Macaulay2 » Documentation
Packages » Matroids :: nonbases
next | previous | forward | backward | up | index | toc

nonbases -- nonbases of matroid

Synopsis

Description

In any matroid, all basis elements have the same cardinality r (which is the rank of the matroid). The nonbases of a matroid are the subsets of the ground set of cardinality r that are dependent.

Just as with bases and circuits, nonbases 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 : nonbases M

o2 = {set {1, 2}, set {0, 3}, set {1, 3}, set {2, 3}}

o2 : List

See also

Ways to use nonbases:

For the programmer

The object nonbases is a method function.