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# extension(...,CheckWellDefined=>...) -- check whether the list is a modular cut or linear subclass

- Usage:
    `extension(M, L, CheckWellDefined => true)`
- Inputs:
  - M, a matroid
  - L, a list, a list of flats or hyperplanes of the matroid forming a modular cut/linear subclass
- Outputs:
  - a matroid, the extension of the matroid associated to modular cut/linear subclass

## Description

This option is provided by the package Matroids.

When producing the single-element extension of a matroid M corresponding to a list of flats or hyperplanes L, setting this option to true calls isModularCut or isLinearSubclass to check that the list is a modular cut or linear subclass respectively.

    i1 : A = matrix {{1, 0, 0, 1, 1}, {0, 1, 0, 1, -1}, {0, 0, 1, 0, 0}}

    o1 = | 1 0 0 1 1  |
         | 0 1 0 1 -1 |
         | 0 0 1 0 0  |

                  3       5
    o1 : Matrix ZZ  <-- ZZ

    i2 : M = matroid A

    o2 = a "matroid" of rank 3 on 5 elements

    o2 : Matroid

    i3 : K = modularCut(M, drop(hyperplanes M, 1))

    o3 = {set {2}, set {4, 2}, set {2, 3}, set {1, 2}, set {0, 2}, set {0, 1, 2,
         ------------------------------------------------------------------------
         3, 4}}

    o3 : List

    i4 : extension(M, K, CheckWellDefined => true)

    o4 = a "matroid" of rank 3 on 6 elements

    o4 : Matroid

## See also

- extension -- of a matroid relative to a flat or modular cut

## Functions with optional argument named CheckWellDefined:

- `relaxation(...,CheckWellDefined=>...)` -- see CheckWellDefined -- an optional argument
- elementaryQuotient(...,CheckWellDefined=>...) -- check whether the list is a modular cut or linear subclass
- extension(...,CheckWellDefined=>...) -- check whether the list is a modular cut or linear subclass
- linearSubclass(...,CheckWellDefined=>...) -- check whether the list is a modular cut
- modularCut(...,CheckWellDefined=>...) -- check whether the list is a linear subclass

## Further information

- Default value: false
- Function: extension -- of a matroid relative to a flat or modular cut
- Option key: CheckWellDefined -- an optional argument

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Matroids/doc-Matroids.m2:3961:0.