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-- Status: rewritten July 2018
-- Author: Lily Silverstein
doc///
Key
subsets
(subsets, ZZ)
(subsets, ZZ, ZZ)
(subsets, List)
(subsets, List, ZZ)
(subsets, Sequence, ZZ)
(subsets, Set)
(subsets, Set, ZZ)
Headline
produce the subsets of a set or list
Usage
subsets(A)
subsets(A, n)
Inputs
A: List
, sequence, set or integer
n: ZZ
optional input to specify subsets of a particular size
Outputs
L: List
of subsets (of size {\tt n} if given)
Description
Text
If {\tt A} is an integer, {\tt subsets(A)} lists the subsets of {\tt \{0, 1, ..., A-1\}}.
Example
subsets(3)
subsets(5, 3)
Text
{\tt A} can be a list, sequence, or set. The elements need not be of the same type.
Example
subsets({"apple", "banana", {1,2,3}, 7.1}, 3)
Text
If a list contains repetitions, so will the subsets of that list.
Since a @TO Set@ has no repetitions, neither do its subsets. Also,
the subsets of a set will again be sets (while the subsets of a list are lists).
Example
subsets({"apple", "apple", "banana"})
subsets(set{"apple", "apple", "banana"})
Text
The subsets of a Sequence are lists, not sequences. Also, a subset size {\bf must} be
specified when calling {\tt subsets} on a sequence.
SeeAlso
partition
set
sublists
substring
"lists and sequences"
///
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