isElementaryQuotient -- whether a matroid is an elementary quotient of another matroid

Synopsis

• Usage:

  isElementaryQuotient(M, N)

• Inputs:
  • M, a matroid
  • N, a matroid
• Outputs:
  • a Boolean value, whether the first matroid is an elementary quotient of the second

Description

This function is provided by the package Matroids.

An elementary quotient of a matroid N is a quotient M whose rank is the rank of N minus one. Elementary quotients are completely determined by the modular cut of flats in M (which are also flats of N) whose rank in M is one less than their rank in N. Examples of elementary quotients of N are its principal truncations with respect to a given flat F.

i1 : N = matroid completeGraph 5

o1 = a "matroid" of rank 4 on 10 elements

o1 : Matroid

i2 : F = set {0,1,4};

i3 : TFN = truncate(F, N)

o3 = a "matroid" of rank 3 on 10 elements

o3 : Matroid

i4 : isElementaryQuotient(TFN, N)

o4 = true

i5 : T2N = truncate(2, N)

o5 = a "matroid" of rank 2 on 10 elements

o5 : Matroid

i6 : isElementaryQuotient(T2N, N)

o6 = false

See also

• elementaryQuotient -- associated to a modular cut or linear subclass
• isModularCut -- whether a list of flats of a matroid is a modular cut
• isQuotient -- whether a matroid is a quotient of another matroid
• modularCut -- associated to an elementary quotient or linear subclass
• truncate(Set,Matroid) -- the truncation of a matroid with respect to a flat