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How accurate is the solution for high degree algebraic equation?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg128484] How accurate is the solution for high degree algebraic equation?
  • From: Alexandra <watanabe.junzo at gmail.com>
  • Date: Wed, 24 Oct 2012 03:32:27 -0400 (EDT)
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I wanted to know all the solutions of f = (-z - 1)^d - (-z^d - 1)==0, where  d=54.
I did the following:

d = 54; f = (-z - 1)^d - (-z^d - 1);
sol = NSolve[f == 0,z]; 
a = z /. sol;

So    a    is a set of solutions. 

If I  compute  
f /. z -> a[[50]] // N
It returns a number very close to zero.  This is natural.  

But if I compute  
f /. (z -> a[[1]]) // N

Then 
Mathematica returns  
12.0047 + 14.7528 I

I cannot say a[[1]] is a solution of f=0. 

Many other elements in the solution set    a    does not seem to satisfy the equation. 
Only the last few terms in   a   are satisfactory enough as solutions.  

Is the degree too high? 


  






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