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# hyperplanes -- hyperplanes of a matroid

- 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

## See also

- flats -- flats of a matroid
- rank(Matroid) -- rank of a matroid

## 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 /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Matroids/doc-Matroids.m2:1168:0.