Description
M must be a matrix over
ZZ or
QQ where the source space is the space of the bundle, i.e., the matrix must have $k$ columns if the bundle has rank $k$. Then the new bundle is given on each ray $\rho$ by the following filtration of image$(E,M)^\rho := M(E^\rho)$ :
image$(E,M)^\rho(i) := M(E^\rho(i))$.
i1 : E = tangentBundle hirzebruchFan 2
o1 = {dimension of the variety => 2 }
number of affine charts => 4
number of rays => 4
rank of the vector bundle => 2
o1 : ToricVectorBundleKlyachko
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i2 : E = E ** E
o2 = {dimension of the variety => 2 }
number of affine charts => 4
number of rays => 4
rank of the vector bundle => 4
o2 : ToricVectorBundleKlyachko
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i3 : M = matrix {{1,0,1,0},{0,1,0,1/1}}
o3 = | 1 0 1 0 |
| 0 1 0 1 |
2 4
o3 : Matrix QQ <-- QQ
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i4 : E1 = image(E,M)
o4 = {dimension of the variety => 2 }
number of affine charts => 4
number of rays => 4
rank of the vector bundle => 2
o4 : ToricVectorBundleKlyachko
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i5 : details E1
o5 = HashTable{| -1 | => (| -1/2 1/2 |, | -2 -1 |)}
| 2 | | 1 0 |
| 0 | => (| 0 1 |, | -2 -1 |)
| -1 | | 1 0 |
| 0 | => (| 0 1 |, | -2 -1 |)
| 1 | | 1 0 |
| 1 | => (| 1 0 |, | -2 -1 |)
| 0 | | 0 1 |
o5 : HashTable
|