Re: Simplify Oddity
- To: mathgroup at smc.vnet.net
- Subject: [mg59407] Re: Simplify Oddity
- From: albert <awnl at arcor.de>
- Date: Mon, 8 Aug 2005 06:17:11 -0400 (EDT)
- References: <dd7337$3q5$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
AES wrote:
> I'm supposing that the following rather odd result has something to do
> with Mathematica being concerned that g or r (or k?) might be complex
> numbers?
>
> In[151] :=
>
> f1 = g (g/r)^(k-1);
>
> f2 = g^k/r^(k-1);
>
> f1/f2 // FullSimplify
>
> Out[151] = g^(-k) (g/r)^k r^k
>
No, as you suppose, mathematica takes into account that everything could be
a complex number ... including 0. The expression f1/f2 will only simplify
to 1 if g and r are not 0 and k is e.g. an integer. You can check that by
hand or with:
In[5]:= f1/f2 /. {g -> 1, r -> -2, k -> 1/2}
Out[5]= -1
In[6]:= Assuming[{r < 0, g > 0}, Simplify[f1/f2]]//InputForm
Out[6]//InputForm= E^((2*I)*k*Pi)
but when given these assumption, mathematica will simplify (it implicitly
assumes r and g to be reals when you specify something like r<0 or r!=0 I
think):
In[7]:= Assuming[{g != 0, r != 0, Element[k,Integers]},Simplify[f1/f2]]
Out[7]= 1
> But shouldn't Mathematic be able to simplify this to unity nonetheless?
> -- maybe without even invoking Simplify?
Hm, you might find very different opinions about what Mathematica should do
or not do even when you look at posts to this group. The point is in most
cases whether to stick to strict mathematics and not give simple answers or
whether implicitly making assumptions and presenting simple answers that
might for special cases be wrong. Usually mathematica tries to stick to
strictly mathematical correct results, but by far not in every single case.
So you will find many posts where people complain about these very cases,
calling them bugs.
It helps a lot if you accept that mathematica is a much more usefull tool to
do mathematics than a pen and a piece of paper, but be aware that it won't
make it possible to get correct results if you don't understand the
mathematics you are doing. Checks of any results that are computed
automatically are always a good idea...
Albert
- Follow-Ups:
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