Re: Newbie question: equations with sums.
- To: mathgroup at smc.vnet.net
- Subject: [mg92866] Re: Newbie question: equations with sums.
- From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
- Date: Thu, 16 Oct 2008 05:04:26 -0400 (EDT)
- Organization: The Open University, Milton Keynes, UK
- References: <gd4dlf$bgb$1@smc.vnet.net>
Vend wrote:
> FullSimplify[\!\(
> \*UnderoverscriptBox[\(\[Sum]\), \(i = 0\), \(\(-1\) + n\)]i\ f[
> i]\) == \!\(
> \*UnderoverscriptBox[\(\[Sum]\), \(k = 0\), \(\(-1\) + n\)]k\ f[k]\)]
>
> Evaluates to:
>
> \!\(
> \*UnderoverscriptBox[\(\[Sum]\), \(i = 0\), \(\(-1\) + n\)]i\ f[
> i]\) == \!\(
> \*UnderoverscriptBox[\(\[Sum]\), \(k = 0\), \(\(-1\) + n\)]k\ f[k]\)
>
> Why doesn't it evaluate to true? Is there a way to make the system
> solve this kind of equations?
Here, what you should test is sameness (===), which is more appropriate
for symbolic expression, rather than equality (==). For instance,
In[1]:= FullSimplify[\!\(
\*UnderoverscriptBox[\(\[Sum]\), \(i = 0\), \(\(-1\) + n\)]\(i\ f[
i]\)\) === \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(k = 0\), \(\(-1\) + n\)]\(k\ f[
k]\)\)]
Out[1]= False
Note the triple equal sign (function SameQ).
The following document might be worth reading:
"What is the difference between =, ==, and === in Mathematica?"
http://support.wolfram.com/mathematica/kernel/features/differentequals.html
Regards,
-- Jean-Marc