define an equivariant toric vector bundle if they satisfy the cocycle condition. I.e. in this implementation of complete fans this means that for every codimension 2 cone of the fan the cycle of transition matrices of codimension 1 cones containing the codimension 2 cone gives the identity when multiplied.
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
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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
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i3 : A = matrix{{1,2},{0,1}};
2 2
o3 : Matrix ZZ <-- ZZ
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i4 : B = matrix{{1,0},{3,1}};
2 2
o4 : Matrix ZZ <-- ZZ
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i5 : C = matrix{{1,-2},{0,1}};
2 2
o5 : Matrix ZZ <-- ZZ
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i6 : E1 = addBaseChange(E,{A,B,C,matrix{{1,0},{0,1}}})
o6 = {dimension of the variety => 2 }
number of affine charts => 4
rank of the vector bundle => 2
o6 : ToricVectorBundleKaneyama
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i7 : cocycleCheck E1
o7 = false
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i8 : D = inverse(B)*A*C
o8 = | 1 0 |
| -3 1 |
2 2
o8 : Matrix ZZ <-- ZZ
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i9 : E1 = addBaseChange(E,{A,B,C,D})
o9 = {dimension of the variety => 2 }
number of affine charts => 4
rank of the vector bundle => 2
o9 : ToricVectorBundleKaneyama
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i10 : cocycleCheck E1
o10 = true
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