Module: ppl/ppl Branch: master Commit: cb165556dd22a919425ed9803156dfcb63896f62 URL: http://www.cs.unipr.it/git/gitweb.cgi?p=ppl/ppl.git;a=commit;h=cb165556dd22a...
Author: Roberto Bagnara bagnara@cs.unipr.it Date: Wed Mar 24 06:43:33 2010 +0400
The `|' character cannot be used to produce proper paired delimiters.
---
doc/definitions.dox | 17 +++++++++-------- doc/ppl.sty | 3 +++ 2 files changed, 12 insertions(+), 8 deletions(-)
diff --git a/doc/definitions.dox b/doc/definitions.dox index 1a2a048..6e9ec24 100644 --- a/doc/definitions.dox +++ b/doc/definitions.dox @@ -2211,11 +2211,12 @@ the frequency \f$f\f$ and a value \f$\mathrm{val} = \langle \vect{a}, \vect{w} \rangle + b\f$ where \f$\vect{w} \in \cL\f$ and \f[ - |\mathrm{val}| - = \min\Bigl{, - \big|\langle \vect{a}, \vect{v} \rangle + b - \big| \Bigm| \vect{v} \in \cL - ,\Bigr}. + \lvert\mathrm{val}\rvert + = \min\Bigl{, + \bigl\lvert\langle \vect{a}, \vect{v} \rangle + b \bigr\rvert + \Bigm| + \vect{v} \in \cL + ,\Bigr}. \f]
Observe that the above definition is also applied to other simple objects in @@ -4786,13 +4787,13 @@ For \f$x\f$, \f$y \in \Zset\f$ with \f$y \ne 0\f$, we have x \brem y = \begin{cases} - x \brem |y|, & \text{if $x \ge 0$;} \ - -(|x| \brem |y|), & \text{if $x < 0$.} + x \brem \abs{y}, & \text{if $x \ge 0$;} \ + -(\abs{x} \brem \abs{y}), & \text{if $x < 0$.} \end{cases} \f]
<B><EM>Proof</EM></B> -Throughout the proof we write \f$x_0 = |x|\f$ and \f$y_0 = |y|\f$. +Throughout the proof we write \f$x_0 = \abs{x}\f$ and \f$y_0 = \abs{y}\f$. First, assume that \f$x \ge 0\f$ and that \f$y < 0\f$. Let \f$k = \phi(x / y_0) = - \phi(x / y)\f$, by the property above. We have diff --git a/doc/ppl.sty b/doc/ppl.sty index 0678319..43fc889 100644 --- a/doc/ppl.sty +++ b/doc/ppl.sty @@ -136,6 +136,9 @@ \newcommand*{\relsym}{\mathrel{\bowtie}} \newcommand*{\relsyms}[1]{\mathrel{\bowtie_{#1}}}
+% Absolute value. +\newcommand*{\abs}[1]{\lvert #1 \rvert} + % Vectors. \renewcommand*{\vec}[1]{\mathchoice{\mbox{\boldmath$\displaystyle#1$}} {\mbox{\boldmath$\textstyle#1$}}