Ultrametric Root Counting
نویسندگان
چکیده
If K is a complete non-archimedean field with a discrete valuation and f ∈ K[X ] is a polynomial with non-vanishing discriminant. The first main result of this paper is about connecting the number of roots of f to the number of roots of its reduction modulo a power of the maximal ideal of the valuation ring of K. If the polynomial f is regular, we give an algorithmic method to compute the exact number of roots of f in K and show that the number of roots of f equals the sum of the numbers of roots of its lower binomials.
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