Extracting Re and Im parts of a symbolic expression
- To: mathgroup at smc.vnet.net
- Subject: [mg41983] Extracting Re and Im parts of a symbolic expression
- From: carlos at colorado.edu (Carlos Felippa)
- Date: Mon, 16 Jun 2003 03:56:31 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Apologies if this topic has been posted before (I did only a
perfunctory back search of this NG).
Is there a simple way to extract the real and imaginary part of
a complex expression, assuming *all* variables are real? For
definiteness assume x,y are reals and z = x+I*y. Then
Re[z] gives -Im[y] + Re[x] Im[z] gives Im[x] + Re[y]
because is no way to tell Re and Im that x,y are real. (The lack of a
variable-type global database clearly hurts here.) Here are 5 ideas.
(1) Re[ComplexExpand[z]] Im[ComplexExpand[z]] do not work since
the "reality" effect of ComplexExpand does not propagate.
(2) (z+Conjugate(z))/2 (z-Conjugate(z))/2 fails as expected
(3) Coefficient[z,I] complains: I is not a variable, so lets make it one ...
(4) Coefficient[ComplexExpand[z]/.I->iunit,iunit] for imaginary part
z-I*Coefficient[ComplexExpand[z]/.I->iunit,iunit] for real part
This works in the cases I tried but looks contrived.
(5) Print ComplexExpand[z] in InputForm, do cut and paste. Works
but is time consuming (human in the loop) and error prone.
In my program x and y were actually fairly complicate
functions (one screenful each)
Clearly missing is a ComplexExpandReIm (say) function which
assumes all variables in z are real, so that I can write
{x,y}=ComplexExpandReIm[z]
Of course one can define
ComplexExpandReIm[z_]:= Module[{iunit},
{z-I*Coefficient[ComplexExpand[z]/.I->iunit,iunit],
Coefficient[ComplexExpand[z]/.I->iunit,iunit]}];
to hide the ugliness of scheme (4). Any suggestions on a cleaner
method?
- Follow-Ups:
- Re: Extracting Re and Im parts of a symbolic expression
- From: Daniel Lichtblau <danl@wolfram.com>
- Re: Extracting Re and Im parts of a symbolic expression