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- W2896810030 abstract "Given an order, a fundamental problem is deciding whether a univariate polynomial has a zero. It is a special case of deciding whether $text{Hom}(A,B)$ is non-empty for two orders $A$ and $B$. For fixed separable orders, deciding whether a polynomial has a zero is in $P$. If we instead fix a separable polynomial, the problem is NP-complete with probability $1$. We provide several theorems about NP-completeness, culminating into a complete classification of the problem for quadratic and cubic polynomials. A main ingredient is a new type of algebraic NP-complete group-theoretic problems, as seen in [Spe21]." @default.
- W2896810030 created "2018-10-26" @default.
- W2896810030 creator A5080441137 @default.
- W2896810030 date "2018-01-01" @default.
- W2896810030 modified "2023-09-23" @default.
- W2896810030 title "The Complexity of Root-Finding in Orders" @default.
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