coloops -- coloops of matroid

Usage:

coloops M
Inputs:
- M, a matroid,
Outputs:
- a list,

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

Ways to use coloops:

coloops(Matroid)

For the programmer

The object coloops is a method function.

The source of this document is in Matroids/doc-Matroids.m2:889:0.

coloops -- coloops of matroid

Description

See also

Ways to use coloops:

For the programmer