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MathGroup Archive 2004

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Re: Simplifying with assumptions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg49010] Re: Simplifying with assumptions
  • From: "Dana DeLouis" <delouis at bellsouth.net>
  • Date: Mon, 28 Jun 2004 04:14:00 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

This should work, but it returns an error:

FindInstance[Sqrt[48 - n^2 + 8*x] == k, n, x, k}, Integers, 1]

The methods available to FindInstance are insufficient to find the requested
\
instances or prove they do not exist.

However, it can find two. Go figure!

FindInstance[Sqrt[48 - n^2 + 8*x] == k, {n, x, k}, Integers, 2]

{{n -> -500, x -> 31244, k -> 0}, {n -> 72, x -> 642, k -> 0}}

It also won't work without adding n > x, or n < x for some unknown reason.

You would think that this would work, but it doesn't.

FindInstance[k > 0 && n > x && k == Sqrt[48 - n^2 + 8*x], {n, x, k},
Integers, 5]

The methods available to FindInstance are insufficient to find the requested
\
instances or prove they do not exist.

You then have to remember the "Huge" bug in the program where order of
variables make a difference.

So, instead of {n, x, k}, try {k, n, x}

FindInstance[k > 0 && n > x && k == Sqrt[48 - n^2 + 8*x], {k, n, x},
Integers, 5]

{ {k -> 2, n -> -2, x -> -5},
  {k -> 2, n -> 6, x -> -1},
  {k -> 2, n -> 10, x -> 7},
  {k -> 4, n -> 0, x -> -4},
  {k -> 4, n -> 4, x -> -2}}

HTH
Dana
$Version
"5.0 for Microsoft Windows (June 10, 2003)"


= = = =
"Mietek Bak" <mietek at icpnet.pl> wrote in message
news:cbgjae$cef$1 at smc.vnet.net...
> Hello,
>
> I'm a complete newcomer to Mathematica, so please excuse this possibly
> silly question.
>
> I'm trying to determine if a formula will ever give an integer result,
> assuming that all variables used in it are integer.  I've been searching
> through the built-in documentation, but my best guess didn't really do
> anything:
>
> Simplify[Element[Sqrt[48 - n^2 + 8*x],Integers],Element[{n, x},Integers]]
>
> It would be best if I could somehow determine the set of combinations of
> variables that would give an integer result -- if there are any.  Is
> there a way to do that in Mathematica?
>
> Thanks in advance,
> Mietek Bak.



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