Re: Using a list as a variable

*To*: mathgroup at smc.vnet.net*Subject*: [mg67096] Re: Using a list as a variable*From*: dh <dh at metrohm.ch>*Date*: Fri, 9 Jun 2006 01:08:00 -0400 (EDT)*References*: <e68qc9$d2i$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Hi Bonny, The domains that "Element" accepts are well defined (see manual) and do not include Subsets[S]. You may have to iterate over the subsets e.g. using Scan. Daniel Bonny Banerjee wrote: > I would like to use a list (or set) as a variable. I am working on the > Subset-Sum problem. Given a set S of integers, the goal is to find a subset > of S (say Q) whose elements add to a given integer x. This is how I would > like to define the function: > > SubsetSum(S, x) := {Q such that Q is a subset of S and sum of the elements > of Q is x} > > In Mathematica functional programming language, this would look like: > > SubsetSum[S_, x_] := Reduce[Q \[Element] Subsets[S] && Sum[Q, > {i,1,Length[Q]}]==x, Q, Reals] > > Now when I try to evaluate SubsetSum[{1, 3, 5, 2, 7, 100, 6}, 101], the > output is as follows: > > Reduce : : naqs : > \[Exists]{Q} Q is not a quantified system of equations and > inequalities. More ... > > Out[365]= Reduce[Q, False, Q, Reals] > > > I guess, Mathematica is not being able to understand from my statement that > the variable Q is not an atom but a list. But it should since I stated that > Q is an element of the power set of S. > > Note that I know how to write a function for Subset-Sum using a Module. But > I am interested in functional programming, similar to the format shown > above. > > Any help would be appreciated. > > Thanks much, > Bonny. > >