Shortest power set implementation
Mathematica 16

Code 

Subsets is native to Mathematica.

Column@Subsets@s


The code (without column) can be verified on WolframAlpha. (I had to use brackets instead of @; they mean the same thing.

Usage

s={1,2,3}
Column@Subsets@s






This method (55 chars) uses the approach suggested by @w0lf.

s #&amp;/@Tuples[{0,1},Length@s]/.{0:&gt;Sequence[]}//Column


Breakdown

Generate the tuples, composed of 0 and 1's of length Length[s]

Tuples[{0, 1}, Length@s]



  {{0, 0, 0}, {0, 0, 1}, {0, 1, 0}, {0, 1, 1}, {1, 0, 0}, {1, 0, 1}, {1,
     1, 0}, {1, 1, 1}}


Multiply the original list (vector) by each tuple:

s # &amp; /@ Tuples[{0, 1}, Length@s]



  {{0, 0, 0}, {0, 0, 3}, {0, 2, 0}, {0, 2, 3}, {1, 0, 0}, {1, 0, 3}, {1,
     2, 0}, {1, 2, 3}}


Delete the 0's. % is shorthand for "the preceding output".

%/. {0 :> Sequence[]}


  {{}, {3}, {2}, {2, 3}, {1}, {1, 3}, {1, 2}, {1, 2, 3}}


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