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Re: Using a list as a variable

  • To: mathgroup at
  • Subject: [mg67096] Re: Using a list as a variable
  • From: dh <dh at>
  • Date: Fri, 9 Jun 2006 01:08:00 -0400 (EDT)
  • References: <e68qc9$d2i$>
  • Sender: owner-wri-mathgroup at

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.


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. 



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