Re: complex functions handling in M8
- To: mathgroup at smc.vnet.net
- Subject: [mg121401] Re: complex functions handling in M8
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Wed, 14 Sep 2011 05:12:41 -0400 (EDT)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- Reply-to: hanlonr at cox.net
T0 = 11/10;
alph = 1;
bet = 1;
gam = 1/2;
gam0 = 1/2;
Ie = 5;
Y0 = 0;
Ga[x_, y_, z_] :=
gam*Ie/((1 + x)^2) - x*z/((1 + x)^2 + I*T0*y*(1 + x));
Gb[x_, y_, z_] := Sqrt[Ga[x, y, z]^2 - bet^2*y^4 + 2*Ie*gam0*bet*y^2];
FM[x_, y_, z_] := -alph*y^2 + Ga[x, y, z] - Gb[x, y, z];
FP[x_, y_, z_] := -alph*y^2 + Ga[x, y, z] + Gb[x, y, z];
Frm[x_, y_, z_] := Re[FM[x, y, z]];
Fim[x_, y_, z_] := Im[FM[x, y, z]];
Frp[x_, y_, z_] := Re[FP[x, y, z]];
Fip[x_, y_, z_] := Im[FP[x, y, z]];
Frm[x, Y0, 3] // FullSimplify[#, Element[x, Reals]] &
Piecewise[{{(5 - 6*x)/(1 + x)^2, 6*x > 5}}, 0]
Fim[x, Y0, 3] // FullSimplify[#, {Element[x, Reals], x != -1}] &
0
Limit[Fim[x, Y0, 3], x -> -1]
0
Frp[x, Y0, 3] // FullSimplify[#, Element[x, Reals]] &
Piecewise[{{(5 - 6*x)*Re[1/(1 + x)^2], 6*x <= 5}}, 0]
Fip[x, Y0, 3] // FullSimplify[#, {Element[x, Reals], x != -1}] &
0
Limit[Fip[x, Y0, 3], x -> -1]
0
Bob Hanlon
---- Dikande <amdikande at googlemail.com> wrote:
=============
I wish to generate curves from a 3-variable complex function under
Mathematica 8. The results (shape of the curves) I get do not reflect
expectations. I am a rather old mathematica user and used this program
to solve quite complicated complex problems, including root
extractions from functions involving special several complex arguments
functions and never experienced such a failure from Mathematica. In
fact I have always used old versions M7 of latest), and only today I
decided to try M8 and came across this problem. The might be a problem
with handling of complex functions under M8 oder??? This is the code
having a problem:
T0 = 1.1;
alph = 1.0;
bet = 1.0;
gam = 0.5;
gam0 = 0.5;
Ie = 5.0;
Y0 = 0.0;
Ga[x_, y_, z_] :=
gam*Ie/((1.0 + x)^2) - x*z/((1.0 + x)^2 + I*T0*y*(1.0 + x));
Gb[x_, y_, z_] :=
Sqrt[Ga[x, y, z]^2 - bet^2*y^4 + 2.0*Ie*gam0*bet*y^2];
FM[x_, y_, z_] := -alph*y^2 + Ga[x, y, z] - Gb[x, y, z];
FP[x_, y_, z_] := -alph*y^2 + Ga[x, y, z] + Gb[x, y, z];
Frm[x_, y_, z_] := Re[FM[x, y, z]];
Fim[x_, y_, z_] := Im[FM[x, y, z]];
Frp[x_, y_, z_] := Re[FP[x, y, z]];
Fip[x_, y_, z_] := Im[FP[x, y, z]];
Plot[Frm[x, Y0, 3.0], {x, 0.0, 10}]
Plot[Frp[x, Y0, 3.0], {x, 0.0, 10}]
Normally Frm[x, Y0, 3] is always zero but M8 displays nonzero data but
not M7!