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coloops -- coloops of matroid

Description

The coloops of a matroid M are the loops of the dual matroid. The set of coloops of M equals both the intersection of the bases of M, and the complement of the union of the circuits of M.

i1 : M = matroid({a,b,c,d},{{a,b},{a,c}})

o1 = a "matroid" of rank 2 on 4 elements

o1 : Matroid
 
i2 : circuits M

o2 = {set {1, 2}, set {3}}

o2 : List
 
i3 : C = set coloops M

o3 = set {0}

o3 : Set
 
i4 : C === M.groundSet - fold(circuits M, (a, b) -> a + b)

o4 = true
 
i5 : C === fold(bases M, (a, b) -> a*b)

o5 = true
 
i6 : M_C

o6 = set {a}

o6 : Set
 
i7 : D = dual M; peek D

o8 = Matroid{bases => {set {2, 3}, set {1, 3}}}
             cache => CacheTable{...2...}
             groundSet => set {0, 1, 2, 3}
             rank => 2
 
i9 : coloops matroid completeGraph 4 == {}

o9 = true

See also

Ways to use coloops:

  • coloops(Matroid)

For the programmer

The object coloops is a method function.

The source of this document is in /__w/M2/M2/macaulay2-1.26.05+ds/M2/Macaulay2/packages/Matroids/doc-Matroids.m2:889:0.