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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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