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Reduction mod p of a polynomial

Hi everyone,

I have a question about the factorization of a polynomial modulo a prime ideal that I would like to help with.

Specifically, let $K$ be a number field (for my problem, we can assume that $K=\mathbb{Q}[i]$ or $K=\mathbb{Q}[\omega]$). I have a polynomial $f$ in $O_K[x]$ and a prime ideal $\mathfrak{p}$ in $O_K$ and I want to compute the factorization of $f$ over $O_K/\mathfrak{p}$.

When $K=\mathbb{Q}$, I use the following built-in function.


I wonder whether we can do the same for a general number field.

Thank you for your help.