add description for what how the vanishing polynomial is calculated as X^N - 1

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narodnik
2021-09-11 09:20:34 +02:00
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doc/vanishing-poly.md Normal file
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We have a vanishing polynomial $Z(X) = X^N - 1$. Implicitly we are proving that
$$X^N = 1$$
What are the solutions to this polynomial? Well the answer is $\omega$ which is any root of $1$.
Therefore the solution to the formula $X^N - 1$ will be all the values of $X^N = 1$ or
$$X^N - 1 = (\omega - 1)(\omega^2 - 1)\cdots(\omega^{N - 1} - 1)$$