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Results tagged with algorithms
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user 37555
Informally, an algorithm is a set of explicit instructions used to solve a problem (e.g. Euclid's algorithm for computing the greatest common divisor of two integers). For more specific questions on algorithms, this tag may be used in conjunction with the approximation-algorithms, algorithmic-randomness and algorithmic-topology tags.
6
votes
Equality of Euclidean numbers / constructible numbers
If $\alpha$ is constructible, you can construct a minimal polynomial of $\alpha$ recursively as follows: If $\alpha=\sqrt{\beta}$, and $\beta$ has minimal polynomial $P(x)$, then $P(x^2)$ is a polynom …
4
votes
0
answers
139
views
In what range can we find diophantine approximations using the LLL-algorithm?
Let $\alpha_1, \ldots, \alpha_n$ be $\mathbb{Q}$-linearly independent real numbers. I want to show that for all $x_1, \ldots, x_n\in\mathbb{Z}$, $|x_i|<N$ we have some lower bound for $\left|\sum x_i\ …
3
votes
Accepted
Parallel algorithm for modular multiplication of polynomials over Z/nZ
This problem is covered in great detail in Knuth's "The art of computer programming, volume II: Seminumerical algorithms". …