# target(ToricMap) -- get the target of the map

## Synopsis

• Function: target
• Usage:
Y = target f
• Inputs:
• f, ,
• Outputs:
• Y, , that is the target of the map f

## Description

Given a toric map $f : X \to Y$, this method returns the normal toric variety $Y$.

We illustrate how to access this defining feature of a toric map with the projection from the second Hirzebruch surface to the projective line.

 i1 : X = hirzebruchSurface 2; i2 : Y = toricProjectiveSpace 1; i3 : f = map(Y, X, matrix {{1, 0}}) o3 = | 1 0 | o3 : ToricMap Y <--- X i4 : target f o4 = Y o4 : NormalToricVariety i5 : assert (isWellDefined f and target f === Y)

Any normal toric variety is the target of the projection onto a factor of its Cartesian square.

 i6 : X2 = X ** X o6 = X2 o6 : NormalToricVariety i7 : pi0 = X2^ o7 = | 1 0 0 0 | | 0 1 0 0 | o7 : ToricMap X <--- X2 i8 : target pi0 o8 = X o8 : NormalToricVariety i9 : assert (isWellDefined pi0 and target pi0 === X) i10 : pi1 = X2^ o10 = | 0 0 1 0 | | 0 0 0 1 | o10 : ToricMap X <--- X2 i11 : target pi1 o11 = X o11 : NormalToricVariety i12 : assert (isWellDefined pi1 and target pi1 === X)

In a well-defined toric map, the number of rows in the underlying matrix equals the dimension of the target.

 i13 : assert (numRows matrix f == dim Y)

Since this is a defining attribute of a toric map, no computation is required.