The powerset(s) calling sequence constructs the power set of a set, list, or non-negative integer.

If s is a set, then powerset command returns the power set of s, that is, a set consisting of all the subsets of s.  The power set has $2^n$ entries, where $n$ is the number of elements in s.

If s is a non-negative integer, powerset interprets it as a set of the first s integers.

If s is a list, powerset returns a list of all the sublists of s.  The number of sublists depends on the multiplicities of s.

To iterate through the subsets of a given set without generating all subsets beforehand, use combinat[subsets].

$\mathrm{with}\left(\mathrm{combinat}\,\mathrm{powerset}\right)$

$\left[\mathrm{powerset}\right]$

$\mathrm{powerset}\left(3\right)$

$\left\{\varnothing \,\left\{1\right\}\,\left\{2\right\}\,\left\{3\right\}\,\left\{1\,2\right\}\,\left\{1\,3\right\}\,\left\{2\,3\right\}\,\left\{1\,2\,3\right\}\right\}$

$\mathrm{powerset}\left(\left\{a\,b\right\}\right)$

$\left\{\varnothing \,\left\{a\right\}\,\left\{b\right\}\,\left\{a\,b\right\}\right\}$

$\mathrm{powerset}\left(\left[a\,a\,b\right]\right)$

$\left[\left[\right]\,\left[a\right]\,\left[b\right]\,\left[a\,b\right]\,\left[a\,a\right]\,\left[a\,a\,b\right]\right]$