Matroid _ List -- elements of matroid

Synopsis

Operator: _
Usage:

M_S

M_i

M_*
Inputs:
- M, a matroid,
- 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.

Ways to use this method:

Matroid _ List -- elements of matroid
Matroid _ Set
Matroid _ ZZ

Matroid _ List -- elements of matroid

Synopsis

Description

Caveat

See also

Ways to use this method: