b^4 c^4 y^6 z-a^8 b^6 c^4 y^6 z-4 a^12 c^6 y^6 z+5 a^10 b^2 c^6 y^6 z-2 a^8 b^4 c^6 y^6 z+a^6 b^6 c^6 y^6 z+6 a^10 c^8 y^6 z-a^8 b^2 c^8 y^6 z-a^6 b^4 c^8 y^6 z-4 a^8 c^10 y^6 z-a^6 b^2 c^10 y^6 z+a^6 c^12 y^6 z-a^8 b^8 c^2 x^5 z^2+5 a^6 b^10 c^2 x^5 z^2-7 a^4 b^12 c^2 x^5 z^2+3 a^2 b^14 c^2 x^5 z^2+3 a^8 b^6 c^4 x^5 z^2-6 a^6 b^8 c^4 x^5 z^2+9 a^4 b^10 c^4 x^5 z^2-4 a^2 b^12 c^4 x^5 z^2-2 b^14 c^4 x^5 z^2-5 a^6 b^6 c^6 x^5 z^2-a^4 b^8 c^6 x^5 z^2+4 a^2 b^10 c^6 x^5 z^2+8 b^12 c^6 x^5 z^2-a^4 b^6 c^8 x^5 z^2-8 a^2 b^8 c^8 x^5 z^2-12 b^10 c^8 x^5 z^2+5 a^2 b^6 c^10 x^5 z^2+8 b^8 c^10 x^5 z^2-2 b^6 c^12 x^5 z^2-3 a^10 b^6 c^2 x^4 y z^2+17 a^8 b^8 c^2 x^4 y z^2-23 a^6 b^10 c^2 x^4 y z^2+7 a^4 b^12 c^2 x^4 y z^2+2 a^2 b^14 c^2 x^4 y z^2-4 a^8 b^6 c^4 x^4 y z^2+19 a^6 b^8 c^4 x^4 y z^2-17 a^2 b^12 c^4 x^4 y z^2+2 b^14 c^4 x^4 y z^2+4 a^8 b^4 c^6 x^4 y z^2-a^6 b^6 c^6 x^4 y z^2-18 a^4 b^8 c^6 x^4 y z^2+28 a^2 b^10 c^6 x^4 y z^2-7 b^12 c^6 x^4 y z^2-13 a^6 b^4 c^8 x^4 y z^2-4 a^4 b^6 c^8 x^4 y z^2-20 a^2 b^8 c^8 x^4 y z^2+8 b^10 c^8 x^4 y z^2+15 a^4 b^4 c^10 x^4 y z^2+14 a^2 b^6 c^10 x^4 y z^2-2 b^8 c^10 x^4 y z^2-7 a^2 b^4 c^12 x^4 y z^2-2 b^6 c^12 x^4 y z^2+b^4 c^14 x^4 y z^2-3 a^12 b^4 c^2 x^3 y^2 z^2+21 a^10 b^6 c^2 x^3 y^2 z^2-24 a^8 b^8 c^2 x^3 y^2 z^2-4 a^6 b^10 c^2 x^3 y^2 z^2+11 a^4 b^12 c^2 x^3 y^2 z^2-a^2 b^14 c^2 x^3 y^2 z^2-3 a^12 b^2 c^4 x^3 y^2 z^2-8 a^8 b^6 c^4 x^3 y^2 z^2+44 a^6 b^8 c^4 x^3 y^2 z^2-33 a^4 b^10 c^4 x^3 y^2 z^2+21 a^10 b^2 c^6 x^3 y^2 z^2-8 a^8 b^4 c^6 x^3 y^2 z^2-44 a^6 b^6 c^6 x^3 y^2 z^2+22 a^4 b^8 c^6 x^3 y^2 z^2-3 a^2 b^10 c^6 x^3 y^2 z^2-24 a^8 b^2 c^8 x^3 y^2 z^2+44 a^6 b^4 c^8 x^3 y^2 z^2+22 a^4 b^6 c^8 x^3 y^2 z^2+8 a^2 b^8 c^8 x^3 y^2 z^2-4 a^6 b^2 c^10 x^3 y^2 z^2-33 a^4 b^4 c^10 x^3 y^2 z^2-3 a^2 b^6 c^10 x^3 y^2 z^2+11 a^4 b^2 c^12 x^3 y^2 z^2-a^2 b^2 c^14 x^3 y^2 z^2-a^14 b^2 c^2 x^2 y^3 z^2+11 a^12 b^4 c^2 x^2 y^3 z^2-4 a^10 b^6 c^2 x^2 y^3 z^2-24 a^8 b^8 c^2 x^2 y^3 z^2+21 a^6 b^10 c^2 x^2 y^3 z^2-3 a^4 b^12 c^2 x^2 y^3 z^2-33 a^10 b^4 c^4 x^2 y^3 z^2+44 a^8 b^6 c^4 x^2 y^3 z^2-8 a^6 b^8 c^4 x^2 y^3 z^2-3 a^2 b^12 c^4 x^2 y^3 z^2-3 a^10 b^2 c^6 x^2 y^3 z^2+22 a^8 b^4 c^6 x^2 y^3 z^2-44 a^6 b^6 c^6 x^2 y^3 z^2-8 a^4 b^8 c^6 x^2 y^3 z^2+21 a^2 b^10 c^6 x^2 y^3 z^2+8 a^8 b^2 c^8 x^2 y^3 z^2+22 a^6 b^4 c^8 x^2 y^3 z^2+44 a^4 b^6 c^8 x^2 y^3 z^2-24 a^2 b^8 c^8 x^2 y^3 z^2-3 a^6 b^2 c^10 x^2 y^3 z^2-33 a^4 b^4 c^10 x^2 y^3 z^2-4 a^2 b^6 c^10 x^2 y^3 z^2+11 a^2 b^4 c^12 x^2 y^3 z^2-a^2 b^2 c^14 x^2 y^3 z^2+2 a^14 b^2 c^2 x y^4 z^2+7 a^12 b^4 c^2 x y^4 z^2-23 a^10 b^6 c^2 x y^4 z^2+17 a^8 b^8 c^2 x y^4 z^2-3 a^6 b^10 c^2 x y^4 z^2+2 a^14 c^4 x y^4 z^2-17 a^12 b^2 c^4 x y^4 z^2+19 a^8 b^6 c^4 x y^4 z^2-4 a^6 b^8 c^4 x y^4 z^2-7 a^12 c^6 x y^4 z^2+28 a^10 b^2 c^6 x y^4 z^2-18 a^8 b^4 c^6 x y^4 z^2-a^6 b^6 c^6 x y^4 z^2+4 a^4 b^8 c^6 x y^4 z^2+8 a^10 c^8 x y^4 z^2-20 a^8 b^2 c^8 x y^4 z^2-4 a^6 b^4 c^8 x y^4 z^2-13 a^4 b^6 c^8 x y^4 z^2-2 a^8 c^10 x y^4 z^2+14 a^6 b^2 c^10 x y^4 z^2+15 a^4 b^4 c^10 x y^4 z^2-2 a^6 c^12 x y^4 z^2-7 a^4 b^2 c^12 x y^4 z^2+a^4 c^14 x y^4 z^2+3 a^14 b^2 c^2 y^5 z^2-7 a^12 b^4 c^2 y^5 z^2+5 a^10 b^6 c^2 y^5 z^2-a^8 b^8 c^2 y^5 z^2-2 a^14 c^4 y^5 z^2-4 a^12 b^2 c^4 y^5 z^2+9 a^10 b^4 c^4 y^5 z^2-6 a^8 b^6 c^4 y^5 z^2+3 a^6 b^8 c^4 y^5 z^2+8 a^12 c^6 y^5 z^2+4 a^10 b^2 c^6 y^5 z^2-a^8 b^4 c^6 y^5 z^2-5 a^6 b^6 c^6 y^5 z^2-12 a^10 c^8 y^5 z^2-8 a^8 b^2 c^8 y^5 z^2-a^6 b^4 c^8 y^5 z^2+8 a^8 c^10 y^5 z^2+5 a^6 b^2 c^10 y^5 z^2-2 a^6 c^12 y^5 z^2+3 a^10 b^6 c^2 x^4 z^3-8 a^8 b^8 c^2 x^4 z^3+4 a^6 b^10 c^2 x^4 z^3+4 a^4 b^12 c^2 x^4 z^3-3 a^2 b^14 c^2 x^4 z^3-9 a^8 b^6 c^4 x^4 z^3+10 a^6 b^8 c^4 x^4 z^3-12 a^4 b^10 c^4 x^4 z^3+10 a^2 b^12 c^4 x^4 z^3+b^14 c^4 x^4 z^3+4 a^6 b^6 c^6 x^4 z^3-18 a^2 b^10 c^6 x^4 z^3-4 b^12 c^6 x^4 z^3+8 a^4 b^6 c^8 x^4 z^3+18 a^2 b^8 c^8 x^4 z^3+6 b^10 c^8 x^4 z^3-7 a^2 b^6 c^10 x^4 z^3-4 b^8 c^10 x^4 z^3+b^6 c^12 x^4 z^3+2 a^12 b^4 c^2 x^3 y z^3-4 a^10 b^6 c^2 x^3 y z^3-4 a^8 b^8 c^2 x^3 y z^3+8 a^6 b^10 c^2 x^3 y z^3+2 a^4 b^12 c^2 x^3 y z^3-4 a^2 b^14 c^2 x^3 y z^3-6 a^10 b^4 c^4 x^3 y z^3-20 a^6 b^8 c^4 x^3 y z^3+24 a^4 b^10 c^4 x^3 y z^3+2 a^2 b^12 c^4 x^3 y z^3+4 a^8 b^4 c^6 x^3 y z^3+8 a^6 b^6 c^6 x^3 y z^3-20 a^4 b^8 c^6 x^3 y z^3+8 a^2 b^10 c^6 x^3 y z^3+4 a^6 b^4 c^8 x^3 y z^3-4 a^2 b^8 c^8 x^3 y z^3-6 a^4 b^4 c^10 x^3 y z^3-4 a^2 b^6 c^10 x^3 y z^3+2 a^2 b^4 c^12 x^3 y z^3-a^14 b^2 c^2 x^2 y^2 z^3-3 a^10 b^6 c^2 x^2 y^2 z^3+8 a^8 b^8 c^2 x^2 y^2 z^3-3 a^6 b^10 c^2 x^2 y^2 z^3-a^2 b^14 c^2 x^2 y^2 z^3+11 a^12 b^2 c^4 x^2 y^2 z^3-33 a^10 b^4 c^4 x^2 y^2 z^3+22 a^8 b^6 c^4 x^2 y^2 z^3+22 a^6 b^8 c^4 x^2 y^2 z^3-33 a^4 b^10 c^4 x^2 y^2 z^3+11 a^2 b^12 c^4 x^2 y^2 z^3-4 a^10 b^2 c^6 x^2 y^2 z^3+44 a^8 b^4 c^6 x^2 y^2 z^3-44 a^6 b^6 c^6 x^2 y^2 z^3+44 a^4 b^8 c^6 x^2 y^2 z^3-4 a^2 b^10 c^6 x^2 y^2 z^3-24 a^8 b^2 c^8 x^2 y^2 z^3-8 a^6 b^4 c^8 x^2 y^2 z^3-8 a^4 b^6 c^8 x^2 y^2 z^3-24 a^2 b^8 c^8 x^2 y^2 z^3+21 a^6 b^2 c^10 x^2 y^2 z^3+21 a^2 b^6 c^10 x^2 y^2 z^3-3 a^4 b^2 c^12 x^2 y^2 z^3-3 a^2 b^4 c^12 x^2 y^2 z^3-4 a^14 b^2 c^2 x y^3 z^3+2 a^12 b^4 c^2 x y^3 z^3+8 a^10 b^6 c^2 x y^3 z^3-4 a^8 b^8 c^2 x y^3 z^3-4 a^6 b^10 c^2 x y^3 z^3+2 a^4 b^12 c^2 x y^3 z^3+2 a^12 b^2 c^4 x y^3 z^3+24 a^10 b^4 c^4 x y^3 z^3-20 a^8 b^6 c^4 x y^3 z^3-6 a^4 b^10 c^4 x y^3 z^3+8 a^10 b^2 c^6 x y^3 z^3-20 a^8 b^4 c^6 x y^3 z^3+8 a^6 b^6 c^6 x y^3 z^3+4 a^4 b^8 c^6 x y^3 z^3-4 a^8 b^2 c^8 x y^3 z^3+4 a^4 b^6 c^8 x y^3 z^3-4 a^6 b^2 c^10 x y^3 z^3-6 a^4 b^4 c^10 x y^3 z^3+2 a^4 b^2 c^12 x y^3 z^3-3 a^14 b^2 c^2 y^4 z^3+4 a^12 b^4 c^2 y^4 z^3+4 a^10 b^6 c^2 y^4 z^3-8 a^8 b^8 c^2 y^4 z^3+3 a^6 b^10 c^2 y^4 z^3+a^14 c^4 y^4 z^3+10 a^12 b^2 c^4 y^4 z^3-12 a^10 b^4 c^4 y^4 z^3+10 a^8 b^6 c^4 y^4 z^3-9 a^6 b^8 c^4 y^4 z^3-4 a^12 c^6 y^4 z^3-18 a^10 b^2 c^6 y^4 z^3+4 a^6 b^6 c^6 y^4 z^3+6 a^10 c^8 y^4 z^3+18 a^8 b^2 c^8 y^4 z^3+8 a^6 b^4 c^8 y^4 z^3-4 a^8 c^10 y^4 z^3-7 a^6 b^2 c^10 y^4 z^3+a^6 c^12 y^4 z^3+a^12 b^6 x^3 z^4-4 a^10 b^8 x^3 z^4+6 a^8 b^10 x^3 z^4-4 a^6 b^12 x^3 z^4+a^4 b^14 x^3 z^4-7 a^10 b^6 c^2 x^3 z^4+18 a^8 b^8 c^2 x^3 z^4-18 a^6 b^10 c^2 x^3 z^4+10 a^4 b^12 c^2 x^3 z^4-3 a^2 b^14 c^2 x^3 z^4+8 a^8 b^6 c^4 x^3 z^4-12 a^4 b^10 c^4 x^3 z^4+4 a^2 b^12 c^4 x^3 z^4+4 a^6 b^6 c^6 x^3 z^4+10 a^4 b^8 c^6 x^3 z^4+4 a^2 b^10 c^6 x^3 z^4-9 a^4 b^6 c^8 x^3 z^4-8 a^2 b^8 c^8 x^3 z^4+3 a^2 b^6 c^10 x^3 z^4+a^14 b^4 x^2 y z^4-2 a^12 b^6 x^2 y z^4-2 a^10 b^8 x^2 y z^4+8 a^8 b^10 x^2 y z^4-7 a^6 b^12 x^2 y z^4+2 a^4 b^14 x^2 y z^4-7 a^12 b^4 c^2 x^2 y z^4+14 a^10 b^6 c^2 x^2 y z^4-20 a^8 b^8 c^2 x^2 y z^4+28 a^6 b^10 c^2 x^2 y z^4-17 a^4 b^12 c^2 x^2 y z^4+2 a^2 b^14 c^2 x^2 y z^4+15 a^10 b^4 c^4 x^2 y z^4-4 a^8 b^6 c^4 x^2 y z^4-18 a^6 b^8 c^4 x^2 y z^4+7 a^2 b^12 c^4 x^2 y z^4-13 a^8 b^4 c^6 x^2 y z^4-a^6 b^6 c^6 x^2 y z^4+19 a^4 b^8 c^6 x^2 y z^4-23 a^2 b^10 c^6 x^2 y z^4+4 a^6 b^4 c^8 x^2 y z^4-4 a^4 b^6 c^8 x^2 y z^4+17 a^2 b^8 c^8 x^2 y z^4-3 a^2 b^6 c^10 x^2 y z^4+2 a^14 b^4 x y^2 z^4-7 a^12 b^6 x y^2 z^4+8 a^10 b^8 x y^2 z^4-2 a^8 b^10 x y^2 z^4-2 a^6 b^12 x y^2 z^4+a^4 b^14 x y^2 z^4+2 a^14 b^2 c^2 x y^2 z^4-17 a^12 b^4 c^2 x y^2 z^4+28 a^10 b^6 c^2 x y^2 z^4-20 a^8 b^8 c^2 x y^2 z^4+14 a^6 b^10 c^2 x y^2 z^4-7 a^4 b^12 c^2 x y^2 z^4+7 a^12 b^2 c^4 x y^2 z^4-18 a^8 b^6 c^4 x y^2 z^4-4 a^6 b^8 c^4 x y^2 z^4+15 a^4 b^10 c^4 x y^2 z^4-23 a^10 b^2 c^6 x y^2 z^4+19 a^8 b^4 c^6 x y^2 z^4-a^6 b^6 c^6 x y^2 z^4-13 a^4 b^8 c^6 x y^2 z^4+17 a^8 b^2 c^8 x y^2 z^4-4 a^6 b^4 c^8 x y^2 z^4+4 a^4 b^6 c^8 x y^2 z^4-3 a^6 b^2 c^10 x y^2 z^4+a^14 b^4 y^3 z^4-4 a^12 b^6 y^3 z^4+6 a^10 b^8 y^3 z^4-4 a^8 b^10 y^3 z^4+a^6 b^12 y^3 z^4-3 a^14 b^2 c^2 y^3 z^4+10 a^12 b^4 c^2 y^3 z^4-18 a^10 b^6 c^2 y^3 z^4+18 a^8 b^8 c^2 y^3 z^4-7 a^6 b^10 c^2 y^3 z^4+4 a^12 b^2 c^4 y^3 z^4-12 a^10 b^4 c^4 y^3 z^4+8 a^6 b^8 c^4 y^3 z^4+4 a^10 b^2 c^6 y^3 z^4+10 a^8 b^4 c^6 y^3 z^4+4 a^6 b^6 c^6 y^3 z^4-8 a^8 b^2 c^8 y^3 z^4-9 a^6 b^4 c^8 y^3 z^4+3 a^6 b^2 c^10 y^3 z^4-2 a^12 b^6 x^2 z^5+8 a^10 b^8 x^2 z^5-12 a^8 b^10 x^2 z^5+8 a^6 b^12 x^2 z^5-2 a^4 b^14 x^2 z^5+5 a^10 b^6 c^2 x^2 z^5-8 a^8 b^8 c^2 x^2 z^5+4 a^6 b^10 c^2 x^2 z^5-4 a^4 b^12 c^2 x^2 z^5+3 a^2 b^14 c^2 x^2 z^5-a^8 b^6 c^4 x^2 z^5-a^6 b^8 c^4 x^2 z^5+9 a^4 b^10 c^4 x^2 z^5-7 a^2 b^12 c^4 x^2 z^5-5 a^6 b^6 c^6 x^2 z^5-6 a^4 b^8 c^6 x^2 z^5+5 a^2 b^10 c^6 x^2 z^5+3 a^4 b^6 c^8 x^2 z^5-a^2 b^8 c^8 x^2 z^5-2 a^14 b^4 x y z^5+6 a^12 b^6 x y z^5-4 a^10 b^8 x y z^5-4 a^8 b^10 x y z^5+6 a^6 b^12 x y z^5-2 a^4 b^14 x y z^5+8 a^12 b^4 c^2 x y z^5-12 a^10 b^6 c^2 x y z^5+8 a^8 b^8 c^2 x y z^5-12 a^6 b^10 c^2 x y z^5+8 a^4 b^12 c^2 x y z^5-12 a^10 b^4 c^4 x y z^5+12 a^8 b^6 c^4 x y z^5+12 a^6 b^8 c^4 x y z^5-12 a^4 b^10 c^4 x y z^5+8 a^8 b^4 c^6 x y z^5-4 a^6 b^6 c^6 x y z^5+8 a^4 b^8 c^6 x y z^5-2 a^6 b^4 c^8 x y z^5-2 a^4 b^6 c^8 x y z^5-2 a^14 b^4 y^2 z^5+8 a^12 b^6 y^2 z^5-12 a^10 b^8 y^2 z^5+8 a^8 b^10 y^2 z^5-2 a^6 b^12 y^2 z^5+3 a^14 b^2 c^2 y^2 z^5-4 a^12 b^4 c^2 y^2 z^5+4 a^10 b^6 c^2 y^2 z^5-8 a^8 b^8 c^2 y^2 z^5+5 a^6 b^10 c^2 y^2 z^5-7 a^12 b^2 c^4 y^2 z^5+9 a^10 b^4 c^4 y^2 z^5-a^8 b^6 c^4 y^2 z^5-a^6 b^8 c^4 y^2 z^5+5 a^10 b^2 c^6 y^2 z^5-6 a^8 b^4 c^6 y^2 z^5-5 a^6 b^6 c^6 y^2 z^5-a^8 b^2 c^8 y^2 z^5+3 a^6 b^4 c^8 y^2 z^5+a^12 b^6 x z^6-4 a^10 b^8 x z^6+6 a^8 b^10 x z^6-4 a^6 b^12 x z^6+a^4 b^14 x z^6-a^10 b^6 c^2 x z^6-a^8 b^8 c^2 x z^6+5 a^6 b^10 c^2 x z^6-3 a^4 b^12 c^2 x z^6-a^8 b^6 c^4 x z^6-2 a^6 b^8 c^4 x z^6+3 a^4 b^10 c^4 x z^6+a^6 b^6 c^6 x z^6-a^4 b^8 c^6 x z^6+a^14 b^4 y z^6-4 a^12 b^6 y z^6+6 a^10 b^8 y z^6-4 a^8 b^10 y z^6+a^6 b^12 y z^6-3 a^12 b^4 c^2 y z^6+5 a^10 b^6 c^2 y z^6-a^8 b^8 c^2 y z^6-a^6 b^10 c^2 y z^6+3 a^10 b^4 c^4 y z^6-2 a^8 b^6 c^4 y z^6-a^6 b^8 c^4 y z^6-a^8 b^4 c^6 y z^6+a^6 b^6 c^6 y z^6=0