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

- Function: isWellDefined
- Usage:
    `isWellDefined(FM)`
- Inputs:
  - FM, a flag matroid,
- Outputs:
  - a Boolean value,

## 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

## See also

- FlagMatroid -- the class of all flag matroids
- flagMatroid(List) -- construct a flag matroid

## Ways to use this method:

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

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/GKMVarieties/Documentation_GKMVarieties.m2:1894:0.