# bases(FlagMatroid) -- compute the bases of a flag matroid

## Synopsis

• Function: bases
• Usage:
B = bases(FM)
• Inputs:
• FM, ,
• Outputs:

## Description

An ordered list $\{B_1, \ldots, B_k\}$ of sets is a basis of a flag matroid $\mathbf M = \{M_1, \ldots, M_k\}$ if $B_i$ is a basis of $M_i$ and $B_i \subseteq B_{i+1}$ for all $i$. This method computes the bases of a flag matroid.

 i1 : FM = flagMatroid {uniformMatroid(2,4),uniformMatroid(3,4)} o1 = a "flag matroid" with rank sequence {2, 3} on 4 elements o1 : FlagMatroid i2 : bases FM o2 = {{set {0, 1}, set {0, 1, 2}}, {set {0, 1}, set {0, 1, 3}}, {set {0, 2}, ------------------------------------------------------------------------ set {0, 2, 3}}, {set {0, 2}, set {0, 1, 2}}, {set {1, 2}, set {1, 2, ------------------------------------------------------------------------ 3}}, {set {1, 2}, set {0, 1, 2}}, {set {0, 3}, set {0, 2, 3}}, {set {0, ------------------------------------------------------------------------ 3}, set {0, 1, 3}}, {set {1, 3}, set {1, 2, 3}}, {set {1, 3}, set {0, 1, ------------------------------------------------------------------------ 3}}, {set {2, 3}, set {0, 2, 3}}, {set {2, 3}, set {1, 2, 3}}} o2 : List