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Re: Complexes, Reals, FullSimplify

• To: mathgroup at smc.vnet.net
• Subject: [mg48815] Re: [mg48782] Complexes, Reals, FullSimplify
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Thu, 17 Jun 2004 04:07:32 -0400 (EDT)
• References: <200406160854.EAA12221@smc.vnet.net> <3FF51E64-BF8F-11D8-890A-000A95B4967A@mimuw.edu.pl>
• Sender: owner-wri-mathgroup at wolfram.com

Of course I meant:


ComplexExpand[Re[(1 - 6*I)*Cos[x] - (1 + 2*I)*Sin[0.5*x]]]


Cos[x] - Sin[0.5*x]

(that Element[x,Reals] was there only because I forgot to delete it 
form your original code.)

Andrzej


On 16 Jun 2004, at 21:18, Andrzej Kozlowski wrote:

>
> On 16 Jun 2004, at 17:54, Stergios J. Papadakis wrote:
>
>> Dear group,
>> I am trying to use expressions of the below form as boundary 
>> conditions
>> in NDSolve.  I keep getting "non-numerical" errors.  I have tried a 
>> lot
>> of things and reduced the problem to this:
>>
>> These give different outputs:
>>
>> FullSimplify[Re[(1 - 6* I)* Cos[x] - (1 + 2*I)*Sin[(1/2)* 
>> x]],Element[x,
>> Reals]]
>>
>> FullSimplify[Re[(1 - 6* I)* Cos[x] - (1 + 2*I)*Sin[0.5*x]],Element[x,
>> Reals]]
>>
>> I get:
>>
>> \!\(Cos[x] - Sin[x\/2]\)
>>
>> Re[(1 - 6 \[ImaginaryI]) Cos[x] - (1 + 2 \[ImaginaryI]) Sin[0.5 x]]
>>
>>
>> I think I can get my NDSolve to work if I can make the second
>> FullSimplify above give me an output without an Re in it.  Mathematica
>> assumes that 0.5 may have some tiny imaginary part and therefore keeps
>> everything for full generality.  How do I eliminate
>> this?  Note that I have simplified things a lot here, the actual
>> expression that I will be using has many terms that all have the
>> form above, with many significant digits, which depend on earlier
>> calculations.  I have tried using Chop,
>>
>> FullSimplify[Chop[Re[(1 -
>>    6* I)* Cos[x] - (1 + 2*I)*Sin[0.5* x]]], Element[x, Reals]]
>>
>> And that does not work, I get the same result.
>>
>>
>>
>>
>>
>>
>> Thanks,
>> Stergios
>>
>>
>
> The simplest way is to use ComplexExpand; you do not even need 
> FullSimplify:
>
> ComplexExpand[Re[(1 - 6* I)* Cos[x] - (1 + 2*I)*Sin[0.5*x]], Element[x,
> Reals]]
>
> Cos[x] - Sin[0.5*x]
>
>
> Andrzej Kozlowski
> Chiba, Japan
> http://www.mimuw.edu.pl/~akoz/
>

• References:
  • Complexes, Reals, FullSimplify
    • From: "Stergios J. Papadakis" <stergios.papadakis@jhuapl.edu>