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Matroids :: areIsomorphic(Matroid,Matroid)

areIsomorphic(Matroid,Matroid) -- whether two matroids are isomorphic

Synopsis

Description

Two matroids are isomorphic if there is a bijection between their ground sets which induces a bijection between bases, or equivalently, circuits (of which there are often fewer than bases).

This method first runs quickIsomorphismTest, then isomorphism if the tests are inconclusive.

i1 : M = matroid({a,b,c},{{a,b},{a,c},{b,c}})

o1 = a matroid of rank 2 on 3 elements

o1 : Matroid
i2 : areIsomorphic(M, uniformMatroid(2,3))
Matroids are equal

o2 = true
i3 : M1 = matroid({a,b,c},{{a,b},{a,c}})

o3 = a matroid of rank 2 on 3 elements

o3 : Matroid
i4 : areIsomorphic(M, M1)

o4 = false

Caveat

Isomorphism of matroids should not be confused with equality: cf. == for more details.

See also