CartesianProduct
CartesianProduct
CartesianProduct[ list1, list2 ] returns all pairs of an element of the first list and an element of the second list.
Usages
CartesianProduct[ list1, list2 ]
CartesianProduct[ list1, list2 ] returns a list of all pairs {a, b} with a from list1 and b from list2. The first element of list1 is combined with every element of list2 first, then the second element, and so on.
| Example | in | out |
|---|---|---|
All 3 × 2 = 6 pairs. |
CartesianProduct[ {1, 2, 3}, {4, 5} ] |
{ {1, 4}, {1, 5}, {2, 4}, {2, 5}, {3, 4}, {3, 5} } |
| Pairs of expressions. | CartesianProduct[ {a}, {x, y} ] |
{ {a, x}, {a, y} } |
Details
- Empty list: if one of the lists is empty,
CartesianProductis left unevaluated.
| Invalid input | Result |
|---|---|
CartesianProduct[ {1, 2}, 3 ] |
Error: the 2nd argument should be a list |
CartesianProduct[ {1}, {2}, {3} ] |
Error: the number of arguments should be 2 |