# quickIsomorphismTest -- quick checks for isomorphism between matroids

## Synopsis

• Usage:
quickIsomorphismTest(M, N)
• Inputs:
• M, ,
• N, ,
• Outputs:
• , either "true" or "false" or "Could be isomorphic"

## Description

This method performs relatively quick tests to determine whether or not two matroids are isomorphic. A result of "false" is definitive proof that the matroids are not isomorphic, a result of "true" is definitive proof that the matroids are isomorphic, and a result of "Could be isomorphic" is evidence that the matroids may be isomorphic (although there are nonisomorphic matroids which cannot be detected by this method).

If "true" or "false" is returned, use value to convert to a Boolean.

 i1 : M0 = matroid(toList(a..z)/toString,{{"m","a","t","r","o","i","d"}}) o1 = a matroid of rank 7 on 26 elements o1 : Matroid i2 : M1 = matroid(toList(0..25), {{random(ZZ),23,15,12,19,20,11}}) o2 = a matroid of rank 7 on 26 elements o2 : Matroid i3 : quickIsomorphismTest(M0, M1) o3 = true i4 : quickIsomorphismTest(matroid random(ZZ^5,ZZ^8), uniformMatroid(5, 8)) o4 = true i5 : quickIsomorphismTest(uniformMatroid(5, 9), uniformMatroid(4, 9)) o5 = false i6 : M0 = matroid graph({{a,b},{b,c},{c,d},{d,e},{e,f},{f,g},{f,h},{c,h},{c,f},{a,g},{d,g}}) o6 = a matroid of rank 7 on 11 elements o6 : Matroid i7 : M1 = matroid graph({{a,b},{b,c},{c,d},{d,e},{e,f},{f,g},{f,h},{c,h},{c,f},{a,g},{a,h}}) o7 = a matroid of rank 7 on 11 elements o7 : Matroid i8 : R = ZZ[x,y]; tuttePolynomial(M0, R) == tuttePolynomial(M1, R) o9 = true i10 : time quickIsomorphismTest(M0, M1) -- used 0.0234161 seconds o10 = false i11 : value oo === false o11 = true