# variety(Ring) -- the variety previously associated to a given ring

## Synopsis

• Function: variety
• Usage:
variety A
• Inputs:
• A, a ring, the intersection ring of a variety $X$, say, or the homogeneous (Cox) ring of a normal toric variety, or another ring that has been associated to a variety, or an element in such a ring
• Outputs:
• $X$, the variety associated with A, or with the ring of A, if A is a RingElement

## Description

 i1 : needsPackage "NormalToricVarieties" o1 = NormalToricVarieties o1 : Package i2 : X = toricProjectiveSpace 1 o2 = X o2 : NormalToricVariety i3 : S = ring X o3 = S o3 : PolynomialRing i4 : X === variety S o4 = true
 i5 : needsPackage "Schubert2" o5 = Schubert2 o5 : Package i6 : Y = abstractProjectiveSpace 1 o6 = Y o6 : a flag bundle with subquotient ranks {2:1} i7 : IY = intersectionRing Y o7 = IY o7 : QuotientRing i8 : Y === variety IY o8 = true

If a RingElement is provided, then the variety of its ring is returned.

 i9 : variety S_0 o9 = X o9 : NormalToricVariety i10 : variety IY_0 o10 = Y o10 : a flag bundle with subquotient ranks {2:1}

For package developers: All this function does is to look up the symbol variety in A. This is currently used in two packages, but can be used in other settings, if desired.