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Computing coefficients of polynomials from roots in $O(n\log{n})$ time

Suppose I have a univariate polynomial $p$ over a prime-order finite field $\mathbb{F}_q$ whose roots I know. Suppose that the roots of $p$ are always an $n$-sized subset of $R=\{1,2,\dots,N\}, N < q …
Alin Tomescu's user avatar