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MathGroup Archive 2005

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Re: Simplify and FullSimplify

  • To: mathgroup at smc.vnet.net
  • Subject: [mg58559] Re: Simplify and FullSimplify
  • From: Bill Rowe <readnewsciv at earthlink.net>
  • Date: Thu, 7 Jul 2005 05:35:48 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

On 7/6/05 at 3:11 AM, fizzycist at knology.net (fizzy) wrote:

>A result of a calculation I was doing generated this expression....

>q-q Exp[-a x] + c Exp[-a x]

>naturally my next step was Simplify and I thought I'd  get the
>Exp[- ax] collected.....to my complete surprize I got the
>following:

>Exp[-a x] (c + (-1+ Exp[a x]) q

>How on Earth did Mathematica come up with this?   I checked
>FullSimplify which did collect Exp[-a x]....

>On re-reading my question before I submitted it, I see that with
>Simplify Mathematica  'collected' using Exp[- a x] q.....of course,
>visually this expression seems quite complex and would seem to take
>much more 'thinking' to get ......why do Simplify and FullSimplify
>have such a vast difference in what is considered 'Simpler'?

The issue isn't a difference between what is considered simpler by Simplify and FullSimplify. Instead, FullSimplify tries more transformations than Simplify.

For any method to simplify an expression, there will always be a trade between execution time and results. Simplify tries fewer transformations, enhancing execution time at the cost of not finding a transformation that may make the expression simpler. FullSimplify tries more transformations, significantly increasing the probability of finding a transformation that leads to a simpler expression at the cost of execution time.
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