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

## Synopsis

• Function: variety
• Usage:
variety D
normalToricVariety D
• 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 PP2 i3 : variety D1 o3 = PP2 o3 : NormalToricVariety i4 : normalToricVariety D1 o4 = PP2 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 X i8 : variety D2 o8 = X o8 : NormalToricVariety i9 : assert(X === variety D2 and X === normalToricVariety D2)

Since the underlying normal toric variety is a defining attribute of a toric divisor, this method does not computation.