# Matroid _ List -- elements of matroid

## Synopsis

• Operator: _
• Usage:
M_S
M_i
M_*
• Inputs:
• M, ,
• S, a list, or set, of indices in M.groundSet
• Outputs:
• a list, of elements of M

## Description

Converts a list or set of indices to the list of elements of the matroid with those indices. The inverse of this function is indicesOf.

 i1 : M = matroid({a,b,c,d},{{a,b},{a,c}}) o1 = a "matroid" of rank 2 on 4 elements o1 : Matroid i2 : M_2 o2 = c o2 : Symbol i3 : M_{0,2,3} o3 = {a, c, d} o3 : List i4 : B = (bases M)#0 o4 = set {0, 1} o4 : Set i5 : M_B o5 = set {a, b} o5 : Set

If used with the operator _*, then the list of all elements in M is returned. This is useful in conjunction with apply, to iterate over all elements in a matroid.

 i6 : F7 = specificMatroid "fano" o6 = a "matroid" of rank 3 on 7 elements o6 : Matroid i7 : M4 = matroid completeGraph 4 o7 = a "matroid" of rank 3 on 6 elements o7 : Matroid i8 : all(F7_*, x -> areIsomorphic(F7 \ {x}, M4)) o8 = true

## Caveat

There are important differences between this method and groundSet: see that page for more details.