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From: Peter Pein <pet...@dordos.net>
Newsgroups: comp.soft-sys.math.maple
Subject: Re: Maple does not simplify if variables have "assume"s on them
Date: Fri, 10 Aug 2012 23:26:22 +0200
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Am 10.08.2012 22:28, schrieb unruh:
> On 2012-08-10, Axel Vogt <&nore...@axelvogt.de> wrote:
>> On 10.08.2012 20:53, unruh wrote:
>>> I am having trouble with Maple not simplifying expressions with
>>> "assumes" on them.
>>>
>>> For example, the answer to one of my integrations was
>>> N12:=1/4 I (-epsilon~^2 -4IOmega~ +epsilon~^2)
>>>
>>> where the ~ are the expressions with "assume"
>>> (assume(epsilon>0);assume(Omega>0))
>>> The correct answer should be just Omega~, but there is no way I can get
>>> that answer no matter how many "simplify" or "expand" I put around the
>>> original expression of N12.
>>> Ie, maple seems to think that one of those epsilon~ is a different
>>> variable from the other one.
>>>
>>> If I copy that output to another input line, then maple simplifies the
>>> expression.
>>
>> It would help if you provide your full code (as far as needed),
>> otherwise it is hard to understand.
>>
>> PS: you may wish to provide it with all operational signs
>> (like multiplication etc), for copy & paste.
>>
>> It seems a bit that this may be the reason, since Maple
>> would simplify it to what you expect.
>
> OK. Here it is.
>
>   > Gamma:=epsilon^2/2:assume(epsilon>0); assume(Omega>0); assume(t,real):
>   > phi1:=proc(t,x); -epsilon/2*exp((I*Omega+Gamma)*(t-x)); end proc:
>   > phi2:=proc(t,x); epsilon/2*exp((I*Omega-Gamma)*(t+x)); end proc:
>   > pi1:=proc(t,x); diff (phi1(t,x),t);end proc:
>   > pi2:=proc(t,x); diff (phi2(t,x),t);end proc:
>   > q1:=proc(t); exp((I*Omega+Gamma)*t);end proc:q2:=proc(t);
>   > exp((I*Omega-Gamma)*t);end proc:
>   > p1:=proc(t); -diff(q1(t),t);end proc:
>   > p2:=proc(t);-diff(q2(t),t);end proc:
>   > N12:=simplify(I/2*
>      ( 2*int(conjugate(phi1(t,x))*pi2(t,x)-conjugate(pi1(t,x))*phi2(t,x),x=0..infinity)
>      +conjugate(q1(t))*p2(t)-conjugate(p1(t))*q2(t)
>      +epsilon*(conjugate(phi1(t,0))*q2(t)-conjugate(q1(t))*phi2(t,0))  ));
>
>                                   2                        2
>            N12 := 1/4 I (-epsilon~  - 4 I Omega~ + epsilon~ )
>

Hi,

  as it is almost midnight here, I do not have the patience to try it 
myself - sorry.

I would guess that it makes sense to put all assumptions to the very 
beginning of your code and to define Gamma later.

.. just a shot in the dark.

Good luck, Peter