ideal(Variety) -- returns the defining ideal

Synopsis

• Function: ideal

• Usage:

  ideal X

• Inputs:
  • X, a variety
• Outputs:
  • an ideal, which is the defining ideal of X

Description

i1 : R = QQ[w,x,y,z];

i2 : X = Spec(R/(y^2-x*z,x^2*y-z^2,x^3-y*z))

o2 = X

o2 : AffineVariety

i3 : ideal X

             2         2     2   3
o3 = ideal (y  - x*z, x y - z , x  - y*z)

o3 : Ideal of R

i4 : ring X

                    R
o4 = ------------------------------
       2         2     2   3
     (y  - x*z, x y - z , x  - y*z)

o4 : QuotientRing

i5 : Y = Proj(R/(x^2-w*y, x*y-w*z, x*z-y^2))

o5 = Y

o5 : ProjectiveVariety

i6 : ideal Y

             2                      2
o6 = ideal (x  - w*y, x*y - w*z, - y  + x*z)

o6 : Ideal of R

See also

• ring -- get the associated ring of an object
• ideal(Ring) -- returns the defining ideal
• Spec -- make an affine variety
• AffineVariety -- the class of all affine varieties
• Proj -- make a projective variety
• ProjectiveVariety -- the class of all projective varieties