variety(Ideal) -- the closed projective subvariety defined by an ideal

Synopsis

• Function: variety
• Usage:
variety I
• Inputs:
• I, an ideal, a homogeneous ideal
• Outputs:
• the closed subvariety defined by an ideal

Description

In the example, we compute the dimension of a line in the projective plane.
 i1 : R = QQ[x..z] o1 = R o1 : PolynomialRing i2 : variety ideal x R o2 = Proj(-) x o2 : ProjectiveVariety i3 : dim oo o3 = 1

Caveat

An alternative task for this function would be to define the affine subvariety, so if something like this eventually becomes useful, we may have to redesign it. Suggestions welcome.

Ways to use this method:

• variety(Ideal) -- the closed projective subvariety defined by an ideal