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relabel -- relabel a matroid

Synopsis

Description

This method yields another matroid isomorphic to the input matroid M with labels specified by a hash table, or list of options. The keys of the hash table should be (a subset of) $\{0, ..., n-1\}$ where n is the number of elements in the groundSet of M. Since any unused elements are assumed to remain unchanged, the set of values should coincide with the set of keys.

Alternatively, the images of $\{0, ..., n-1\}$ (in order) can be specified (as a list, whose elements are not options). If neither a list nor hash table is provided, then a random permutation is chosen.

i1 : Q6 = specificMatroid "Q6"

o1 = a "matroid" of rank 3 on 6 elements

o1 : Matroid
 
i2 : M = relabel_Q6 {3 => 0, 0 => 3}

o2 = a "matroid" of rank 3 on 6 elements

o2 : Matroid
 
i3 : (nonbases Q6, nonbases M)

o3 = ({set {0, 1, 2}, set {4, 0, 3}}, {set {1, 2, 3}, set {4, 0, 3}})

o3 : Sequence
 
i4 : (M == Q6, areIsomorphic(M, Q6))

o4 = (false, true)

o4 : Sequence
 
i5 : nonbases relabel Q6

o5 = {set {0, 5, 3}, set {4, 5, 1}}

o5 : List

See also

Ways to use relabel:

For the programmer

The object relabel is a method function.