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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!





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