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

narodnik преди 4 години
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променени са 1 файла, в които са добавени 10 реда и са изтрити 0 реда
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      doc/vanishing-poly.md

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doc/vanishing-poly.md

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+We have a vanishing polynomial $Z(X) = X^N - 1$. Implicitly we are proving that
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+$$X^N = 1$$
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+What are the solutions to this polynomial? Well the answer is $\omega$ which is any root of $1$.
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+Therefore the solution to the formula $X^N - 1$ will be all the values of $X^N = 1$ or
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+$$X^N - 1 = (\omega - 1)(\omega^2 - 1)\cdots(\omega^{N - 1} - 1)$$
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