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Re: Solve / NSolve take too much time or fail

• To: mathgroup at smc.vnet.net
• Subject: [mg60874] Re: Solve / NSolve take too much time or fail
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Sat, 1 Oct 2005 02:55:49 -0400 (EDT)
• Organization: The Open University, Milton Keynes, U.K.
• References: <dhirn9$ltd$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

grimey wrote:
> Hello,
> I'm working with Mathematica (version 5.0) for perhaps 3 month.
> And now I have a problem, I try to solve an equation like this:
> 
> cf=(a1*x (a2 + a3*x + a^2))/(b1 + b2*x - b3*x^2 + b4*x^3);
> 
> w=(1-c1*Sqrt[1-(1-c1^2)*x/c2])^2 / (1-c1)^2;
> 
> This is the main equation:
> 
> Solve[Numerator[cf]-I d1 w Denominator[cf]==0,x]
> 
> And even after hours of working I don't get any solution, whether I
> take Solve or NSolve. And I gave a lot of virtual memory free for
> Mathematica to work with.
> 
> Are there any tricks to help solving difficult polynomial equations
> faster (or at all)? I want to get, of course, a set of Root-functions
> for x (complex), depending on a1, a2, a3, b1, b2, b3, b4, c1, c2, d1,
> so I have no numerical number to start with for the FindRoot-function.
> Can anyone help me? Some other equations, not always that different
> from this one, could be solved more easily...
> 
> Thank you very much!
> 
> Thomas Geyer
> (tfgeyer at yahoo.com)
> 
Hi Thomas,

I tried your equation with Mathematica 5.2 for Windows (Pentium IV 2.6 
GHz, 512 Mo), first with Solve then with Reduce, but I eventually abort 
both commands after more than two hour of processing (elapsed time).

However, I got the answer using another CAS (I sent a private email with 
a MS Word document containing the solution).

Best regards,
/J.M.