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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.
>
>
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