# swirl -- swirl matroid

## Synopsis

• Usage:
M = swirl r
• Inputs:
• Outputs:
• , a free swirl

## Description

The family of swirls appears in Oxley, p. 664. The rank-r free swirl has 2r elements and rank r.

 i1 : areIsomorphic(swirl 3, uniformMatroid_3 6) o1 = true i2 : M = swirl 4 o2 = a "matroid" of rank 4 on 8 elements o2 : Matroid i3 : betti ideal M 0 1 o3 = total: 1 44 0: 1 . 1: . . 2: . . 3: . 4 4: . 40 o3 : BettiTally i4 : M == dual M o4 = true i5 : getSeparation(M, 3) o5 = set {0, 1, 6, 7} o5 : Set