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^[0] 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^[1] 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.