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Re: Abs and variables
Posted:
Jun 28, 1996 9:54 AM


> > How can I have the Abs function treat real variables properly? >I seem to recall a way of declaring a variable real, but I don't >remember how. If there is such a way, would this work with Abs; i.e. >fix the variable a so that "Abs[a]" will give a result of "a"? > >Thanks. > >/ >:@) Scott >\
Hi, Scott I think you can obtain what want by using ComplexExpand with the Option TargetFunctions>{Re, Im}. The optional second argument of ComplexExpand specifies parameters to be Complex (the rest is assumed to be real).
Below are two examples that I hope may be of some help. (I think the manual is too brief on ComplexExpand)
Espen
IN: z = 1 / (1/r1 + I w c) + r2
1 OUT: r2 +  1  + I c w r1
IN: ComplexExpand[Abs[z], TargetFunctions>{Re, Im} ] //Simplify
2 2 2 2 2 2 r1 + 2 r1 r2 + r2 + c r1 r2 w OUT: Sqrt[] 2 2 2 1 + c r1 w
IN: z = 1 / (1/r1 + I w c) + z2
1 OUT:  + z2 1  + I c w r1
IN: ComplexExpand[Abs[z], {z2}, TargetFunctions>{Re, Im} ] //Simplify
c w 2 OUT: Sqrt[(() + Im[z2]) + 2 2 2 r1 + c w 1 2 ( + Re[z2]) ] 1 2 2  + c r1 w r1



