# dim(NormalToricVariety) -- get the dimension of a normal toric variety

## Synopsis

• Function: dim
• Usage:
dim X
• Inputs:
• X, ,
• Outputs:
• an integer, the dimension of the normal toric variety

## Description

The dimension of a normal toric variety equals the dimension of its dense algebraic torus. In this package, the fan associated to a normal $d$-dimensional toric variety lies in the rational vector space $\QQ^d$ with underlying lattice $N = \ZZ^d$. Hence, the dimension simply equals the number of entries in a minimal nonzero lattice point on a ray.

The following examples illustrate normal toric varieties of various dimensions.

 i1 : dim toricProjectiveSpace 1 o1 = 1 i2 : dim affineSpace 2 o2 = 2 i3 : dim toricProjectiveSpace 5 o3 = 5 i4 : dim hirzebruchSurface 7 o4 = 2 i5 : dim weightedProjectiveSpace {1,2,2,3,4} o5 = 4 i6 : X = normalToricVariety ({{4,-1,0},{0,1,0}},{{0,1}}) o6 = X o6 : NormalToricVariety i7 : dim X o7 = 3 i8 : isDegenerate X o8 = true

In this package, number of entries in any ray equals the dimension of both the underlying lattice and the normal toric variety, so this method does essentially no computation.