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

## Synopsis

• Function: areIsomorphic
• Usage:
areIsomorphic(M, N)
• Inputs:
• M, ,
• N, ,
• Outputs:
• , 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.