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circuits -- circuits of matroid

Synopsis

Usage:

circuits M
Inputs:
- M, a matroid,
Outputs:
- a list, of circuits

Description

The circuits of a matroid are the minimal dependent subsets of the ground set.

Just as with bases and nonbases, circuits are stored via their indices (rather than the elements of the ground set themselves).

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

See also

ideal(Matroid) -- Stanley-Reisner (circuit) ideal of matroid
fundamentalCircuit -- fundamental circuit of independent set
loops -- loops of matroid

Ways to use circuits:

circuits(Matroid)

For the programmer

The object circuits is a method function.