linearSubclass(...,CheckWellDefined=>...) -- check whether the list is a modular cut

Synopsis

• Usage:

  linearSubclass(M, K, CheckWellDefined => true)

• Inputs:
  • M, a matroid
  • K, a list, a list of flats of the matroid forming a modular cut
• Outputs:
  • a list, a list of hyperplanes of the matroid forming a linear subclass

Description

This option is provided by the package Matroids.

When producing the linear subclass of a matroid M corresponding to a list of flats K, setting this option to true calls isModularCut to check that the list K is in fact a modular cut.

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 = {{2}, {2, 4}, {2, 3}, {1, 2}, {0, 2}, {0, 1, 2, 3, 4}};

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

o4 = {set {0, 2}, set {4, 2}, set {1, 2}, set {2, 3}}

o4 : List

Further information

• Default value: false
• Function: linearSubclass -- associated to an elementary quotient or modular cut
• Option key: CheckWellDefined -- an optional argument

See also

• linearSubclass -- associated to an elementary quotient 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