Re: Maximize returning approximate values
- To: mathgroup at smc.vnet.net
- Subject: [mg101325] Re: [mg101297] Maximize returning approximate values
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Wed, 1 Jul 2009 06:35:25 -0400 (EDT)
- References: <200906301035.GAA10701@smc.vnet.net>
On 30 Jun 2009, at 19:35, Nacho wrote:
> Hello.
>
>> From Maximize documentation in V7.0.3:
>
> * Maximize will return exact results if given exact input.
>
> I've tried to maximize n/n! without success:
>
> In[8]:= Maximize[n/n!, n]
> Out[8]= Maximize[n/n!, n]
>
> But a Plot shows that the maximum is around 1.5, so I tried:
>
> In[9]:= Maximize[{n/n!, 0 <= n <= 3}, n]
> During evaluation of In[9]:= Maximize::nint: Warning: Maximize used
> numeric integration to show that the result is a global maximum. >>
> Out[9]= {Root[{-#1! + Gamma[1 + #1] PolyGamma[0, 1 + #1] #1 &,
> 1.46163214496836234126265954233}]/
> Root[{-#1! + Gamma[1 + #1] PolyGamma[0, 1 + #1] #1 &,
> 1.46163214496836234126265954233}]!, {n ->
> Root[{-#1! + Gamma[1 + #1] PolyGamma[0, 1 + #1] #1 &,
> 1.46163214496836234126265954233}]}}
>
>
> It is partially symbolic, partially numeric.
> Is it a bug?
>
> Regards.
What makes you think this could be a bug? What other answer could you
possibly imagine? Mathematica since version 7 is able to find
solutions of transcendental (analytic) equations which it expresses in
symbolic form providing as a last argument an approximate value, which
is sufficient to isolate the root from other roots of the same
equation. A root given in this way can be computed to arbitrary
precision, e.g.
N[Root[{-#1! + Gamma[1 + #1] PolyGamma[0, 1 + #1] #1 &,
1.46163214496836234126265954233}], 100]
1.4616321449683623412626595423257213284681962040064463512959884085987864403538
\
01810243074992733725593
Here you have got it with 100 digits; you can get 1000 or more if you
like. You can do the same sort of things with this representation as
you can do with Pi or E, which are also exact representations. The
presence of the approximate number just gives you additional
information - how could additional information be a bug?
Andrzej Kozlowski