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1 + 3xyz + x^5 + y^5 + z^5
1 + 4x + x^2 + 4y + 4xy + y^2 + 4z + 4xz + 4yz + z^2
1 + 9x + 9x^2 + x^3 + 9y + 36xy + 9x^2y + 9y^2 + 9xy^2 + y^3 + 9z + 36xz + 9x^2z + 36yz + 36xyz + 9y^2z + 9z^2 + 9xz^2 + 9yz^2 + z^3
1 + 16x + 36x^2 + 16x^3 + x^4 + 16y + 144xy + 144x^2y + 16x^3y + 36y^2 + 144xy^2 + 36x^2y^2 + 16y^3 + 16xy^3 + y^4 + 16z + 144xz + 144x^2z + 16x^3z + 144yz + 576xyz + 144x^2yz + 144y^2z + 144xy^2z + 16y^3z + 36z^2 + 144xz^2 + 36x^2z^2 + 144yz^2 + 144xyz^2 + 36y^2z^2 + 16z^3 + 16xz^3 + 16yz^3 + z^4
xy + xz + yz + 7ixyz + x^2yz + xy^2z + xyz^2
1 + xz + yz^3
OptimalPolynomial CrossPolytope[3,2,1]
OptimalPolynomial CrossPolytope[3,4,1]
2x + 2y + 768xy + 2x^2y + 2xy^2 + 2z + 768xz + 2x^2z + 768yz + 177147xyz + 768x^2yz + 2y^2z + 768xy^2z + 2x^2y^2z + 2xz^2 + 2yz^2 + 768xyz^2 + 2x^2yz^2 + 2xy^2z^2
2 + x + y + 2xy + z + 2xz + 2yz + 16xyz + 2x^2yz + 2xy^2z + x^2y^2z + 2xyz^2 + x^2yz^2 + xy^2z^2 + 2x^2y^2z^2
3 + 3x + 3y + 3xy + 3z + 3xz + 3yz + xyz + 3Ix^2yz + 3Ixy^2z + 3Ix^2y^2z + 3Ixyz^2 + 3Ix^2yz^2 + 3Ixy^2z^2 + 3Ix^2y^2z^2
x,y,z = [-1,1]
3 + 3x + 3y + 3xy + 3z + 3xz + 3yz + xyz + 3Ix^2yz + 3Ixy^2z + 3Ix^2y^2z + 3Ixyz^2 + 3Ix^2yz^2 + 3Ixy^2z^2 + 3Ix^2y^2z^2
1 + Ix + x^2 + Iy + Ixy-Ix^2y + y^2-Ixy^2 + x^2y^2 + Iz + Ixz-Ix^2z + Iyz + Ixyz-Ix^2yz + Iy^2z + xy^2z-Ix^2y^2z + z^2 + Ixz^2 + x^2z^2 + Iyz^2-Ixyz^2-Ix^2yz^2 + y^2z^2-Ixy^2z^2 + x^2y^2z^2
x^6y^6 + x^10y^6 + x^6y^10 + x^10y^10 + x^8y^2z^2 + x^2y^8z^2 + x^14y^8z^2 + x^8y^14z^2 + x^6z^6 + x^10z^6 + y^6z^6 + x^16y^6z^6 + y^10z^6 + x^16y^10z^6 + x^6y^16z^6 + x^10y^16z^6 + x^2y^2z^8 + x^14y^2z^8 + x^2y^14z^8 + x^14y^14z^8 + x^6z^10 + x^10z^10 + y^6z^10 + x^16y^6z^10 + y^10z^10 + x^16y^10z^10 + x^6y^16z^10 + x^10y^16z^10 + x^8y^2z^14 + x^2y^8z^14 + x^14y^8z^14 + x^8y^14z^14 + x^6y^6z^16 + x^10y^6z^16 + x^6y^10z^16 + x^10y^10z^16
x,y,z = [-2,2]
x^6y^6 + x^10y^6 + x^6y^10 + x^10y^10 + x^8y^2z^2 + x^2y^8z^2 + x^14y^8z^2 + x^8y^14z^2 + x^6z^6 + x^10z^6 + y^6z^6 + x^16y^6z^6 + y^10z^6 + x^16y^10z^6 + x^6y^16z^6 + x^10y^16z^6 + x^2y^2z^8 + x^14y^2z^8 + x^2y^14z^8 + x^14y^14z^8 + x^6z^10 + x^10z^10 + y^6z^10 + x^16y^6z^10 + y^10z^10 + x^16y^10z^10 + x^6y^16z^10 + x^10y^16z^10 + x^8y^2z^14 + x^2y^8z^14 + x^14y^8z^14 + x^8y^14z^14 + x^6y^6z^16 + x^10y^6z^16 + x^6y^10z^16 + x^10y^10z^16
15 - 160x + 288x^2 - 240y + 2880xy - 5760x^2y - 80z + 960xz - 1920x^2z + 1440yz - 19200xyz + 42240x^2yz
5 - 50*x + 141*x^2 - 152*x^3 + 56*x^4 - 65*y + 495*x*y - 942*x^2*y + 512*x^3*y + 165*y^2 - 840*x*y^2 + 801*x^2*y^2 - 155*y^3 + 395*x*y^3 + 50*y^4 - 35*z + 265*x*z - 502*x^2*z + 272*x^3*z + 345*y*z - 1780*x*y*z + 1722*x^2*y*z - 585*y^2*z + 1515*x*y^2*z + 275*y^3*z + 75*z^2 - 380*x*z^2 + 361*x^2*z^2 - 495*y*z^2 + 1285*x*y*z^2 + 420*y^2*z^2 - 65*z^3 + 165*x*z^3 + 215*y*z^3 + 20*z^4
x^2 + y^2 + z^2 + 1
x*y + x*z + y*z +
a
*x*y*z + I*(x^2*y*z + x*y^2*z + x*y*z^2)