Matroids
AreIsomorphic
determine if two matroids are isomorphic
Calling Sequence
Parameters
Description
Examples
References
AreIsomorphic(M1,M2)
M1
-
Matroid
M2
Two matroids are isomorphic if there is a relabeling of their ground sets so that they are equal.
withMatroids:withPolynomialIdeals:
Even though the following two matrices look quite different, the independence relationships among their columns are the same after relabeling.
A1≔Matrix1,1,0,0,−1,0,1,0,0,−1,−1,0
A1≔1100−10100−1−10
A2≔Matrix0,4,0,2,0,−6,3,0,0,0,−4,−4
A2≔04020−63000−4−4
AreIsomorphicMatroidA1,MatroidA2
true
A3≔Matrix1,1,0,0,0,0,1,1,1,1,0,1
A3≔110000111101
J≔x+y,z+w,x+y+w
AreIsomorphicMatroidA3,MatroidJ
false
AreIsomorphicDualMatroidA3,MatroidJ
AreIsomorphicMatroidJ,MatroidA1
James G. Oxley. Matroid Theory (Oxford Graduate Texts in Mathematics). New York: Oxford University Press. 2006.
See Also
Matroids[Matroid]
Matroids[IndependentSets]
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