Intersection
Intersection[list1,list2,…]
gives a sorted list of the elements common to all the listi.
Details and Options
- If the listi are considered as sets, Intersection gives their intersection.
- Intersection[list1,list2,…] can be input in StandardForm and InputForm as list1⋂list2⋂…. The character ⋂ can be entered as
inter
or \[Intersection]. - The listi must have the same head, but it need not be List.
- Intersection[list1,…,SameTest->test] applies test to each pair of elements in the listi to determine whether they should be considered the same.
- Intersection[a,b] can be entered in StandardForm and InputForm as a⋂b or a \[Intersection]b .
Examples
open all close allBasic Examples (2)
:Generalizations & Extensions (1)
Intersection works with any head, not just List:
Intersection[f[a, b], f[c, a], f[b, b, a]]Options (3)
SameTest (3)
Use equivalence classes based on absolute value:
Intersection[{2, -2, 1, 3, 1}, {2, 1, -2, -1}, SameTest -> (Abs[#1] == Abs[#2]&)]Use equivalence classes based on Floor:
Intersection[{1.1, 3.4, .5, 7.6, 7.1, 1.9}, {1.2, 3.3, 7.7, 1.3}, SameTest -> (Floor[#1] == Floor[#2]&)]Use Total of list elements:
Intersection[{{1, 2}, {3}, {4, 5, 6}, {9, 6}}, {{2, 1}, {8, 4, 3}}, SameTest -> (Total[#1] == Total[#2]&)]Applications (1)
An Elementary Introduction to the Wolfram Language
NKS|OnlineText
Wolfram Research (1988), Intersection, Wolfram Language function, https://reference.wolfram.com/language/ref/Intersection.html (updated 1996).
CMS
Wolfram Language. 1988. "Intersection." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 1996. https://reference.wolfram.com/language/ref/Intersection.html.
APA
Wolfram Language. (1988). Intersection. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Intersection.html