Does Yun's algorithm work with polynomials which have integer coefficients and are not necessary monic?

Wikipedia says "polynomials over a field of characteristic 0" but this is what confuses me. I would say yes because I could add many ones and never reach zero but I thought integers form (are?) a ring, not a field.

Put differently, are those divisions in Yun's algorithm always realizable with plain integers? Are those division always "exact"?

  • $\begingroup$ Why do you think they would be? $\endgroup$ – Arnaud Mortier Jul 2 '18 at 14:41
  • $\begingroup$ @ArnaudMortier I think it all depends whether those polynomials form a field of characteristic 0. But I never had abstract algebra so I seems to me that they should but I'm not sure. Maybe in order for a polynomial with integer coefficients to be a field it has to me monic, I don't know..? $\endgroup$ – minmax Jul 3 '18 at 6:55

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