Re: FullSimplify again ...
- To: mathgroup at smc.vnet.net
- Subject: [mg59160] Re: [mg59138] FullSimplify again ...
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Sun, 31 Jul 2005 01:30:36 -0400 (EDT)
- References: <200507300525.BAA21874@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
On 30 Jul 2005, at 07:25, Detlef Müller 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
>
>
Well, I suspect this is a "legacy bug", dating to the way Mathematica
used to work before the Assumptions mechanism was introduced. The
point is:
what should FullSimplify do with
Pochhammer[-4, n]?
(of course the same holds for other negative integers instead of -4)
For n <=4 this non zero and for n>4 it is 0.
FullSimplify, however, always gives
FullSimplify[Pochhammer[-4,n]]
0
Before the assumption mechanism was indroduced in v.4 of Mathematica,
Simplify or FullSimplify would often introduce their own implicit
assumptions, presumably the ones that the user was "most likely" to
have intended. This was not entirely unreasonable in those days:
after all one woudl expect that a sensible user would not ask
Mathematica to evaluate something wanting to get his own input
returned back to him! Since the assumptions mechanism was introduced
this behaviour was largely eliminated but it seems that some cases
managed to escape scrutiny and survived.
Andrzej Kozlowski
- References:
- FullSimplify again ...
- From: Detlef Müller <dmueller@mathematik.uni-kassel.de>
- FullSimplify again ...