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Differentiation problem/bug?

• To: mathgroup at smc.vnet.net
• Subject: [mg69734] Differentiation problem/bug?
• From: Arturas Acus <acus at itpa.lt>
• Date: Fri, 22 Sep 2006 01:04:00 -0400 (EDT)

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

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,

-- 
Arturas Acus <acus at itpa.lt>

• Follow-Ups:
  • Re: Differentiation problem/bug?
    • From: "Carl K. Woll" <carlw@wolfram.com>