       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: 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: D[inp, r, NonConstants -> {F}]
> Out: 0
>
> how it was found:
>
> In: D[#, r, NonConstants -> {F}] & /@ Expand[inp]
> Out: (((-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: D[Evaluate[inp /. {F -> F[r]}], r] // FullSimplify
> Out: ((-I/8)*((-1 + E^(I*\[Theta]))^4 - E^((4*I)*F[r])*(1 + E^(I*
> \[Theta]))^4)*Derivative[F][r])/E^((2*I)*(\[Theta] + F[r]))
>
>
> I believe I can trust the Out 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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