# hyperplanes -- hyperplanes of a matroid

## Synopsis

• Usage:
hyperplanes M
• Inputs:
• M, ,
• Outputs:

## 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