RE: Extracting Re and Im parts of a symbolic expression
- To: mathgroup at smc.vnet.net
- Subject: [mg42030] RE: [mg41983] Extracting Re and Im parts of a symbolic expression
- From: "David Park" <djmp at earthlink.net>
- Date: Tue, 17 Jun 2003 05:42:55 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Carlos, What's wrong with Re[x + I y] % // ComplexExpand -Im[y] + Re[x] x Still, the following usually doesn't do what you want. Abs[x + I y] % // ComplexExpand Abs[x + I*y] Abs[x + I*y] The solution is to set the TargetFunctions in ComplexExpand. Abs[x + I y] % // ComplexExpand[#, TargetFunctions -> {Re, Im}] & Abs[x + I*y] Sqrt[x^2 + y^2] I found it convenient to define the following function. ReImExpand[expr_] := ComplexExpand[expr, TargetFunctions -> {Re, Im}] ReImExpand[expr_, complexlist_] := ComplexExpand[expr, complexlist, TargetFunctions -> {Re, Im}] Then.. Abs[x + I y] % // ReImExpand Abs[x + I*y] Sqrt[x^2 + y^2] David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ From: Carlos Felippa [mailto:carlos at colorado.edu] To: mathgroup at smc.vnet.net 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?