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MathGroup Archive 2006

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Re: Differentiation problem/bug?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg69820] Re: [mg69734] Differentiation problem/bug?
  • From: "Carl K. Woll" <carlw at wolfram.com>
  • Date: Sat, 23 Sep 2006 23:45:24 -0400 (EDT)
  • References: <200609220504.BAA16344@smc.vnet.net>

Arturas Acus wrote:
> Dear group,
> 
> the only way I can explain the rezults of simple differentiation command
> D[] bellow is the dissapointing bug, which was absent in 5.0, but exist
> in:
> $Version
> 5.2 for Linux (June 20, 2005)
> 
> In[1]: inp = 1/4 + 3/(8*E^((2*I)*F)) + (3*E^((2*I)*F))/8 - 
>     E^((-2*I)*F - I*\[Theta])/4 + E^((2*I)*F - I*\[Theta])/4 - 
>     E^((-2*I)*F + I*\[Theta])/4 + E^((2*I)*F + I*\[Theta])/4 + 
>     E^((-2*I)*F - (2*I)*\[Theta])/16 + E^((2*I)*F - (2*I)*\[Theta])/16+ 
>     E^((-2*I)*F + (2*I)*\[Theta])/16 + E^((2*I)*F + (2*I)*\[Theta])/16- 
>     1/(8*E^((2*I)*\[Theta])) - E^((2*I)*\[Theta])/8
> 
> In[2]: D[inp, r, NonConstants -> {F}]
> Out[2]: 0
> 

The bad news is that this unfortunately is a bug in version 5.2. The 
good news is that it has been corrected in the development version.

Carl Woll
Wolfram Research

> how it was found:
> 
> In[3]: D[#, r, NonConstants -> {F}] & /@ Expand[inp]
> Out[3]: (((-3*I)/4)*D[F, r, NonConstants -> {F}])/E^((2*I)*F) +
> ((3*I)/4)*E^((2*I)*F)*D[F, r, NonConstants -> {F}]
> 
> check:
> 
> In[4]: D[Evaluate[inp /. {F -> F[r]}], r] // FullSimplify
> Out[4]: ((-I/8)*((-1 + E^(I*\[Theta]))^4 - E^((4*I)*F[r])*(1 + E^(I*
> \[Theta]))^4)*Derivative[1][F][r])/E^((2*I)*(\[Theta] + F[r]))
> 
> 
> I believe I can trust the Out[4] rezult. Most dissapointing is that now
> I cannot trust my previous calculations, because somwhere I changed from
> version 5.0 to 5.2, and 5.0 gives correct rezult. Please check this
> behaviour for other versions/OS and be carefull using NonConstants
> option.
> 
> Sincerely,
> 


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