VirtualTally ^** ZZ -- Cartesian power of sets and tallies

Synopsis

• Operator: ^**

• Usage:

  B = A^**n

• Inputs:
  • A, a virtual tally
  • n, an integer
• Outputs:
  • B, a virtual tally, the tally of n-tuples of elements from A

Description

i1 : A = set {1,2}

o1 = set {1, 2}

o1 : Set

i2 : A^**3

o2 = set {((1, 1), 1), ((1, 1), 2), ((1, 2), 1), ((1, 2), 2), ((2, 1), 1), ((2, 1), 2), ((2, 2), 1), ((2, 2), 2)}

o2 : Set

i3 : A = tally {1,1,2}

o3 = Tally{1 => 2}
           2 => 1

o3 : Tally

i4 : A^**3

o4 = Tally{((1, 1), 1) => 8}
           ((1, 1), 2) => 4
           ((1, 2), 1) => 4
           ((1, 2), 2) => 2
           ((2, 1), 1) => 4
           ((2, 1), 2) => 2
           ((2, 2), 1) => 2
           ((2, 2), 2) => 1

o4 : Tally

See also

• Set -- the class of all sets
• Set ** Set -- Cartesian product