Re: complex functions handling in M8

*To*: mathgroup at smc.vnet.net*Subject*: [mg121418] Re: complex functions handling in M8*From*: Daniel Lichtblau <danl at wolfram.com>*Date*: Wed, 14 Sep 2011 05:15:45 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201109131120.HAA05095@smc.vnet.net>

On 09/13/2011 06:20 AM, Dikande 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! Here is what I get for selected values in both version 7 and 8. In[70]:= Table[Frm[x, Y0, 3.0], {x, 0.0, 10., .5}] Out[70]= {0., 0., -0.25, -0.64, -0.777778, -0.816327, -0.8125, \ -0.790123, -0.76, -0.727273, -0.694444, -0.662722, -0.632653, \ -0.604444, -0.578125, -0.553633, -0.530864, -0.509695, -0.49, \ -0.471655, -0.454545} Here is the actual function. In[73]:= Chop[Frm[x, Y0, 3.0]] Out[73]= Re[2.5/(1. + x)^2 - (3.*x)/(1. + x)^2 - Sqrt[(2.5/(1. + x)^2 - (3.*x)/(1. + x)^2)^2]] I would expect the result to be nonzero when 3.*x > 2.5, as this is where the first two terms sum to a negative value, and the last term subtracts off the positive square root of the square of that negative. Daniel Lichtblau Wolfram Research

**References**:**complex functions handling in M8***From:*Dikande <amdikande@googlemail.com>