Re: Abs and derivative problems

*To*: mathgroup at smc.vnet.net*Subject*: [mg14642] Re: Abs and derivative problems*From*: "sylvan" <scd at gopher.chem.wayne.edu>*Date*: Wed, 4 Nov 1998 13:47:11 -0500*Organization*: Wayne State University*References*: <01be0775$8442f020$6a1ad98d@nanolab>*Sender*: owner-wri-mathgroup at wolfram.com

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}] >