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isomorphism(Matroid,Matroid) -- computes an isomorphism between isomorphic matroids

Description

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
 
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
 
i5 : time isomorphism(M5, minorM6)
 -- used 0.0165516s (cpu); 0.0162836s (thread); 0s (gc)

o5 = HashTable{0 => 1}
               1 => 0
               2 => 3
               3 => 2
               4 => 6
               5 => 5
               6 => 4
               7 => 9
               8 => 8
               9 => 7

o5 : HashTable
 
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
 
i7 : N = relabel M6

o7 = a "matroid" of rank 5 on 15 elements

o7 : Matroid
 
i8 : time phi = isomorphism(N,M6)
 -- used 4.75515s (cpu); 3.37489s (thread); 0s (gc)

o8 = HashTable{0 => 11 }
               1 => 0
               2 => 1
               3 => 6
               4 => 9
               5 => 8
               6 => 5
               7 => 12
               8 => 7
               9 => 3
               10 => 10
               11 => 4
               12 => 2
               13 => 13
               14 => 14

o8 : HashTable

See also

Ways to use this method:

The source of this document is in Matroids/doc-Matroids.m2:2396:0.