Re: Subsets

*To*: mathgroup at smc.vnet.net*Subject*: [mg4987] Re: Subsets*From*: Clemens Frey <Clemens.Frey at uni-bayreuth.de>*Date*: Thu, 17 Oct 1996 00:41:03 -0400*Organization*: uni-bayreuth.de*Sender*: owner-wri-mathgroup at wolfram.com

Fabiana Costa Pereira wrote: > > I need to know if there is a function in Mathematica > that generates the set of all subsets of a list. Hi, as far as i am concerned, there is no such function. But I had that problem myself some time ago, and here is how I solved it : addEl[ set_List, el_ ] := Flatten[ {#,Flatten[{#,el}]}& /@ set, 1 ]; allSs[ set_List ] := Fold[ addEl, {{}}, Union[set] ]; Then you can use allSs[...] to obtain a list of all subsets of a given set. Because you cannot be sure that a list contains all its elements exacly once, I use Union[set] to get an (ordered) list of all elements of set. So you can type in this: IN>> allSs[ {1,2,3} ] //Union ...and you will get : OUT>> {{},{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}} Of course, you can also use symbols instead of numbers as elements of your list. Because I used Union[set] in the definition of allSs, the following IN>> allSs[ {a,a} ] will result in OUT>> {{},{a}} and not in NOT OUT>> {{},{a},{a},{a,a}} . Hope I could help you Clemens (-: Clemens.Frey at uni-bayreuth.de :-)