       How accurate is the solution for high degree algebraic equation?

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• 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[] // N
It returns a number very close to zero.  This is natural.

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

Then
Mathematica returns
12.0047 + 14.7528 I

I cannot say a[] 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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