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hyperplanes -- hyperplanes of a matroid

Description

The hyperplanes of a matroid are the flats of rank equal to rank M - 1. The complements of the hyperplanes are precisely the circuits of the dual matroid (which is indeed how this method computes hyperplanes), and thus a matroid is determined by its hyperplanes.

i1 : M = matroid({a,b,c,d},{{a,b},{a,c}})

o1 = a "matroid" of rank 2 on 4 elements

o1 : Matroid
 
i2 : hyperplanes M

o2 = {set {1, 2, 3}, set {0, 3}}

o2 : List

See also

Ways to use hyperplanes:

  • hyperplanes(Cone) -- see hyperplanes -- computes the defining hyperplanes of a Cone or a Polyhedron
  • hyperplanes(Matroid)
  • hyperplanes(Polyhedron) -- see hyperplanes -- computes the defining hyperplanes of a Cone or a Polyhedron

For the programmer

The object hyperplanes is a method function.

The source of this document is in Matroids/doc-Matroids.m2:1168:0.