This method computes a single isomorphism between M and N, if one exists, and returns null if no such isomorphism exists.
The output is a HashTable, where the keys are elements of the groundSet of M, and their corresponding values are elements of (the ground set of) N.
To obtain all isomorphisms between two matroids, use getIsos.
i1 : M = matroid({a,b,c},{{a,b},{a,c}})
o1 = a matroid of rank 2 on 3 elements
o1 : Matroid
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i2 : isomorphism(M, uniformMatroid(2,3)) -- not isomorphic |
i3 : (M5, M6) = (5,6)/completeGraph/matroid o3 = (a matroid of rank 4 on 10 elements, a matroid of rank 5 on 15 elements) o3 : Sequence |
i4 : minorM6 = minor(M6, set{8}, set{4,5,6,7})
o4 = a matroid of rank 4 on 10 elements
o4 : Matroid
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i5 : time isomorphism(M5, minorM6)
-- used 0.0323637 seconds
o5 = HashTable{0 => 1}
1 => 0
2 => 3
3 => 2
4 => 6
5 => 5
6 => 4
7 => 9
8 => 8
9 => 7
o5 : HashTable
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i6 : isomorphism(M5, M5)
o6 = HashTable{0 => 0}
1 => 1
2 => 2
3 => 3
4 => 4
5 => 5
6 => 6
7 => 7
8 => 8
9 => 9
o6 : HashTable
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i7 : N = relabel M6 o7 = a matroid of rank 5 on 15 elements o7 : Matroid |
i8 : time phi = isomorphism(N,M6)
-- used 0.946535 seconds
o8 = HashTable{0 => 8 }
1 => 1
2 => 5
3 => 2
4 => 6
5 => 4
6 => 0
7 => 12
8 => 3
9 => 10
10 => 7
11 => 11
12 => 9
13 => 13
14 => 14
o8 : HashTable
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