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MathGroup Archive 1995

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Re: Help with factoring out an exponential

  • To: mathgroup at smc.vnet.net
  • Subject: [mg2320] Re: Help with factoring out an exponential
  • From: danl (Daniel Lichtblau)
  • Date: Tue, 24 Oct 1995 02:13:46 -0400
  • Organization: Wolfram Research, Inc.

In article <DGvx73.AxH at wri.com> Rob Carscadden  
<carscadd at pps.pubpol.duke.edu> writes:
> I'm am trying to solve and equation but I can't factor out an 
> exponential.
> 
> I have an equation which will be given below, which has two  
exponentials:
> after taking the dervivatives I want to factor these out (throw them  
away 
> really) so that mathematica has an algebraic equation to work with and I 
> can find the critical points. Clearly these wil never be zero so I'm not 
> losing anything.
> Here's my code where c is 5^x
> 
> Print[eqn];              
> 		tempeqn = D[eqn,x];
> 		test = Simplify[tempeqn/(Exp[-x^2/2])];
>                 eqn1 = Simplify[test/c];
> 		soln = Solve[eqn1 == 0,x]//N;
> Print[eqn1];  
> 
> and here's my results:
> 
>                                                   2
>  x        0.75                  0.09375 (1.5 + x)
> 5  (----------------       - ------------------)
>       2                               2
>      x /2                           x /2
>     E     Sqrt[2 Pi]              E     Sqrt[2 Pi]
> 
> 
> 
>                     
>                 x           x            x      2             x      3
> (0.09375 (-3.  5  - 7.75  5   x + 3.   5      x    +   1.   5      x 
> 
>            x
>  + 5.75   5  Log[5] - 
>  
>          x                   x      2                  x
>   3.   5  x Log[5] - 1.    5      x  Log[5]))   /   (5  Sqrt[2 Pi])
> 
> 
> As you can see every term in the numerator has an 5^x but it won't  
cancel 
> with the denominator. Why?
> 
> I'm goin gback to mathematica and try a change of base formula and see  
if 
> this helps. 
> 
> Thanks for your help
> 

  Two things I would recommend.
(1) Print this using InputForm so others can cut-and-paste to try it out.
(2) Make everything exact. The presence of inexact numbers will reliably  
cause Cancel et al to fail. There is a note to this effect in the  
reference manual, section 3.3.4, bottom p. 597. It applies to the  
functions described in the preceding section as well. This is of course a  
defect in the documentation.

  Daniel Lichtblau
  Wolfram Research
  danl at wri.com



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