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# matroid(...,EntryMode=>...) -- select method of specifying matroid

- Usage:
    `matroid(..., EntryMode => "bases")`
    `matroid(..., EntryMode => "nonbases")`
    `matroid(..., EntryMode => "circuits")`

## Description

A matroid is determined by its set of bases, i.e. maximal (with respect to inclusion) independent sets, which are all of the same size (namely, the rank of the matroid). However, many interesting matroids have relatively few dependencies, and thus it may be easier to specify the matroid by its nonbases, i.e. dependent subsets of the ground set, with size equal to the rank of the matroid.

Similarly, a matroid can be specified by its circuits, i.e. minimal dependent sets. This is done e.g. when creating a graphical matroid.

If EntryMode is not specified, then the default value is assumed, which is EntryMode => "bases".

    i1 : M = matroid({{0,1,2}, {3,4,5}}, EntryMode => "circuits") -- bowtie graph / 2 disjoint K3's

    o1 = a "matroid" of rank 4 on 6 elements

    o1 : Matroid

    i2 : bases M

    o2 = {set {1, 2, 4, 5}, set {0, 2, 4, 5}, set {0, 1, 4, 5}, set {1, 2, 3, 5},
         ------------------------------------------------------------------------
         set {0, 2, 3, 5}, set {0, 1, 3, 5}, set {1, 2, 3, 4}, set {0, 2, 3, 4},
         ------------------------------------------------------------------------
         set {0, 1, 3, 4}}

    o2 : List

    i3 : F7 = matroid({{0,1,6},{0,2,4},{0,3,5},{1,2,5},{1,3,4},{2,3,6},{4,5,6}}, EntryMode => "nonbases")

    o3 = a "matroid" of rank 3 on 7 elements

    o3 : Matroid

    i4 : F7 == specificMatroid "fano"

    o4 = true

## See also

- matroid -- constructs a matroid
- nonbases -- nonbases of matroid
- circuits -- circuits of matroid

## Functions with optional argument named EntryMode:

- digraph(...,EntryMode=>...) (missing documentation)
- elementaryQuotient(...,EntryMode=>...) -- use a modular cut or linear subclass
- extension(...,EntryMode=>...) -- use a modular cut or linear subclass
- `graph(...,EntryMode=>...)` -- see graph -- Constructs a simple graph
- matroid(...,EntryMode=>...) -- select method of specifying matroid

## Further information

- Default value: bases
- Function: matroid -- constructs a matroid
- Option key: EntryMode -- Constructs a simple graph

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Matroids/doc-Matroids.m2:361:0.