Re: Refine, assumptions, domains

• To: mathgroup at smc.vnet.net
• Subject: [mg101738] Re: [mg101690] Refine, assumptions, domains
• From: Andrzej Kozlowski <akozlowski at gmail.com>
• Date: Wed, 15 Jul 2009 07:13:11 -0400 (EDT)
• References: <200907140937.FAA02004@smc.vnet.net>

```
On 14 Jul 2009, at 02:37, Richard Fateman wrote:

> What I'm looking for is a simple way to obtain a finite list
>
> { Pi, 2 Pi, 3 Pi}
>
> from  this information:
>
>   0< n*Pi < 10,  Element[n,Integers]
>
> Refine doesn't do this, at least with Mathematica 6.0
> Suggestions? (cc to fateman at gmail.com would be nice.)
>

One way:

Reduce[0 < n*Pi < 10 && Element[n, Integers]]

n == 1 || n == 2 || n == 3

Of course this is not quite in the form you wanted. If you really need
it in that particular form you could use:

n*Pi /. {ToRules[Reduce[0 < n*Pi < 10 && Element[n, Integers]]]}
{Pi, 2*Pi, 3*Pi}

or various other alternatives. But Reduce does the main job.

Andrzej Kozlowski

```

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