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Matroids :: specificMatroid

specificMatroid -- creates built-in matroid

Synopsis

Description

Returns one of the named matroids below.

The matroids provided in this function (together with the infinite families given by the functions affineGeometry, projectiveGeometry, binarySpike, spike, swirl, wheel, whirl, thetaMatroid, uniformMatroid) includes all "interesting matroids" listed in Oxley, p. 639 - 664 (except for the general Dowling geometry).

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 : getRepresentation 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 : getRepresentation 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 $\{0, ..., n-1\}$ rather than $\{1, ..., n\}$.

See also

Ways to use specificMatroid :

For the programmer

The object specificMatroid is a method function.