# variety(ToricDivisor) -- get the underlying normal toric variety

## Synopsis

• Usage:
variety D
normalToricVariety D
• Function: variety
• Inputs:
• D,
• Outputs:
• , namely the underlying variety for D

## Description

This function allows one to easily access the normal toric variety over which the torus-invariant Weil divisor is defined.

 `i1 : PP2 = toricProjectiveSpace 2;` ```i2 : D1 = 2*PP2_0 - 7*PP2_1 + 3*PP2_2 o2 = 2*PP2 - 7*PP2 + 3*PP2 0 1 2 o2 : ToricDivisor on normalToricVariety((({{-1, -1}, {1, 0}, {0, 1}}(,({{0, 1}, {0, 2}, {1, 2}} )))))``` ```i3 : variety D1 o3 = normalToricVariety((({{-1, -1}, {1, 0}, {0, 1}}(,({{0, 1}, {0, 2}, {1, 2}} ))))) o3 : NormalToricVariety``` ```i4 : normalToricVariety D1 o4 = normalToricVariety((({{-1, -1}, {1, 0}, {0, 1}}(,({{0, 1}, {0, 2}, {1, 2}} ))))) o4 : NormalToricVariety``` `i5 : assert(variety D1 === PP2 and normalToricVariety D1 === PP2)`
 `i6 : X = normalToricVariety(id_(ZZ^3) | - id_(ZZ^3));` ```i7 : D2 = X_0 - 5 * X_3 o7 = X - 5*X 0 3 o7 : ToricDivisor on normalToricVariety((({{1, 1, 1}, {-1, 1, 1}, {1, -1, 1}, {-1, -1, 1}, {1, 1, -1}, {-1, 1, -1}, {1, -1, -1}, {-1, -1, -1}}(,({{0, 1, 2, 3}, {0, 1, 4, 5}, {0, 2, 4, 6}, {1, 3, 5, 7}, {2, 3, 6, 7}, {4, 5, 6, 7}} )))))``` ```i8 : variety D2 o8 = normalToricVariety((({{1, 1, 1}, {-1, 1, 1}, {1, -1, 1}, {-1, -1, 1}, {1, 1, -1}, {-1, 1, -1}, {1, -1, -1}, {-1, -1, -1}}(,({{0, 1, 2, 3}, {0, 1, 4, 5}, {0, 2, 4, 6}, {1, 3, 5, 7}, {2, 3, 6, 7}, {4, 5, 6, 7}} ))))) o8 : NormalToricVariety``` `i9 : assert(X === variety D2 and X === normalToricVariety D2)`