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

## Synopsis

• 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 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({{0,1,2},{2,3,4},{2,5,6},{0,4,5},{0,3,6},{1,3,5},{1,4,6}}, EntryMode => "nonbases") o3 = a matroid of rank 3 on 7 elements o3 : Matroid i4 : F7 == specificMatroid "fano" o4 = false

## Further information

• Default value: bases
• Function: matroid -- constructs a matroid
• Option key: EntryMode (missing documentation)