# contraction -- contraction of subset of matroid

## Synopsis

• Usage:
contraction(M, S)
M / S
• Inputs:
• M, ,
• S, a set, of indices, or a list of elements in M
• Outputs:
• , the contraction M / S

## Description

The contraction of M by S is given by M/S := (M* \ S)*, where * stands for dual, and \ is deletion.

 i1 : M = matroid({a,b,c,d},{{a,b},{a,c}}) o1 = a matroid of rank 2 on 4 elements o1 : Matroid i2 : N = M / {c} o2 = a matroid of rank 1 on 3 elements o2 : Matroid i3 : peek N o3 = Matroid{bases => {set {0}} } cache => CacheTable{...3...} groundSet => set {0, 1, 2} rank => 1 i4 : N == M / set{2} o4 = true