# normalToricVariety(Ring) -- get the associated normal toric variety

## Description

If a polynomial ring is constructed as the total coordinate ring of normal toric variety, then this method returns the associated variety.

 i1 : PP3 = toricProjectiveSpace 3; i2 : S = ring PP3 o2 = S o2 : PolynomialRing i3 : gens S o3 = {x , x , x , x } 0 1 2 3 o3 : List i4 : degrees S o4 = {{1}, {1}, {1}, {1}} o4 : List i5 : normalToricVariety S o5 = PP3 o5 : NormalToricVariety i6 : assert (PP3 === normalToricVariety S) i7 : variety S o7 = PP3 o7 : NormalToricVariety i8 : assert (PP3 === variety S)

If the polynomial ring is not constructed from a variety, then this method produces an error: "no variety associated with ring".

 i9 : S = QQ[x_0..x_2]; i10 : gens S o10 = {x , x , x } 0 1 2 o10 : List i11 : degrees S o11 = {{1}, {1}, {1}} o11 : List i12 : assert (try (normalToricVariety S; false) else true) i13 : assert (try (variety S; false) else true)

## Caveat

This methods does not determine if a ring could be realized as the total coordinate ring of a normal toric variety.