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
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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
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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.