A little bit more of mathematical notation.

* Introducing → with an r on the top to decribe randomly chosen variables from a set;
* Replacing the sqrt() function name with isqrt(), to better distinguish the
 different versions of square roots adopted;
* Some notation errors in Wiener, fixing them.

book/math_prequisites.tex

@@ -13,9 +13,13 @@ acceptation of discrete square root.
 The logarithmic $\log$ function is assumed to be in base two, i.e. $\log_2$.
 \\
 The $\idiv$ symbol is the integer division over $\naturalN$, i.e.
-$a \idiv b = \floor{\frac{a}{b}}$.
+$a \idiv b = \floor{\frac{a}{b}}$, as usual in the python language.
 \\
 $\naturalPrime \subset \naturalN$ is the set containing all prime intgers.
+\\
+The binary operator $\getsRandom$, always written as $x \getsRandom S$, has the
+meaning of ``taking a random element $x$ from the set $S$''
+% XXX.  following Dan Boneh notation
 
 \section{Algorithmic Complexity Notation}
 The notation used to describe asymptotic complexity follows the $O$-notation,

book/question_authority.tex

@@ -52,12 +52,14 @@
 \newcommand{\integerZ}{\mathbb{Z}}
 \newcommand{\bigO}[1]{\ensuremath{\operatorname{O}\left(#1\right)}}
 \newcommand{\openssl}{\textsc{OpenSSL}\ }
-\newcommand{\dsqrt}[1]{\ensuremath{sqrt(#1)}}
+%% here adopting Wikipedia's notation <https://en.wikipedia.org/wiki/Isqrt>
+\newcommand{\dsqrt}[1]{\ensuremath{isqrt(#1)}}
 \newcommand{\idiv}{\ensuremath{//}}
 \newcommand{\strong}[1]{\textbf{#1}}
 \newcommand{\eulerphi}[1]{\varphi(#1)}
 \newcommand{\abs}[1]{\left|#1\right|}
 \newcommand{\rfrac}[2]{{}^{#1}\!/_{#2}}
+\newcommand{\getsRandom}{\xleftarrow{r}}
 
 \makeindex
 \let\origdoublepage\cleardoublepage

book/wiener.tex

@@ -64,7 +64,7 @@ Then it is possible to recover $f$, having $f'$, if $\delta$ is small
 enough, where small enough means:
 \begin{align}
   \label{eq:wiener:cf_approx}
-  \delta = 1 - \frac{f'}{f} < \frac{1}{\rfrac{3}{2}{h_1}{d_1}}
+  \delta = 1 - \frac{f'}{f} < \frac{1}{\rfrac{3}{2}{h_1}{k_1}}
 \end{align}
 \\
 The ``continued fraction algorithm'' allowing us to recover $f$ is the
@@ -76,7 +76,7 @@ following:
   \item generate the next $a_i$ of the continued fraction expansion of $f'$;
   \item use ~\ref{eq:wiener:cf} to generate the next fraction $\rfrac{h_i}{k_i}$
     equal to $\angular{a_0, a_1, \ldots, a_{i-1}, a_i}$ %% non e` proprio cosi`
-  \item chech whether $\rfrac{h_i}{k_i}$ is equal to $f$
+  \item check whether $\rfrac{h_i}{k_i}$ is equal to $f$
 \end{enumerate}
 
 \section{The actual attack}