ideal(Variety) -- returns the defining ideal

Synopsis

• Function: ideal
• Usage:
ideal X
• Inputs:
• X,
• Outputs:
• an ideal, which is the defining ideal of X

Description

A variety is defined by a ring. This function returns the defining ideal of the ring of X.
 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