Description
addBaseChange replaces the transition matrices in
E by the matrices in the
List L. The matrices in
L must be in GL($k$,
ZZ) or GL($k$,
QQ), where $k$ is the rank of the vector bundle
T. The list has to contain one matrix for each maximal dimensional cone of the underlying fan over which
E is defined. The fan can be recovered with
fan(ToricVectorBundle). The vector bundle already has a list of pairs $(i,j)$ denoting the codim 1 intersections of two maximal cones with $i<j$ and they are ordered in lexicographic order. The matrices will be assigned to the pairs $(i,j)$ in that order. To see which codimension 1 cone corresponds to the pair $(i,j)$ use
details(ToricVectorBundle). The matrix $A$ assigned to $(i,j)$ denotes the transition $(e_i^1,...,e_i^k) = (e_j^1,...,e_j^k)*A$. The matrices need not satisfy the regularity or the cocycle condition. These can be checked with
regCheck and
cocycleCheck.
i1 : E = toricVectorBundle(2,pp1ProductFan 2,"Type" => "Kaneyama")
o1 = {dimension of the variety => 2 }
number of affine charts => 4
rank of the vector bundle => 2
o1 : ToricVectorBundleKaneyama
|
i2 : details E
o2 = (HashTable{0 => (| 1 0 |, 0) }, HashTable{(0, 1) => | 1 0 |})
| 0 1 | | 0 1 |
1 => (| 1 0 |, 0) (0, 2) => | 1 0 |
| 0 -1 | | 0 1 |
2 => (| -1 0 |, 0) (1, 3) => | 1 0 |
| 0 1 | | 0 1 |
3 => (| -1 0 |, 0) (2, 3) => | 1 0 |
| 0 -1 | | 0 1 |
o2 : Sequence
|
i3 : F = addBaseChange(E,{matrix{{1,2},{0,1}},matrix{{1,0},{3,1}},matrix{{1,-2},{0,1}},matrix{{1,0},{-3,1}}})
o3 = {dimension of the variety => 2 }
number of affine charts => 4
rank of the vector bundle => 2
o3 : ToricVectorBundleKaneyama
|
i4 : details F
o4 = (HashTable{0 => (| 1 0 |, 0) }, HashTable{(0, 1) => | 1 2 | })
| 0 1 | | 0 1 |
1 => (| 1 0 |, 0) (0, 2) => | 1 0 |
| 0 -1 | | 3 1 |
2 => (| -1 0 |, 0) (1, 3) => | 1 -2 |
| 0 1 | | 0 1 |
3 => (| -1 0 |, 0) (2, 3) => | 1 0 |
| 0 -1 | | -3 1 |
o4 : Sequence
|
i5 : cocycleCheck F
o5 = true
|