K457 :

a^6*b^3*c^2*x^2*y - 2*a^4*b^5*c^2*x^2*y + a^2*b^7*c^2*x^2*y - a^6*b*c^4*x^2*y + b^7*c^4*x^2*y + 2*a^4*b*c^6*x^2*y - 2*b^5*c^6*x^2*y - a^2*b*c^8*x^2*y + b^3*c^8*x^2*y + a^7*b^2*c^2*x*y^2 - 2*a^5*b^4*c^2*x*y^2 + a^3*b^6*c^2*x*y^2 + a^7*c^4*x*y^2 - a*b^6*c^4*x*y^2 - 2*a^5*c^6*x*y^2 + 2*a*b^4*c^6*x*y^2 + a^3*c^8*x*y^2 - a*b^2*c^8*x*y^2 - a^6*b^4*c*x^2*z + 2*a^4*b^6*c*x^2*z - a^2*b^8*c*x^2*z + a^6*b^2*c^3*x^2*z + b^8*c^3*x^2*z - 2*a^4*b^2*c^5*x^2*z - 2*b^6*c^5*x^2*z + a^2*b^2*c^7*x^2*z + b^4*c^7*x^2*z - 2*a^7*b^3*c*x*y*z + 4*a^5*b^5*c*x*y*z - 2*a^3*b^7*c*x*y*z - 2*a^7*b*c^3*x*y*z - 2*a*b^7*c^3*x*y*z + 4*a^5*b*c^5*x*y*z + 4*a*b^5*c^5*x*y*z - 2*a^3*b*c^7*x*y*z - 2*a*b^3*c^7*x*y*z - a^8*b^2*c*y^2*z + 2*a^6*b^4*c*y^2*z - a^4*b^6*c*y^2*z + a^8*c^3*y^2*z + a^2*b^6*c^3*y^2*z - 2*a^6*c^5*y^2*z - 2*a^2*b^4*c^5*y^2*z + a^4*c^7*y^2*z + a^2*b^2*c^7*y^2*z + a^7*b^4*x*z^2 - 2*a^5*b^6*x*z^2 + a^3*b^8*x*z^2 + a^7*b^2*c^2*x*z^2 - a*b^8*c^2*x*z^2 - 2*a^5*b^2*c^4*x*z^2 + 2*a*b^6*c^4*x*z^2 + a^3*b^2*c^6*x*z^2 - a*b^4*c^6*x*z^2 + a^8*b^3*y*z^2 - 2*a^6*b^5*y*z^2 + a^4*b^7*y*z^2 - a^8*b*c^2*y*z^2 + a^2*b^7*c^2*y*z^2 + 2*a^6*b*c^4*y*z^2 - 2*a^2*b^5*c^4*y*z^2 - a^4*b*c^6*y*z^2 + a^2*b^3*c^6*y*z^2 = 0