Re: Generating systems of constraints

• To: mathgroup at smc.vnet.net
• Subject: [mg72393] Re: Generating systems of constraints
• From: "Ray Koopman" <koopman at sfu.ca>
• Date: Mon, 25 Dec 2006 04:52:14 -0500 (EST)
• References: <emdp92\$k3f\$1@smc.vnet.net>

```Alec Resnick wrote:
> Good day!  I was hoping someone might be able to point me in the
> right direction with a problem I ran into.  I'm trying to solve an
> arbitrarily large system of linear, Diophantine equations whose
> solutions are subject to two constraints
> 1) All the variables are distinct; i.e., none of the variables are
> equal to one another.
> 2) All of the variables are bounded by 1 <= x <= # of variables.
>
> So in essence, I have a system of equations with N variables that I
> would like to generate solutions for by assigning {1,2...,N} to each
> variable.
>
> Now, I know that I can use Reduce to solve this system; however, I
> don't know how to generate constraints like this for a given N, and
> I'd rather not type them all out.  Does anyone have any suggestions?
> I don't need to do this for very many systems, but more than four, so
> I don't want to have to do too much of it manually.
>
> Thanks!
>
> Gratefully,
> a.

I'm reading this as saying that you want {x[1],...,x[n]}
to be a permutation of {1,...,n}. If so then how about

Block[{v,x,otherstuff}, v = Array[x,n]; ... Union[v] == Range[n] ...]?

```

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