Use R::=Q[x[1..4]]; I1:=Ideal(x[1]x[3]-x[2]^2, x[1]x[4]-x[2]x[3], x[2]x[4]-x[3]^2, x[2]^2x[3]-x[1]x[3]^2); ------------------ Use S::=Q[x[1..3]]; I2:=Ideal(x[1]^3-x[2]x[3]^2, x[1]^2x[2]x[3]-x[2]^4, x[1]^2+x[2]^3+x[3]^2); ------------------ Use R; I3:=Ideal(x[1]x[2]-x[3]^2, x[2]^2-x[3]x[4], x[1]x[3]-x[4]^3, x[2]x[4]-x[3]^2); ------------------ Use S; I4:=Ideal(x[1]^2-x[1]x[2], x[2]^2-x[2]x[3], x[3]^2-x[3]x[1], x[1]x[2]+x[2]x[3]+x[1]x[3]); ------------------ Use T::=Q[x,y]; J1:=Ideal(x^3, x^2y+x, y^2); ------------------ Use U::=Q[x,y,z]; J2:=Ideal(x^2+2xy+y^2, xz+yz, xy^2+y^3+xy+y^2, y^4+2y^3+y^2, y^2z+yz, z^3-xy); J3:=Ideal(x^2+y+z-1, x+y^2+z-1, x+y+z^2-1); J4:=Ideal(x^3-3x^2y+3xy^2-y^3-z^2, -x^3+3x^2z-3xz^2+z^3-y^2, y^3-3y^2z+3yz^2-z^3-x^2); ------------------ Use T; J5:=Ideal(x^2+y^2-1, 4xy-2x-2y+1); J6:=Ideal(x^2-y, x^2-3x+2); ------------------ Use U; J7:=Ideal(yz+z, y^2+y, x+y+z, z^2-z); ------------------ Use T; J8:=Ideal(x^2+y^2+3, x^2-y^2+1); J9:=Ideal(xy, x^2+x, y^3+2y^2+y); ------------------ Use U; J10:=Ideal(x^3-x, y^2-y, z^2-z); F1:=Ideal(y^2 - (2/375)xz + (22/75)yz + (29/1500)z^2 + (2/75)x - (7/15)y - (7/150)z, xy + (31/150)xz - (1/5)yz - (1/50)z^2 - (8/15)x + y + (1/10)z, x^2 - (7/15)xz + 4yz + (2/5)z^2 + (7/3)x - 20y - 2z, z^3 + (6/5)xz + 24yz - (38/5)z^2 - 6x - 120y + 13z, yz^2 - (3/25)xz - (47/5)yz + (3/50)z^2 + (3/5)x + 22y - (3/10)z, xz^2 - 7xz + 10x); F2:=Ideal(x^2+y^2+z^2-9, 3x^2-y^2z, x^2z-2y^2+2); F3:=Ideal(24xy-x^2-y^2-x^2y^2-13, 24xz -x^2-z^2-x^2z^2-13, 24yz-y^2-z^2-y^2z^2-13);