# 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.