# isWellDefined(FlagMatroid) -- check if a flag matroid is well-defined

## Synopsis

• Function: isWellDefined
• Usage:
isWellDefined(FM)
• Inputs:
• FM, ,
• Outputs:

## Description

A FlagMatroid with constituent matroids $\{M_1, \ldots, M_k\}$ is well-defined if $M_i$ is a matroid quotient of $M_{i+1}$ (i.e. every flat of $M_i$ is a flat of $M_{i+1}$) for all $i = 1, \ldots, k-1$.

 i1 : FM = flagMatroid {uniformMatroid(2,4),uniformMatroid(3,4)} o1 = a flag matroid with rank sequence {2, 3} on 4 elements o1 : FlagMatroid i2 : isWellDefined FM o2 = true i3 : FMbad = flagMatroid {uniformMatroid(2,4), uniformMatroid(1,2)++uniformMatroid(2,2)} o3 = a flag matroid with rank sequence {2, 3} on 4 elements o3 : FlagMatroid i4 : isWellDefined FMbad o4 = false