combinat::cartesian --
Cartesian product of sets
Introductioncombinat::cartesian(set1, set2, ..., setN)
computes the cartesian product of the given sets set1,
set2, ..., setN.
For every positive integer n, the set {1, ...,
n} may be denoted by n, and 0 may be
written instead of the empty set.
Call(s)combinat::cartesian(set1, set2, ..., setN)
Parametersset1, set2, ..., setN |
- | Sets of domain type DOM_SET, or nonnegative
integers. |
ReturnsA set of domain type DOM_SET containing
N-tuples of domain type DOM_LIST, where N is the
number of arguments.
Detailsset1,
set2 is the set set1 x set2 x ... x setN of all
N-tuples [x1,x2,...,xN] with xn in setn for
each 1<=n<=N.combinat::cartesian() is not commutative, as
demonstrated in example 3.
Example
1Which cards exist, if you have the following suits and numbers available?
>> combinat::cartesian({Diamondsuit,Heartsuit,Spadesuit,Clubsuit},{7,8,9,10})
{[Clubsuit, 7], [Clubsuit, 8], [Clubsuit, 9], [Clubsuit, 10],
[Spadesuit, 7], [Spadesuit, 8], [Spadesuit, 9],
[Spadesuit, 10], [Heartsuit, 7], [Heartsuit, 8],
[Heartsuit, 9], [Heartsuit, 10], [Diamondsuit, 7],
[Diamondsuit, 8], [Diamondsuit, 9], [Diamondsuit, 10]}
Example
2The same as above, but with other numbers:
>> combinat::cartesian({Diamondsuit,Heartsuit,Spadesuit,Clubsuit},3)
{[Clubsuit, 1], [Clubsuit, 2], [Clubsuit, 3], [Spadesuit, 1],
[Spadesuit, 2], [Spadesuit, 3], [Heartsuit, 1],
[Heartsuit, 2], [Heartsuit, 3], [Diamondsuit, 1],
[Diamondsuit, 2], [Diamondsuit, 3]}
Example
3The cartesian product isn't commutative:
>> combinat::cartesian({Diamondsuit},2); combinat::cartesian(2,{Diamondsuit})
{[Diamondsuit, 1], [Diamondsuit, 2]}
{[1, Diamondsuit], [2, Diamondsuit]}