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Fabrice Mouhartem
2018-04-12 18:44:45 +02:00
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sec-lattices.tex
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@ -66,7 +66,7 @@ In order to define the $\SIVP$ problem and assumption, let us first define the s
\begin{definition}[Successive minima] \label{de:lattice-lambda}
For a lattice $\Lambda$ of dimension $n$, let us define for $i \in \{1,\ldots,n\}$ the $i$-th successive minimum as
\[ \lambda_i(\Lambda) = \inf \bigl\{ r \mid \dim \left( \Span\left(\lambda \cap \mathcal B\left(\mathbf 0, r \right) \right) \right) \geq i \bigr\}, \]
\[ \lambda_i(\Lambda) = \inf \bigl\{ r \mid \dim \left( \Span\left(\lambda \cap \mathcal B\left(\mathbf{0}, r \right) \right) \right) \geq i \bigr\}, \]
where $\mathcal B(\mathbf{c}, r)$ denotes the ball of radius $r$ centered in $\mathbf{c}$.
\end{definition}