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
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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