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Set ** Set -- Cartesian product

Synopsis

Operator: **
Usage:

x ** y
Inputs:
- x, a set
- y, a set
Outputs:
- whose elements are the sequences (a,b), where a is an element of x, and b is an element of y., a set

Description

i1 : set {1,2} ** set {a,b,c}

o1 = set {(1, a), (2, a), (1, b), (2, b), (1, c), (2, c)}

o1 : Set

Suppose we wish to form the set of all triples with entries either in the set A below.

i2 : A = set{1,2}

o2 = set {1, 2}

o2 : Set

i3 : A ** A ** A

o3 = set {((1, 1), 1), ((1, 2), 1), ((1, 1), 2), ((2, 1), 1), ((2, 2), 1),
     ------------------------------------------------------------------------
     ((1, 2), 2), ((2, 1), 2), ((2, 2), 2)}

o3 : Set

To make this last a set of triples, splice each element together. Or, use VirtualTally ^** ZZ.

i4 : (A ** A ** A)/splice

o4 = set {(1, 1, 1), (1, 1, 2), (1, 2, 1), (2, 1, 1), (2, 1, 2), (2, 2, 1),
     ------------------------------------------------------------------------
     (1, 2, 2), (2, 2, 2)}

o4 : Set

i5 : A^**3

o5 = set {((1, 1), 1), ((1, 2), 1), ((1, 1), 2), ((2, 1), 1), ((2, 2), 1),
     ------------------------------------------------------------------------
     ((1, 2), 2), ((2, 1), 2), ((2, 2), 2)}

o5 : Set

See also

Set -- the class of all sets

Ways to use this method:

Set ** Set -- Cartesian product