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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



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