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Using a list as a variable

• To: mathgroup at smc.vnet.net
• Subject: [mg67069] Using a list as a variable
• From: "Bonny Banerjee" <banerjee at cse.ohio-state.edu>
• Date: Thu, 8 Jun 2006 04:54:33 -0400 (EDT)
• Organization: Ohio State University
• Sender: owner-wri-mathgroup at wolfram.com

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. 

• Follow-Ups:
  • Re: Using a list as a variable
    • From: Daniel Lichtblau <danl@wolfram.com>
  • Re: Using a list as a variable
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>