Intersect

Intersect

Intersect[ list1, list2, ... ] returns the elements of the first list that also occur in all other lists.

Usages

Intersect[ list1, list2 ]

Intersect[ list1, list2 ] returns a new list with the elements of list1 that also occur in list2. The elements keep their order from list1.

Example in out
a and b occur in both lists. Intersect[ {a,b,g}, {a,b,c,d,e,a} ] {a, b}
a occurs twice in both lists, so it is kept twice. Intersect[ {a,b,g,a}, {a,c,a} ] {a, a}
a occurs only once in the second list, so it is kept once. Intersect[ {a,b,g,a}, {a,c} ] {a}
Lists stored in script variables. x := {a,b,c}
y := {b,c,d}
z := Intersect[x, y]		 z = {b, c}

Intersect[ list1, list2, list3, ... ]

With more than two lists, the result contains the elements of list1 that occur in every other list.

Example in out
Only a occurs in all three lists. Intersect[ {a,b,g,a}, {a,b,c,d,e,a}, {g,d,f,a} ] {a}
Details
  • Duplicates are counted separately: an element is kept as many times as it occurs in every list. Each element of list2 can match only one element of list1.
  • Equal elements: elements match if they are the same mathematical expression, regardless of the order of terms or factors. Numbers must have the same form: 2.4 and 12/5 do not match. Numbers with a limited precision, such as PrecisionConstant[3.14,2], match a value within that precision.
  • Empty lists: if any of the lists is empty, the result is {}.
  • Single list: Intersect[ {a,b} ] returns {a, b}.
Example in out
1+x matches x+1. Intersect[ {x+1, 3}, {1+x} ] {x+1}
12/5 does not match 2.4. Intersect[ {2.4, 3}, {12/5, 3} ] {3}
Invalid input Result
Intersect[ {a,b}, b ] Left unevaluated: the result is Intersect[ {a,b}, b ] itself. All arguments must be lists.

See also: IntersectI, Difference, Tally