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

## Synopsis

• Usage:
normalToricVariety S
• Function: normalToricVariety
• Inputs:
• Optional inputs:
• CoefficientRing => a ring, default value QQ, not used
• MinimalGenerators => , default value false, not used
• Variable => , default value x, not used
• WeilToClass => , default value null, not used
• Outputs:

## Description

If a polynomial ring is made 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 = normalToricVariety((({{-1, -1, -1}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}}(,({{0, 1, 2}, {0, 1, 3}, {0, 2, 3}, {1, 2, 3}} ))))) o5 : NormalToricVariety``` `i6 : assert (PP3 === normalToricVariety S)` ```i7 : variety S o7 = normalToricVariety((({{-1, -1, -1}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}}(,({{0, 1, 2}, {0, 1, 3}, {0, 2, 3}, {1, 2, 3}} ))))) o7 : NormalToricVariety``` `i8 : assert (PP3 === variety S)`

If the polynomial ring is not constructed from a variety, then this method returns null.

 `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 (null === normalToricVariety S)` `i13 : assert (null === variety S)`