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Matroids :: specificMatroid

specificMatroid -- creates built-in matroid

Synopsis

Description

Returns one of the named matroids below.

Many of these matroids are interesting for their non-representability or duality properties:

i1 : F7 = specificMatroid "fano"

o1 = a matroid of rank 3 on 7 elements

o1 : Matroid
i2 : all(F7_*, x -> areIsomorphic(matroid completeGraph 4, F7 \ {x}))

o2 = true
i3 : AG32 = specificMatroid "AG32"

o3 = a matroid of rank 4 on 8 elements

o3 : Matroid
i4 : representationOf AG32

o4 = | 1 1 1 1 1 1 1 1 |
     | 0 0 0 0 1 1 1 1 |
     | 0 0 1 1 0 0 1 1 |
     | 0 1 0 1 0 1 0 1 |

             ZZ 4       ZZ 8
o4 : Matrix (--)  <--- (--)
              2          2
i5 : AG32 == dual AG32

o5 = true
i6 : R10 = specificMatroid "R10"

o6 = a matroid of rank 5 on 10 elements

o6 : Matroid
i7 : representationOf R10

o7 = | 1 0 0 0 0 1 1 0 0 1 |
     | 0 1 0 0 0 1 1 1 0 0 |
     | 0 0 1 0 0 0 1 1 1 0 |
     | 0 0 0 1 0 0 0 1 1 1 |
     | 0 0 0 0 1 1 0 0 1 1 |

             ZZ 5       ZZ 10
o7 : Matrix (--)  <--- (--)
              2          2
i8 : areIsomorphic(R10 \ set{0}, matroid completeMultipartiteGraph {3,3})

o8 = true

Caveat

Notice that the ground set is a subset of \{0, ..., n-1\} &nbsp; rather than \{1, ..., n\}.

Ways to use specificMatroid :

For the programmer

The object specificMatroid is a method function.