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combinat::powerset -- power set of a set or list

Introduction

combinat::powerset(set) computes the powerset of the given set set, that is, the set of all subsets of set.

combinat::powerset(list) computes the powerset of the given list list, that is, the set of all sublists of list. In this context, lists are understood as multisets.

combinat::powerset(n) computes the powerset of the set 1,2,...,n.

Call(s)

combinat::powerset(n)
combinat::powerset(set)
combinat::powerset(list)

Parameters

n - a nonnegative integer
set - a set of domain type DOM_SET
list - a list of domain type DOM_LIST

Returns

A set of domain type DOM_SET which contains the computed subsets.

Overloadable:

set

Related Functions

combinat::choose

Details

Example 1

>> combinat::powerset({a, b, c})
          {{}, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}}

Example 2

>> combinat::powerset(3)
          {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Example 3

Here you can see that lists are treated as multisets. There is no sublist [2, 1] since it is identified with the list [1,2] which is in the powerset.

>> combinat::powerset([2, 1, 2])
                 {[], [1], [2], [1, 2], [2, 2], [1, 2, 2]}

Changes




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