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

FranÃ§ois 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.