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] ...]?