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

Synopsis

Function: areIsomorphic
Usage:

areIsomorphic(M, N)
Inputs:
- M, a matroid,
- N, a matroid,
Outputs:
- a Boolean value, true if the matroids are isomorphic, false otherwise

Description

Two matroids are isomorphic if there is a bijection between their ground sets which induces a bijection between bases, or equivalently, circuits (which is what this package actually checks, since there are often fewer circuits 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))

o2 = true

i3 : M0 = matroid({a,b,c},{{a,b},{a,c}})

o3 = a "matroid" of rank 2 on 3 elements

o3 : Matroid

i4 : areIsomorphic(M, M0)

o4 = false

Caveat

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

Ways to use this method: