Leann Kopp's scientific contributions

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Publications (2)

Randomized Polynomial-Time Root Counting in Prime Power Rings
Preprint
  • Aug 2018
Suppose $k,p\!\in\!\mathbb{N}$ with $p$ prime and $f\!\in\!\mathbb{Z}[x]$ is a univariate polynomial with degree $d$ and all coefficients having absolute value less than $p^k$. We give a Las Vegas randomized algorithm that computes the number of roots of $f$ in $\mathbb{Z}/\!\left(p^k\right)$ within time $d^3(k\log p)^{2+o(1)}$. (We in fact prove a...

Citations

... Breiding [4] made an attempt to generalize homotopy continuation methods, but the metric/topological properties of the p-adics made such an attempt fail. In contrast, subdivision methods are commonplace in the p-adic world [20,36,37] and also in the related world of prime power rings [12,31]. Nevertheless, none of these algorithms seems to use Strassman's theorem as the guiding rule of the subdivision, as Strassman does. ...
Reference: A $p$-adic Descartes solver: the Strassman solver