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combinat::cartesian -- Cartesian product of sets

Introduction

combinat::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)

Parameters

set1, set2, ..., setN - Sets of domain type DOM_SET, or nonnegative integers.

Returns

A set of domain type DOM_SET containing N-tuples of domain type DOM_LIST, where N is the number of arguments.

Details

Example 1

Which 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 2

The 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 3

The cartesian product isn't commutative:

>> combinat::cartesian({Diamondsuit},2); combinat::cartesian(2,{Diamondsuit})
                   {[Diamondsuit, 1], [Diamondsuit, 2]}
      
                   {[1, Diamondsuit], [2, Diamondsuit]}

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