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Re: A way around the limitations of Re[] and Im[]

• To: mathgroup at smc.vnet.net
• Subject: [mg51118] Re: A way around the limitations of Re[] and Im[]
• From: carlos at colorado.edu (Carlos Felippa)
• Date: Tue, 5 Oct 2004 04:37:04 -0400 (EDT)
• References: <cjr8lg$opp$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

carlos at colorado.edu (Carlos Felippa) wrote in message news:<cjr8lg$opp$1 at smc.vnet.net>...
> As you know, Re[expr] and Im[expr] are left unevaluated when expr is
> not numeric.  I had good luck in simple cases with the following
> substitution trick:
>   
>         Real[c_]:=c/.I->0;     Imag[c_]:=(c-Real[c])/.I->1;
> 
> Do you see any problem with these definitions?

Not yet there. Found limitations because n*I is internally stored as
Complex[0,n].  This  version has done better:

RealPart[c_]:=ComplexExpand[c]/.{Complex[0,_]->0};

Examples:

Print[     RealPart[(a+I*b)^2]    //InputForm];
Print[     RealPart[(a+I*b)^n]    //InputForm];
Print[     RealPart[Exp[I*x]/I]   //InputForm];
Print[     RealPart[Cosh[x+y*I]]  //InputForm];

Results:

a^2 - b^2
Abs[a]^n*Cos[n*Arg[a]]
Sin[x]
Cos[y]*Cosh[x]

• Follow-Ups:
  • Re: Re: A way around the limitations of Re[] and Im[]
    • From: Murray Eisenberg <murray@math.umass.edu>