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Re: Abs and derivative problems


update on my problem:

Abs does not work on non-numerical stuff. I found a package called
AbsArg in MathSource  that does symbolic. Problem: the required
NonNegativeQ package is missing. I trying to modify the earlier, but if
anybody has a shortcut...

> I could not calculate the modulus of  a complex expression containing
> imaginary parts in both denominator and numerator with Mathematica. An
> Example: 
> 
> (a + I b) / (c + I d)  
> 
> a,b,c,d (real) symbolic variables. 
> 
> In pratice, this should be absolutely trivial. ComplexExpand is not
> effective.
> How do you "tell" mathematica that your variables are real ?? 
> I included an example below (cell format, you can cut and paste).
> 
> Also,  replacement rules like  //. z[t_] -> t^2 do not work well on
> expressions like  z'[t] + b z[t]. the result  is  z'[t] + b t^2... I
could
> not force it to Evaluate z'[t] or D[z[t], t]. 
> 
> Could you help ?? I am sure there is a non-intuitive solution to that. 
> 
> Cell[OutputFormData["\<\
> Abs[(b0*\\[CapitalDelta]z*
>      (Es - I*\\[Eta]*\\[Omega]))/
>    (-I*m*\\[Gamma]*\\[Omega] + 
>      m*\\[Omega] + 
>      b0*(Es - I*\\[Eta]*\\[Omega]) - 
>      m*\\[Omega]^2)]\
> \>", "\<\
> Abs[(b0 \[CapitalDelta]z (Es - I \[Eta] \[Omega])) / 
>                    2
>     (-I m \[Gamma] \[Omega] + m \[Omega]  + b0 (Es - I \[Eta] \[Omega]) -

>           2
>       m \[Omega]0 )]\
> \>"], "Output",
>   CellLabel->"Out[110]//TextForm=",
>   LineSpacing->{1, 0}]
> 


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