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Matroids :: Matroid _ List

Matroid _ List -- elements of matroid

Synopsis

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 = {a, b}

o5 : List

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 -> #getIsos(F7 \ {x}, M4) > 0)

o8 = true

Caveat

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

See also