Generating systems of constraints

• To: mathgroup at smc.vnet.net
• Subject: [mg72358] Generating systems of constraints
• From: Alec Resnick <aresnick at mit.edu>
• Date: Tue, 26 Dec 2006 08:07:12 -0500 (EST)

```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.

```

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