Function Repository Resource:

MultisetProduct

Perform the product operation on multisets

Contributed by: Robert B. Nachbar (Wolfram Solutions)

ResourceFunction["MultisetProduct"][list₁,list₂,…]

gives a sorted list of all the elements that appear in any of the list_i. The number of occurrences of each distinct element is the product of the counts in each of the list_i.

ResourceFunction["MultisetProduct"][list]

effectively sorts the elements of list.

ResourceFunction["MultisetProduct"][assoc₁,assoc₂,…]

gives an Association where the keys are the union of the keys in the associations assoc_i and the values are the product of the merged values.

Details and Options

If the list_i are considered as multisets, ResourceFunction["MultisetProduct"] gives their product.

The list_i must have the same head, but it need not be List.

The values of assoc_i must be counts—that is, non-negative Integer values.

Examples

Basic Examples (2)

Give a sorted list of elements common to all the lists, where the number of each distinct element is the product of the individual cardinalities:

In[1]:=

Out[1]=

Multisets as an Association of counts:

In[2]:=

ResourceFunction[
"MultisetProduct"][<|"a" -> 3, "b" -> 1, "c" -> 2, "d" -> 1|>,
<|"a" -> 2, "b" -> 2, "c" -> 2, "e" -> 1|>,
<|"a" -> 1, "b" -> 2, "c" -> 2, "e" -> 2|>]

Out[2]=

Scope (1)

MultisetProduct works with any head, not just List:

In[3]:=

Out[3]=

Properties and Relations (1)

Compare to Intersection:

In[4]:=

Out[4]=

In[5]:=

Out[5]=

Publisher

Robert Nachbar

Requirements

Wolfram Language 11.3 (March 2018) or above

Version History

1.0.0 – 19 February 2019

Related Resources

License Information

This work is licensed under a Creative Commons Attribution 4.0 International License

Wolfram Function Repository