Re: FullSimplify again ...
- To: mathgroup at smc.vnet.net
- Subject: [mg59209] Re: FullSimplify again ...
- From: Peter Pein <petsie at dordos.net>
- Date: Tue, 2 Aug 2005 00:42:30 -0400 (EDT)
- References: <dcf3d4$lgl$1@smc.vnet.net> <dchnql$7ub$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Jean-Marc Gulliet schrieb:
> Detlef M=FCller wrote:
>
>>Hello.
>>I happened to type the following lines:
>>
>>
>>
>>In[15]:= f=FullSimplify[Product[(5-i)/5,{i,1,n}]]
>>Out[15]= 0
>>
>>In[17]:= Product[(5-i)/5,{i,1,n}]/.(n->4)
>>Out[17]= 24/625
>>
>>Strange, isn't it?
>>
>>Version Number: 5.1.1.0
>>Platform: X
>>
>>Greetings,
>> Detlef
>>
>
> Hi Detlef,
>
> The result might not look so strange when we investigate the behavior of
> Mathematica functions such as *FullSimplify*. First, we notice that your
> product involves special function:
> 0
>
> Only the first four terms are not null. The behavior of *FullSimplify*
> is coherent with the behavior of other Mathematica functions that are
> designed to find general cases rather than specific ones. For instance,
> although *Solve* complains that the solution involves inverse function,
> *Reduce* just agree with the general result is always true (that is if
> we exclude the first four terms in the sequence):
>
> In[10]:=
> Reduce[Product[(5 - i)/5, {i, 1, n}] == 0, n]
>
> Out[10]=
> True
>
> In[11]:=
> $Version
>
> Out[11]=
> "5.2 for Microsoft Windows (June 20, 2005)"
>
> Hope this helps,
> /J.M.
>
>
>
Salut Jean-Marc.
Do NOT trust Reduce in version 5.2. An example:
Version 5.1 gives
someroots = (Root[-160 + 783*x + 54*x^2 - 1059*#1 - 540*x*#1 + 504*#1^2
+ 80*#1^3 & , #1] & ) /@ Range[3];
Reduce[someroots == Re[someroots], x, Reals]
-->
(1/90)*(45 - 23*Sqrt[138]) <= x <= (1/90)*(45 + 23*Sqrt[138]) || x == 14
but Mathematica 5.2 forgets to check the case x==14.
In german, we sometimes call such changes "Verschlimmbesserung", which
may be translated as "improvement toward worse"
--
Peter Pein
Berlin