MaplePrimes - answers and comments on Question, Solving for Complex Roots

Suggestions

Thomas Richard — Fri, 01 Jul 2011 20:26:09 Z

Exact solutions can be obtained via solve, but you have to get rid of the abs expressions first. That can be achieved by evalc. Also, I suggest using exact input wherever possible. See my worksheet for these changes.

complex-roots-evalc-.mw

T vs. ecT

Nate — Fri, 01 Jul 2011 23:28:15 Z

I think there is a subtle problem with how the problem is posed. I don't see what it is, but it will probably be obvious when the solution surfaces :-)

I tried substituting s:= r*exp(I*theta) and the solutions still don't satisfy T. I'm not sure what to do now....

useassumptions

Nate — Fri, 01 Jul 2011 23:38:06 Z

I tried using

solve(ecT,[x], UseAssumptions) assuming x::imaginary;

at the end of the complex-roots-T.mw file. All that was returned was [].

Citing Maple Help

Markiyan Hirnyk — Sat, 02 Jul 2011 01:16:29 Z

"If the solve command does not find any solutions, then if the second argument is a name, then the empty sequence (NULL) is returned and if the second argument is a list, then empty list is returned. This means that there are no solutions, or the solve command cannot find the solutions. In the latter case, a warning is issued and the global variable _SolutionsMayBeLost is set to true"

evalc

Robert Israel — Sat, 02 Jul 2011 02:44:34 Z

Yes, evalc assumes all variables are real. If you want s to be complex, substitute x+I*y for it.

Two solutions by DirectSearch package

mois — Mon, 04 Jul 2011 16:18:51 Z

The DirectSearch package finds two solutions:

with(DirectSearch):

T1:=abs(subs(s=x+I*y,T));

sol:=GlobalSearch(T1, tolerances=10^(-14), distance=10^(-6));

sol:=SolveEquations(T1, AllSolutions, distance=10^(-6));

It seems there are only two solutions, see plot:

plot3d(T1,x=0.185..0.195,y=-0.005..0.005);