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restriction -- restriction to subset of matroid

Usage:

restriction(M, S)

M | S
Inputs:
- M, a matroid,
- S, a set, of indices, or a list of elements in M
Outputs:
- a matroid, the restriction M | S

Description

The restriction of M to S, M | S, has ground set S and independent sets equal to the independent sets of M contained in S.

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 | {a,b,d}

o2 = a "matroid" of rank 2 on 3 elements

o2 : Matroid

i3 : peek N

o3 = Matroid{bases => {set {0, 1}}       }
             cache => CacheTable{...1...}
             groundSet => set {0, 1, 2}
             rank => 2

i4 : N == M | set{0,1,3}

o4 = true

See also

deletion -- deletion of subset of matroid
minor -- minor of matroid

Ways to use restriction:

restriction(Matroid,List)
restriction(Matroid,Set)

For the programmer

The object restriction is a method function.

The source of this document is in Matroids/doc-Matroids.m2:1346:0.