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 0.0362497 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 |
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 : p = {8, 9, 13, 11, 7, 14, 0, 3, 2, 4, 6, 5, 1, 10, 12} -- random permutation of M6.groundSet o7 = {8, 9, 13, 11, 7, 14, 0, 3, 2, 4, 6, 5, 1, 10, 12} o7 : List |
i8 : N = matroid(M6.cache.groundSet, (circuits M6)/(c -> c/(i -> p#i)), EntryMode => "circuits") o8 = a matroid of rank 5 on 15 elements o8 : Matroid |
i9 : time phi = isomorphism(M6,N) -- used 0.407748 seconds o9 = HashTable{0 => 8 } 1 => 9 2 => 13 3 => 11 4 => 7 5 => 14 6 => 0 7 => 3 8 => 2 9 => 4 10 => 6 11 => 5 12 => 1 13 => 10 14 => 12 o9 : HashTable |
i10 : values phi === p o10 = true |