Intersection of all sublists of a list

Question

I want to get the intersection of all sublists of list in an easy way.

list = {{a,b,c},{d,e,a},{c,a,f}]}
Intersection[list[[1]],list[[2]],list[[3]]] 
Intersection[list]

The first Intersection command works well (it gives {a}). But the second one does not work. I understand that there's a syntax error (list is a list of lists, but Intersection only takes individual lists. However, there must be a simple way around it? In my case, list has more than 3 sublists which makes it hard to write them all down.

Thanks

Simply : Apply[Intersection, list] (or Intersection @@ list) — andre314, Oct 09 '15 at 21:48
Please note that list = {{a, b, c}, {d, e, a}, {c, a, f}]} has a mistaken ] — Enrique Pérez Herrero, Oct 09 '15 at 21:49

Jack LaVigne · Accepted Answer · 2015-10-11T13:45:55.927

3

As pointed out by Sjoerd C de Vries and andre an easy way is to replace the head of your list with Intersection by using Apply (i.e, @@)

Intersection @@ list

(* {a} *)

edited Oct 11 '15 at 13:45

answered Oct 09 '15 at 22:25

Jack LaVigne

14,462
2
25
37

4

IMHO Intersection @@ list would be easier. – Sjoerd C. de Vries Oct 09 '15 at 22:33
@SjoerdC.deVries IMO you are 100% correct :) Answer edited accordingly. – Jack LaVigne Oct 11 '15 at 13:42

score 2 · Answer 2 · answered Oct 10 '15 at 07:14

2

As I said in the comments :
Apply[Intersection, list] (or Intersection @@ list)

answered Oct 10 '15 at 07:14

andre314

18,474
1
36
69

Intersection of all sublists of a list

2 Answers2