hyperplanes -- hyperplanes of a matroid

Synopsis

Usage:

hyperplanes M
Inputs:
- M, a matroid,
Outputs:
- a list,

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

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.

hyperplanes -- hyperplanes of a matroid

Synopsis

Description

See also

Ways to use hyperplanes:

For the programmer