source(ToricMap) -- get the source of the map

Synopsis

Function: source
Usage:

X = source f
Inputs:
- f, a toric map,
Outputs:
- X, a normal toric variety, that is the source of the map f

Description

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

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 : source f

o4 = X

o4 : NormalToricVariety

i5 : assert (isWellDefined f and source f === X)

Any normal toric variety is the source of its diagonal map.

i6 : delta = diagonalToricMap X;

o6 : ToricMap normalToricVariety ({{1, 0, 0, 0}, {0, 1, 0, 0}, {-1, 2, 0, 0}, {0, -1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {0, 0, -1, 2}, {0, 0, 0, -1}}, {{0, 1, 4, 5}, {0, 1, 4, 7}, {0, 1, 5, 6}, {0, 1, 6, 7}, {0, 3, 4, 5}, {0, 3, 4, 7}, {0, 3, 5, 6}, {0, 3, 6, 7}, {1, 2, 4, 5}, {1, 2, 4, 7}, {1, 2, 5, 6}, {1, 2, 6, 7}, {2, 3, 4, 5}, {2, 3, 4, 7}, {2, 3, 5, 6}, {2, 3, 6, 7}}) <--- X

i7 : source delta

o7 = X

o7 : NormalToricVariety

i8 : assert (isWellDefined delta and source delta === X)

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

i9 : assert (numColumns matrix delta == dim X)

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

Ways to use this method: