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MathGroup Archive 2005

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Re: Reduce bug?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg63196] Re: Reduce bug?
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Sat, 17 Dec 2005 03:46:39 -0500 (EST)
  • Organization: The Open University, Milton Keynes, UK
  • References: <dnv49q$ocp$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

François Wirion wrote:
> In[22]:=$Version
> Out[22]=5.2 for Microsoft Windows (June 20, 2005)
> 
> Trying to reduce the following simple non-algebraic equation, I get the
> following:
> In[7]:=
> Reduce[4^n*(n - 1)*(n - 2) == 0, n]
> Out[7]=
> True
> 
> This is of course a bit odd since e.g. when n = 0,
> In[23]:=
> 4^n*(n - 1)*(n - 2) == 0 /. n -> 0
> Out[23]=
> False
> 
> It seems that this problem occurs not only with 4^n in the equation but
> more generally for even integers other than -2, 0 and 2. I had a look
> through the archives but could not find a related entry on a first
> glance.
> 
Hi Francois,

I use the same version as yours and have got various warning/error 
messages using *Reduce*. *Solve*, however, works fine. These difference 
of of behavior could be explained by the internal use of different set 
of algorithms.

Table[{p, Reduce[p^n*(n - 1)*(n - 2) == 0, n, Integers]}, {p, -10, 10}]

Reduce::nsmet: This system cannot be solved with the methods available to \
Reduce

Reduce::ztest: Unable to decide whether numeric quantities {-2 Log[3] + \
Log[9]} are equal to zero. Assuming they are.

\!\({{\(-10\), n â?? Integers ||
        n == 1 || n == 2}, {\(-9\), Reduce[\((\(-9\))\)\^n\ \((\(-2\) + 
n)\)\ \
\((\(-1\) +
         n)\) == 0, n, Integers]}, {\(-8\), n â?? Integers || n ==
               1 || n == 2}, {\(-7\), n == 1 || n ==
                2}, {\(-6\), n â?? Integers || n ==
           1 || n == 2}, {\(-5\), n == 1 || n ==
      2}, {\(-4\), n â??
       Integers || n == 1 || n == 2}, {\(-3\), n ==
         1 || n == 2}, {\(-2\), n == 1 || n == 2}, {\(-1\), n ==
         1 || n == 2}, {0, n â?? Integers && n â?¥ 1}, {
       1, n == 1 || n == 2}, {2, n == 1 || n == 2}, {3, n == 1 || n == 2}, {
     4, n â?? Integers || n == 1 || n == 2}, {5, n == 1 || n ==
     2}, {6, n â?? Integers || n == 1 || n == 2}, {7, n == 1 || n == 2}, {8,
         n â?? Integers || n == 1 || n == 2}, {
       9, Reduce[9\^n\ \((\(-2\) + n)\)\ \((\(-1\) + n)\) == 0,
        n, Integers]}, {10, n â?? Integers || n == 1 || n == 2}}\)

In[2]:=
Solve[4^n*(n - 1)*(n - 2) == 0, n]

Out[2]=
{{n -> 1}, {n -> 2}}

Best regards,
/J.M.


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