extension(...,EntryMode=>...) -- use a modular cut or linear subclass

Synopsis

• Usage:

  extension(M, L, Entry => "hyperplanes")

• 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.

A single-element extension of a matroid M can be produced from a list of flats forming a modular cut of M or a list of hyperplanes of M forming a linear subclass. By default, it is assumed the specified list is a modular cut, but setting this option to "hyperplanes" allows passing a much shorter list of hyperplanes forming a linear subclass instead.

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 : H = drop(hyperplanes M, 1)

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

o3 : List

i4 : extension(M, H, EntryMode => "hyperplanes")

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

o4 : Matroid

Further information

• Default value: modular cut
• Function: extension -- of a matroid relative to a flat or modular cut
• Option key: EntryMode -- Constructs a simple graph

See also

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

Functions with optional argument named EntryMode:

• digraph(...,EntryMode=>...) (missing documentation)
• elementaryQuotient(...,EntryMode=>...) -- use a modular cut or linear subclass
• extension(...,EntryMode=>...) -- use a modular cut or linear subclass
• graph(...,EntryMode=>...) -- see graph -- Constructs a simple graph
• matroid(...,EntryMode=>...) -- select method of specifying matroid