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

- 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.

## See also

- working with toric maps -- information about toric maps and the induced operations
- target(ToricMap) -- get the target of the map
- matrix(ToricMap) -- get the underlying map of lattices
- isWellDefined(ToricMap) -- whether a toric map is well defined
- map(NormalToricVariety,NormalToricVariety,Matrix) -- make a torus-equivariant map between normal toric varieties
- NormalToricVariety ** NormalToricVariety -- make the Cartesian product of two normal toric varieties

## Ways to use this method:

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

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/NormalToricVarieties/ToricMapsDocumentation.m2:155:0.