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MathGroup Archive 2006

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Re: Differentiation problem/bug?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg69783] Re: Differentiation problem/bug?
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Sat, 23 Sep 2006 04:44:06 -0400 (EDT)
  • Organization: The University of Western Australia
  • References: <eevrea$gfd$1@smc.vnet.net>

In article <eevrea$gfd$1 at smc.vnet.net>, Arturas Acus <acus at itpa.lt> 
wrote:

> 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
> 
> 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.

I never use NonConstants. Also, it is a good idea to avoid using 
variables involving capital letters. For calculations where there is 
implicit dependence with respect to a variable I use Dt instead. 

 inp = 1/4 + 3/8/E^(2 I f) + (3/8) E^(2 I f) - (1/4) E^(-2 I f - I t) + 
 (1/4) E^(2 I f - I t) - (1/4) E^(I t - 2 I f) + (1/4) E^(2 I f + I t) +
 (1/16) E^(-2 I f - 2 I t) + (1/16) E^(2 I f - 2 I t) + 
 (1/16) E^(2 I t - 2 I f) + (1/16) E^(2 I f + 2 I t) - 
 1/8/E^(2 I t) - (1/8) E^(2 I t)

 Dt[t, r] ^= 0;

 Dt[inp, r] // FullSimplify

Cheers,
Paul

_______________________________________________________________________
Paul Abbott                                      Phone:  61 8 6488 2734
School of Physics, M013                            Fax: +61 8 6488 1014
The University of Western Australia         (CRICOS Provider No 00126G)    
AUSTRALIA                               http://physics.uwa.edu.au/~paul


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