--- /dev/null
+#LyX 1.5.4svn created this file. For more info see http://www.lyx.org/
+\lyxformat 276
+\begin_document
+\begin_header
+\textclass scrartcl
+\begin_preamble
+% DO NOT ALTER THIS PREAMBLE!!!
+%
+% This preamble is designed to ensure that the file prints
+% out as advertised. If you mess with this preamble,
+% parts of this document may not print out as expected. If you
+% have problems LaTeXing this file, please contact
+% the documentation team
+% email: lyx-docs@lists.lyx.org
+
+
+% if pdflatex is used
+\usepackage{ifpdf}
+\ifpdf
+
+% set fonts for nicer pdf view
+\IfFileExists{lmodern.sty}
+ {\usepackage{lmodern}}{}
+
+% link all cross references and URLs
+% in pdf output
+ \usepackage[colorlinks=true, bookmarks, bookmarksnumbered,
+ bookmarksopen, bookmarksopenlevel=1,
+ linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue,
+ pdfpagelayout=OneColumn, pdfnewwindow=true,
+ pdfstartview=XYZ, plainpages=false, pdfpagelabels,
+ pdfauthor={L'équipe LyX}, pdftex,
+ pdftitle={Manuel mathématique de LyXl},
+ pdfsubject={Documentation sur les mathématiques avec LyX},
+ pdfkeywords={LyX, Mathed}]{hyperref}
+
+\else % if dvi or ps is produced
+
+ % link all cross references and URLs in DVI output
+ \usepackage[ps2pdf, colorlinks=true,
+ linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue]{hyperref}
+
+\fi % end if pdflatex is used
+
+% Folgendes Problem lösen:
+% Besteht die Kapitelnummer aus zu vielen Ziffern, wird die
+% Kapitelüberschrift im Inhaltsverzeichnis direkt an oder über
+% die Kapitelnummer geschrieben.
+% Als Lösung wird mehr Platz zwischen Nummer und
+% Überschrift eingefügt.
+\renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
+\renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
+
+% To be able to enter the character ° and · directly in LyX,
+% see sec. 22.11
+\DeclareInputText{176}{\ifmmode^\circ\else\textdegree\fi}
+\DeclareInputText{183}{\ifmmode\cdot\else\textperiodcentered\fi}
+
+% increase link area for cross-references and autoname them,
+% see sec. 22.18.1
+\AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
+%\renewcommand{\sectionautorefname}{sec.\negthinspace}
+\renewcommand{\subsectionautorefname}{sec.\negthinspace}
+\renewcommand{\subsubsectionautorefname}{sec.\negthinspace}
+\newlength{\abc}
+\settowidth{\abc}{\space}
+\renewcommand{\equationautorefname}{\hspace{-\abc}}
+
+% don't load packages twice
+% see first footnote in sec. 9.3
+\@ifundefined{textcolor}{\usepackage{color}}{}
+
+% the pages of the TOC are numbered roman
+% and a PDF-bookmark for the TOC is added
+\pagenumbering{Roman}
+\let\myTOC\tableofcontents
+\renewcommand{\tableofcontents}{%
+ \vspace{1cm}
+ \pdfbookmark[1]{Contents}{}
+ \myTOC
+ \cleardoublepage
+ \pagenumbering{arabic}}
+
+% insert additional vertical space of 1.5 mm between footnotes,
+% see sec. 22.16
+\let\myFoot\footnote
+\renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
+
+% provides caption formatting
+\setkomafont{captionlabel}{\bfseries}
+
+% used in Kap. 22.4
+\usepackage{braket}
+
+% used in Kap. 22.6
+\usepackage[samesize]{cancel}
+
+% enables calculation of values,
+\usepackage{calc}
+
+% for multiple table row and column cells
+\usepackage{multirow}
+\usepackage{multicol}
+
+% needed for diagrams
+\usepackage{amscd}
+
+% needed in sec. 19.4
+\usepackage{remreset}
+
+% center multirows (e.g. in sec. 13.3)
+\renewcommand{\multirowsetup}{\centering}
+
+% define a color, used in sec.9.3
+\definecolor{vertfonce}{cmyk}{0.5, 0, 1, 0.5}
+
+% declare operators (see sec. 10.4 and sec. 15.2)
+\DeclareMathOperator*{\Losange}{\blacklozenge}
+\DeclareMathOperator{\sgn}{sgn}
+
+\newcommand{\spce}{\textvisiblespace}
+
+% example definitions for sec. 20.1
+\newcommand{\gr}{\Longrightarrow}
+\newcommand{\us}[1]{\underline{#1}}
+\newcommand{\fb}[3]{\framebox#1#2{$#3$}}
+\newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
+\newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
+
+% example macro from sec. 19.4
+%\def\tagform@#1{\maketag@@@{|#1|}}
+
+% macro from sec. 10.2
+\def\clap#1{\hbox to 0pt{\hss #1\hss}}
+\def\mathclap {\mathpalette \mathclapinternal}
+\def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
+
+% redefine the greyed out note
+\renewenvironment{lyxgreyedout}
+ {\textcolor{blue}\bgroup}{\egroup}
+
+% check for package eurosym
+% used for the Euro symbol
+\newboolean{eurosym}
+\IfFileExists{eurosym.sty}
+ {\usepackage[gennarrow]{eurosym}
+ \setboolean{eurosym}{true}}
+ {\setboolean{eurosym}{false}}
+
+% needed in sec. 22.10
+% check for package upgreek
+\newboolean{upgreek}
+\IfFileExists{upgreek.sty}
+ {\usepackage{upgreek}
+ \setboolean{upgreek}{true}}
+ {\setboolean{upgreek}{false}}
+\end_preamble
+\options bibtotoc,idxtotoc,BCOR7.5mm,titlepage,tablecaptionabove
+\language french
+\inputencoding auto
+\font_roman default
+\font_sans default
+\font_typewriter default
+\font_default_family default
+\font_sc false
+\font_osf false
+\font_sf_scale 100
+\font_tt_scale 100
+\graphics default
+\paperfontsize 12
+\spacing single
+\papersize a4paper
+\use_geometry false
+\use_amsmath 2
+\use_esint 1
+\cite_engine basic
+\use_bibtopic false
+\paperorientation portrait
+\secnumdepth 4
+\tocdepth 3
+\paragraph_separation skip
+\defskip medskip
+\quotes_language english
+\papercolumns 1
+\papersides 2
+\paperpagestyle plain
+\bullet 1 0 6 -1
+\bullet 2 2 35 -1
+\bullet 3 2 7 -1
+\tracking_changes false
+\output_changes false
+\author ""
+\author ""
+\end_header
+
+\begin_body
+
+\begin_layout Title
+Manuel mathématique détaillé de LyX
+\end_layout
+
+\begin_layout Author
+par l'équipe LyX
+\begin_inset Foot
+status open
+
+\begin_layout Standard
+\noindent
+Si vous avez des commentaires ou des corrections d'erreurs, faites les parvenir
+ à la liste de diffusion de la documentation de LyX:
+\family typewriter
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{mailto:lyx-docs@lists.lyx.org?subject=LyX's Math manual}{
+\end_layout
+
+\end_inset
+
+lyx-docs@lists.lyx.org
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+auteur: Uwe Stöhr
+\end_layout
+
+\begin_layout Standard
+traducteur: Siegfried MEUNIER-GUTTIN-CLUZEL
+\end_layout
+
+\end_inset
+
+
+\newline
+
+\newline
+
+\family sans
+Version 1.5.4-
+\family default
+1
+\end_layout
+
+\begin_layout Standard
+\begin_inset LatexCommand tableofcontents
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+Pour pouvoir exporter ce document en PDF, PS, ou DVI les paquetages LaTeX
+
+\series bold
+eurosym,
+\series default
+
+\series bold
+multirow,
+\series default
+ et
+\series bold
+was
+\series default
+ doivent être installés.
+ S'ils ne sont pas installés, vous pouvez quand même exporter votre document,
+ mais les sections où ces paquetages sont nécessaires ne seront pas visibles
+ sur la sortie finale.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\newpage
+
+\end_layout
+
+\begin_layout Section
+Introduction
+\begin_inset LatexCommand label
+name "sec:Introduction"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Ce document explique les fonctions mathématiques de LyX et c'est aussi une
+ collection de commandes LaTeX utilisées pour les symboles et les constructions
+ mathématiques.
+ Les explications mettent l'accent sur l'utilisation des commandes, il est
+ donc indispensable que vous ayez déjà lu la section sur les
+\family typewriter
+Formules Mathématiques
+\family default
+ du Manuel de l'Utilisateur.
+\end_layout
+
+\begin_layout Standard
+La plupart des symboles et plusieurs constructions expliquées dans ce manuel
+ sont aussi accessibles par le menu
+\family sans
+ Insérer\SpecialChar \menuseparator
+Math
+\family default
+, ou par la
+\family sans
+barre d'outils mathématique.
+
+\family default
+Mais quand on tape beaucoup de formules, on constate vite qu'il est plus
+ rapide d'utiliser une commande plutôt que la barre d'outils.
+ C'est pourquoi ce manuel se focalise sur les commandes tout en mentionnant
+ les boutons correspondants quand il y en a de disponibles.
+\end_layout
+
+\begin_layout Standard
+Sauf mention contraire les commandes ne sont disponibles qu'au sein d'une
+ formule.
+ Pour pouvoir utiliser toutes les commandes expliquées dans ce document
+ il faut utiliser l'option
+\family sans
+Utiliser le paquetage math AMS
+\family default
+ dans les paramètres du document (menu
+\family sans
+ Document\SpecialChar \menuseparator
+Paramètres\SpecialChar \menuseparator
+Options mode math
+\family default
+)
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+L'option
+\family sans
+Utiliser automatiquement le paquetage math AMS
+\family default
+ n'utilise les maths-
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+AmS
+\end_layout
+
+\end_inset
+
+\InsetSpace ~
+que si on utilise des constructions mathématiques qui sont reconnues par
+ LyX.
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+Ce document ne liste pas la totalité des commandes math-
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+AmS
+\end_layout
+
+\end_inset
+
+\InsetSpace ~
+pour des raisons de bon sens
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+On trouve une liste de toutes les commandes math-
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+AmS
+\end_layout
+
+\end_inset
+
+\InsetSpace ~
+dans le fichier
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps}{
+\end_layout
+
+\end_inset
+
+
+\family sans
+amsguide.ps
+\family default
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+, qui est inclus dans toutes les installations LaTeX standard.
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Section
+Instructions générales
+\begin_inset LatexCommand label
+name "sec:Instructions-générales"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Pour créer une formule en ligne
+\begin_inset LatexCommand index
+name "Formules ! en ligne"
+
+\end_inset
+
+ c'est-à-dire qui soit incorporée à la ligne de texte, appuyez sur
+\family sans
+Ctrl-m
+\family default
+ ou sur le bouton
+\begin_inset Graphics
+ filename ../../images/math-mode.png
+ scale 85
+
+\end_inset
+
+ de la barre d'outils
+\newline
+Pour créer une formule hors ligne
+\begin_inset LatexCommand index
+name "Formules ! hors ligne"
+
+\end_inset
+
+ c'est-à-dire qui apparaîtra plus grosse et qui aura son propre paragraphe,
+ appuyez sur
+\family sans
+Ctrl-M
+\family default
+.
+\end_layout
+
+\begin_layout Standard
+Pour changer une formule en ligne en une formule hors ligne, placez le curseur
+ dans la formule et appuyez sur
+\family sans
+Ctrl-M
+\family default
+ ou utilisez
+\family sans
+Éditer\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Changer le type de formule
+\family default
+.
+ De la même façon, on peut changer une formule hors ligne en une formule
+ en ligne.
+\end_layout
+
+\begin_layout Standard
+Pour afficher des parties d'une formule en ligne avec la même taille qu'une
+ formule hors ligne, entrez la commande
+\series bold
+
+\backslash
+displaystyle
+\begin_inset LatexCommand index
+name "Commandes ! D ! \\textbackslash displaystyle"
+
+\end_inset
+
+
+\series default
+ dans la formule.
+ Une nouvelle boîte bleue apparaît alors dans laquelle on peut insérer les
+ parties de formules qui doivent avoir la taille hors ligne.
+\end_layout
+
+\begin_layout Standard
+Seules les formules en ligne sont autorisées dans les tableaux.
+\end_layout
+
+\begin_layout Standard
+La barre d'outils mathématique peut être activée avec le menu
+\family sans
+Visualiser\SpecialChar \menuseparator
+Barres d'outils
+\family default
+.
+ Quand vous y cliquez sur
+\begin_inset Quotes eld
+\end_inset
+
+Math
+\begin_inset Quotes erd
+\end_inset
+
+ la barre d'outils s'affiche de façon permanente en bas de l'interface;
+ cet état est visualisé dans le menu
+\family sans
+Barres\InsetSpace ~
+d'outils
+\family default
+par une coche.
+ Si, dans cet état, vous cliquez une nouvelle fois sur
+\begin_inset Quotes eld
+\end_inset
+
+Math
+\begin_inset Quotes erd
+\end_inset
+
+ la barre d'outils ne s'affichera plus que lorsque le curseur se trouvera
+ à l'intérieur d'une formule; cet état est visualisé en changeant l'entrée
+ de menu de
+\begin_inset Quotes eld
+\end_inset
+
+Math
+\begin_inset Quotes erd
+\end_inset
+
+ en
+\begin_inset Quotes eld
+\end_inset
+
+Math (auto)
+\begin_inset Quotes erd
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+Le mode TeX
+\begin_inset LatexCommand index
+name "Mode TeX"
+
+\end_inset
+
+ est activé en appuyant sur le bouton
+\begin_inset Graphics
+ filename ../../images/ert-insert.png
+ scale 85
+
+\end_inset
+
+ de la barre d'outils ou en utilisant le menu
+\family sans
+Insérer\SpecialChar \menuseparator
+Code\InsetSpace ~
+T
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
+e
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+X
+\family default
+ (raccourci
+\family sans
+Ctrl-l
+\family default
+).
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+Dans LyX il y a trois
+\begin_inset Quotes eld
+\end_inset
+
+nom propres
+\begin_inset Quotes erd
+\end_inset
+
+ qui apparaissent dans la sortie finale avec des lettres mises en indice
+ ou en exposant: TeX, LaTeX, et LyX
+\end_layout
+
+\begin_layout Standard
+Pour éviter que ces noms soient reconnus comme des noms propres, les accolades
+ TeX sont placées autour d'une des lettres du nom.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Pour modifier le préambule LaTeX
+\begin_inset LatexCommand index
+name "Préambule LaTeX"
+
+\end_inset
+
+, on utilise le menu
+\family sans
+Document\SpecialChar \menuseparator
+Paramètres\SpecialChar \menuseparator
+Préambule\InsetSpace ~
+La
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
+T
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+eX
+\family default
+.
+\end_layout
+
+\begin_layout Standard
+Pour éditer des matrices, des différentiations de cas et des formules multiligne
+s après coup, on peut utiliser les menus
+\family sans
+Éditer\SpecialChar \menuseparator
+Math
+\family default
+ and
+\family sans
+Éditer\SpecialChar \menuseparator
+Lignes\InsetSpace \thinspace{}
+&\InsetSpace \thinspace{}
+colonnes,
+\family default
+ ou la barre d'outils
+\family sans
+Tableau
+\family default
+.
+ Quand deux lignes ou deux colonnes sont permutées à l'aide du menu, la
+ ligne ou la colonne où se trouve le curseur est échangée avec la ligne
+ d'en dessous ou la colonne directement à droite.
+ Si le curseur se trouve dans la dernière ligne ou colonne, l'échange se
+ fera avec la ligne précédente ou la colonne directement à gauche.
+\end_layout
+
+\begin_layout Standard
+Quand on veut écrire du texte dans des formules
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Pour les formules multilignes, on utilise la commande
+\series bold
+
+\backslash
+intertext,
+\series default
+ voir
+\begin_inset LatexCommand ref
+reference "sub:Texte-dans-multi-lignes"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+, on doit utiliser du
+\emph on
+texte mathématique
+\emph default
+
+\begin_inset LatexCommand index
+name "Texte ! dans les formules"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Mathématique, texte"
+
+\end_inset
+
+.
+ Ce mode est invoqué à l'aide du raccourci
+\family sans
+ Alt-m\InsetSpace ~
+m
+\family default
+ ou en insérant la commande
+\series bold
+
+\backslash
+text
+\begin_inset LatexCommand index
+name "Commandes ! T ! \\textbackslash text"
+
+\end_inset
+
+
+\series default
+.
+ Dans LyX, le texte apparaît en noir et peut donc être distingué des autres
+ parties de la formule qui apparaissent en bleu.
+ Dans la sortie finale, le texte mathématique est en caractères droits,
+ contrairement aux autres éléments de formule.
+\end_layout
+
+\begin_layout Subsection*
+Syntaxe des commandes
+\end_layout
+
+\begin_layout Standard
+La plupart des commandes LaTeX utilisées dans les constructions mathématiques
+ suivent la syntaxe suivante:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+nomdelacommande[argument optionnel]{argument obligatoire}
+\end_layout
+
+\begin_layout Standard
+Une commande commence toujours par une barre de fraction inverse (anti-slash)
+
+\begin_inset Quotes gld
+\end_inset
+
+
+\series bold
+
+\backslash
+
+\series default
+
+\begin_inset Quotes grd
+\end_inset
+
+.
+ Pour omettre l'argument optionnel, il faut aussi omettre les crochets qui
+ vont avec.
+ Les accolades placées autour des arguments obligatoires seront nommées
+ accolade TeX dans ce document
+\begin_inset LatexCommand index
+name "Accolades TeX"
+
+\end_inset
+
+.
+ Si dans une formule, vous ajoutez à un nom de commande une accolade gauche,
+ LyX créera automatiquement une accolade droite.
+ Dans tous les autres cas les accolades TeX sont créées dans des formules
+ avec la commande
+\series bold
+
+\backslash
+{
+\series default
+.
+ Les accolades TeX apparaissent en rouge dans LyX, contrairement aux accolades
+ normales qui apparaissent en bleu.
+ En mode TeX, on n'a pas besoin d'une commande pour obtenir des accolades
+ TeX.
+ Les accolades TeX n'apparaissent pas dans la sortie finale.
+\end_layout
+
+\begin_layout Standard
+Quand on entre en mode TeX des commandes sans argument, comme les commandes
+ pour les symboles, on doit
+\emph on
+toujours
+\emph default
+ placer une espace après la commande pour la terminer.
+ Cette espace n'apparaît pas dans la sortie finale.
+
+\emph on
+
+\emph default
+Si une espace doit apparaître dans la sortie finale, l'espace doit être
+ suivie par une espace insécable en texte normal.
+\end_layout
+
+\begin_layout Standard
+On insère une espace insécable avec
+\family sans
+Ctrl-Space
+\family default
+.
+\end_layout
+
+\begin_layout Subsection*
+
+\newpage
+Explications sur la syntaxe
+\end_layout
+
+\begin_layout Itemize
+Le symbole
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Ce caractère espace visible peut être obtenu en utilisant la commande
+\series bold
+
+\backslash
+textvisiblespace
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! T ! \\textbackslash textvisiblespace"
+
+\end_inset
+
+, insérée en mode TeX.
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+\InsetSpace ~
+indique que l'on doit mettre une espace.
+\end_layout
+
+\begin_layout Itemize
+Une flèche comme celle-ci
+\begin_inset Formula $\to$
+\end_inset
+
+ indique que l'on doit appuyer sur la flèche correspondante du clavier.
+\end_layout
+
+\begin_layout Subsection*
+Unités utilisées
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Float table
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+\align center
+\begin_inset Caption
+
+\begin_layout Standard
+\begin_inset LatexCommand label
+name "tab:Unités-utilisées"
+
+\end_inset
+
+Unités utilisées
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="13" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Unité
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Nom / Description
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+mm
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Millimètre
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+cm
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Centimètre
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+in
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Pouce (1\InsetSpace \thinspace{}
+in = 2,54\InsetSpace \thinspace{}
+cm)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+pt
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Point (72.27\InsetSpace \thinspace{}
+pt = 1\InsetSpace \thinspace{}
+in)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+pc
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Pica (1\InsetSpace \thinspace{}
+pc = 12\InsetSpace \thinspace{}
+pt)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+sp
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+scaled point (65536\InsetSpace \thinspace{}
+sp = 1\InsetSpace \thinspace{}
+pt)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+bp
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+big point (72\InsetSpace \thinspace{}
+bp = 1\InsetSpace \thinspace{}
+in)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+dd
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Didot (1\InsetSpace \thinspace{}
+dd
+\begin_inset Formula $\approx$
+\end_inset
+
+ 0.376\InsetSpace \thinspace{}
+mm)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+cc
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Cicero (1\InsetSpace \thinspace{}
+cc = 12\InsetSpace \thinspace{}
+dd)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+ex
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Hauteur de la lettre
+\emph on
+
+\begin_inset Quotes eld
+\end_inset
+
+x
+\emph default
+
+\begin_inset Quotes erd
+\end_inset
+
+ dans la police courante
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+em
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Largeur de la lettre
+\begin_inset Quotes eld
+\end_inset
+
+
+\emph on
+M
+\emph default
+
+\begin_inset Quotes erd
+\end_inset
+
+ dans la police courante
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+mu
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+unité math (1\InsetSpace \thinspace{}
+mu =
+\begin_inset Formula $\nicefrac{1}{18}$
+\end_inset
+
+\InsetSpace \thinspace{}
+em)
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+La commande
+\series bold
+
+\backslash
+textfrac
+\series default
+ est expliquée sec.\InsetSpace \thinspace{}
+
+\begin_inset LatexCommand ref
+reference "sub:Fractions-personnalisées"
+
+\end_inset
+
+
+\lang english
+.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\newpage
+
+\end_layout
+
+\begin_layout Section
+Fonctions de base
+\end_layout
+
+\begin_layout Subsection
+Exposants
+\begin_inset LatexCommand index
+name "Exposants"
+
+\end_inset
+
+ et indices
+\begin_inset LatexCommand index
+name "Indices"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Les indices sont créés avec le caractère souligné
+\begin_inset Quotes eld
+\end_inset
+
+_
+\begin_inset Quotes erd
+\end_inset
+
+ ou avec le bouton
+\begin_inset Graphics
+ filename ../../images/math-subscript.png
+ scale 85
+
+\end_inset
+
+de la barre d'outils mathématique, les exposants avec un accent circonflexe
+
+\begin_inset Quotes eld
+\end_inset
+
+^
+\begin_inset Quotes erd
+\end_inset
+
+ ou avec le bouton
+\begin_inset Graphics
+ filename ../../images/math-superscript.png
+ scale 85
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox est seulement utilisée pour faire de la place
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+B_V
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $B_{V}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+B^V
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}B^{V}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+B^
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}B^{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Pour éviter que l'accent se retrouve sur la lettre qui le suit au lieu de
+ la mettre en exposant, vous pouvez soit appuyer sur
+\family sans
+Espace
+\family default
+après l'accent circonflexe comme dans le dernier exemple ou utiliser l'accent
+ qui se trouve sur la touche du 9.
+\end_layout
+
+\begin_layout Subsection
+Fractions
+\begin_inset LatexCommand label
+name "sub:Fractions"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Fractions"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Les fractions sont créées avec la commande
+\series bold
+
+\backslash
+frac
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! F ! \\textbackslash frac"
+
+\end_inset
+
+ ou avec le bouton
+\begin_inset Graphics
+ filename ../../images/math/frac.png
+ scale 50
+
+\end_inset
+
+ de la barre d'outils mathématique.
+ La taille de la police est ajustée automatiquement selon que l'on se trouve
+ dans une formule en ligne ou hors ligne.
+ Avec le bouton
+\begin_inset Graphics
+ filename ../../images/math/frac-square.png
+ scale 85
+
+\end_inset
+
+ de la barre d'outils mathématique, vous pouvez choisir entre différents
+ types de fractions.
+\end_layout
+
+\begin_layout Standard
+Avec la commande
+\series bold
+
+\backslash
+dfrac
+\begin_inset LatexCommand index
+name "Commandes ! D ! \\textbackslash dfrac"
+
+\end_inset
+
+
+\series default
+ on peut créer une fraction qui a dans tous les cas la taille d'une fraction
+ qui se trouverait dans une formule hors ligne.
+ Avec
+\series bold
+
+\backslash
+tfrac
+\begin_inset LatexCommand index
+name "Commandes ! T ! \\textbackslash tfrac"
+
+\end_inset
+
+
+\series default
+ la fraction aura toujours la taille d'une formule en ligne.
+ Un exemple:
+\end_layout
+
+\begin_layout Standard
+Une ligne avec la fraction
+\begin_inset Formula $\frac{1}{2}$
+\end_inset
+
+ créée avec la commande
+\series bold
+
+\backslash
+frac
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+Une ligne avec la fraction
+\begin_inset Formula $\dfrac{1}{2}$
+\end_inset
+
+ créée avec la commande
+\series bold
+
+\backslash
+dfrac
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox est seulement utilisée pour faire de la place
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+frac
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+dfrac
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+dfrac
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+e^
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\backslash
+frac
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+1
+\begin_inset Formula $\downarrow$
+\end_inset
+
+2
+\begin_inset Formula $\downarrow\downarrow$
+\end_inset
+
+3
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+
+\newpage
+Pour des fractions emboîtées, on peut utiliser la commande
+\series bold
+
+\backslash
+cfrac
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! C ! \\textbackslash cfrac"
+
+\end_inset
+
+.
+ Voici un exemple:
+\begin_inset VSpace -3mm
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \begin{align*}
+\textrm{créée avec \textbf{\textbackslash frac}} & & \textrm{créée avec \textbf{\textbackslash cfrac}}\\
+\frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}\end{align*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+La commande pour l'exemple précédent est:
+\end_layout
+
+\begin_layout Standard
+
+\backslash
+cfrac{A
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{B+
+\backslash
+cfrac{C+
+\backslash
+cfrac{E
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{F
+\begin_inset Formula $\to\to$
+\end_inset
+
+
+\backslash
+{D
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+cfrac
+\series default
+ met toujours la fraction dans la taille d'une formule hors ligne, même
+ si elle est une partie d'une autre fraction.
+ La commande
+\series bold
+
+\backslash
+cfrac
+\series default
+ a la syntaxe suivante:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+cfrac[position du numérateur]{numérateur}{dénominateur}
+\end_layout
+
+\begin_layout Standard
+La position du numérateur peut être
+\emph on
+l
+\emph default
+ ,
+\emph on
+c
+\emph default
+, ou
+\emph on
+r
+\emph default
+ .
+ l ou r aligne le numérateur respectivement à gauche ou à droite par rapport
+ à la barre de fraction.
+ Quand on met
+\emph on
+c
+\emph default
+ou rien, le numérateur apparaît centré.
+ Les fractions qui suivent illustrent les différents alignements:
+\newline
+
+\series bold
+
+\begin_inset Formula $\cfrac[l]{A}{B+C}$
+\end_inset
+
+,
+\begin_inset Formula $\cfrac{A}{B+C}$
+\end_inset
+
+,
+\begin_inset Formula $\cfrac[r]{A}{B+C}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Il est souvent intéressant de combiner
+\series bold
+
+\backslash
+cfrac
+\series default
+ et
+\series bold
+
+\backslash
+frac
+\series default
+:
+\begin_inset Formula \[
+\cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Pour des fractions en ligne avec une barre de fraction en diagonale, vous
+ pouvez utiliser la commande
+\series bold
+
+\backslash
+nicefrac
+\begin_inset LatexCommand index
+name "Commandes ! N ! \\textbackslash nicefrac"
+
+\end_inset
+
+
+\series default
+:
+\begin_inset Formula $\nicefrac{5}{31}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Dans
+\begin_inset LatexCommand ref
+reference "sub:Fractions-personnalisées"
+
+\end_inset
+
+ on explique comment définir des fractions personnalisées en modifiant les
+ barres de fractions .
+\end_layout
+
+\begin_layout Subsection
+Racines
+\begin_inset LatexCommand index
+name "Racines"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+On obtient les racines carrées avec la commande
+\series bold
+
+\backslash
+sqrt
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! S ! \\textbackslash sqrt"
+
+\end_inset
+
+ ou avec le bouton
+\begin_inset Graphics
+ filename ../../images/math/sqrt.png
+ scale 85
+
+\end_inset
+
+ de la barre d'outils mathématique, et toutes les autres racines avec la
+ commande
+\series bold
+
+\backslash
+root
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! R ! \\textbackslash root"
+
+\end_inset
+
+ ou avec le bouton
+\begin_inset Graphics
+ filename ../../images/math/root.png
+ scale 85
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox est seulement utilisée pour faire de la place
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sqrt
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A-B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+root
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+3
+\begin_inset Formula $\downarrow$
+\end_inset
+
+A-B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+On peut aussi obtenir une racine carrée avec
+\series bold
+
+\backslash
+root
+\series default
+ en laissant le champ réservé au degré de la racine vide.
+\end_layout
+
+\begin_layout Standard
+Dans certains cas, la distance entre le degré et la racine est trop petite
+ comme dans cette formule:
+\begin_inset Formula $\sqrt[\beta]{B}$
+\end_inset
+
+
+\newline
+Le
+\begin_inset Formula $\beta$
+\end_inset
+
+ touche la racine, ce qui peut être évité en utilisant les commandes
+\series bold
+
+\backslash
+leftroot
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! L ! \\textbackslash leftroot"
+
+\end_inset
+
+ et
+\series bold
+
+\backslash
+uproot
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! U ! \\textbackslash uproot"
+
+\end_inset
+
+ avec la syntaxe suivante:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+leftroot{distance}
+\series default
+ et
+\series bold
+
+\backslash
+uproot{distance}
+\end_layout
+
+\begin_layout Standard
+Distance est le nombre de Big Points (unité bp;
+\begin_inset Formula $\mathrm{72\, bp=1\, pouce}$
+\end_inset
+
+), dont le degré doit être déplacé, respectivement vers la gauche ou vers
+ le haut.
+ Les commandes doivent être placées dans la case du degré.
+ Par exemple, la commande
+\newline
+
+\series bold
+
+\backslash
+root
+\backslash
+leftroot{-1
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+uproot{2
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+beta
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula $\to$
+\end_inset
+
+B
+\newline
+
+\series default
+produit une formule correctement mise en forme:
+\begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Coefficients binomiaux
+\begin_inset LatexCommand index
+name "Binomiaux, coefficients"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Les coefficients binomiaux sont insérés avec la commande
+\series bold
+
+\backslash
+binom
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! B ! \\textbackslash binom"
+
+\end_inset
+
+ ou avec le bouton
+\begin_inset Graphics
+ filename ../../images/math/frac-square.png
+ scale 85
+
+\end_inset
+
+de la barre d'outils mathématique.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox est seulement utilisée pour faire de la place
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+binom
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+dbinom{A
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Comme pour les fraction (
+\series bold
+
+\backslash
+frac
+\series default
+) il y a avec
+\series bold
+
+\backslash
+binom
+\series default
+ les commandes
+\series bold
+
+\backslash
+dbinom
+\begin_inset LatexCommand index
+name "Commandes ! D ! \\textbackslash dbinom"
+
+\end_inset
+
+
+\series default
+ et
+\series bold
+
+\backslash
+tbinom
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! T ! \\textbackslash tbinom"
+
+\end_inset
+
+ avec les syntaxes suivantes:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+dbinom{numérateur}{dénominateur}
+\series default
+ et
+\newline
+
+\series bold
+
+\backslash
+tbinom{numérateur}{dénominateur}
+\end_layout
+
+\begin_layout Subsection
+Différentiation de cas
+\begin_inset LatexCommand index
+name "Différentiation de cas "
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+cases
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\begin_inset Formula $\to$
+\end_inset
+
+B>0
+\begin_inset LatexCommand index
+name "Commandes ! C ! \\textbackslash cases"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\begin{cases}
+A & B>0\end{cases}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+cases
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+Ctrl-Enter
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\begin{cases}
+A & \textrm{pour }\hat{x}>0\\
+B & \textrm{pour }\hat{x}=0\end{cases}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Après avoir inséré
+\series bold
+
+\backslash
+cases
+\series default
+ ou avoir utilisé le bouton
+\begin_inset Graphics
+ filename ../../images/math/cases.png
+ lyxscale 50
+ scale 50
+
+\end_inset
+
+ de la barre d'outils mathématique, vous pouvez ajouter de nouvelles lignes
+ avec le raccourci
+\family sans
+Ctrl-Entrée
+\family default
+ ou avec le bouton
+\begin_inset Graphics
+ filename ../../images/tabular-feature_append-row.png
+ scale 85
+
+\end_inset
+
+.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Les accents et autres trémas, comme ceux présents dans la formule précédente,
+ sont expliqués dans
+\begin_inset LatexCommand ref
+reference "sub:Accents-sur-un-caractère"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+La commande
+\series bold
+
+\backslash
+cases
+\series default
+ est aussi accessible par le menu
+\family sans
+Insérer\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Environnement\InsetSpace ~
+Cas
+\family default
+.
+\end_layout
+
+\begin_layout Subsection
+Négations
+\begin_inset LatexCommand index
+name "Négations"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+En insérant la commande
+\series bold
+
+\backslash
+not
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! N ! \\textbackslash not"
+
+\end_inset
+
+ chaque caractère peut être affiché barré.
+ Les caractères sont en quelque sorte accentués par une barre de fraction.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+not=
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\not=$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+not
+\backslash
+le
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\not\le$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+not
+\backslash
+parallel
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\not\parallel$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Le dernier exemple montre que toutes les négations n'ont pas forcément un
+ bel aspect.
+ C'est pourquoi il existe des commandes spéciales pour certaines négations
+ (voir
+\begin_inset LatexCommand ref
+reference "sub:Symboles-mathématiques"
+
+\end_inset
+
+ et
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+renewcommand{
+\backslash
+sectionautorefname}{
+\backslash
+hspace{-
+\backslash
+abc}}
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand ref
+reference "sec:Relations"
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+renewcommand{
+\backslash
+sectionautorefname}{sec.
+\backslash
+negthinspace}
+\end_layout
+
+\end_inset
+
+).
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+Les commandes
+\backslash
+renewcommand en mode TeX sont nécessaires pour éviter que le nom de référence
+ croisée
+\begin_inset Quotes eld
+\end_inset
+
+sec.
+\begin_inset Quotes erd
+\end_inset
+
+ n'apparaisse pas deux fois.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Garnitures
+\begin_inset LatexCommand label
+name "sub:Garnitures"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Garnitures"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Symboles chimiques ! Isotopes"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Isotopes|see{Symboles chimiques}"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Quand on affiche par exemple des isotopes
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Plus d'information sur les symboles chimiques dans
+\begin_inset LatexCommand ref
+reference "sub:Symboles-chimiques"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+, on rencontre le problème suivant:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="2">
+<features>
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Indices avec les indices et exposants:
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Indices corrects:
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+\lang english
+
+\backslash
+raisebox
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+L'indice le plus petit est placé par défaut au dessus ou en dessous du premier
+ caractère le l'indice le plus long.
+ Pour éviter ce problème il y a la commande
+\series bold
+
+\backslash
+phantom
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! P ! \\textbackslash phantom"
+
+\end_inset
+
+ ou le bouton\InsetSpace ~
+
+\begin_inset Graphics
+ filename ../../images/math/phantom.png
+ scale 85
+
+\end_inset
+
+ qui crée un ou plusieurs caractères fantômes.
+ Quand on insère la commande
+\series bold
+
+\backslash
+phantom
+\series default
+ une petite boîte avec deux flèches rouges apparaît.
+ Les flèches indiquent que la garniture
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Traduction de placeholder, c'est un terme de typographie (NdT).
+\end_layout
+
+\end_inset
+
+ créée aura la même largeur et la même hauteur que le contenu de la boîte.
+ De la même façon, les caractères fantômes sont des garnitures qui ont la
+ taille du caractère concerné.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox est seulement utilisée pour faire de la place
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+^19
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+_
+\backslash
+phantom
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+1
+\begin_inset Formula $\to$
+\end_inset
+
+9
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+F
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+^235
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+_
+\backslash
+phantom
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+23
+\begin_inset Formula $\to$
+\end_inset
+
+9
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+F
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Lambda^
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\backslash
+phantom
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+ii
+\begin_inset Formula $\to$
+\end_inset
+
+t
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+_MMt
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+En plus, il y a les commandes
+\series bold
+
+\backslash
+vphantom
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! V ! \\textbackslash vphantom"
+
+\end_inset
+
+ (bouton\InsetSpace ~
+
+\begin_inset Graphics
+ filename ../../images/math/vphantom.png
+ scale 85
+
+\end_inset
+
+ de la barre d'outils) et
+\series bold
+
+\backslash
+hphantom
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! H ! \\textbackslash hphantom"
+
+\end_inset
+
+ (bouton\InsetSpace ~
+
+\begin_inset Graphics
+ filename ../../images/math/hphantom.png
+ scale 85
+
+\end_inset
+
+).
+
+\series bold
+
+\backslash
+hphantom
+\series default
+ crée seulement de l'espace pour la hauteur maximale des caractères de la
+ boîte, mais pas pour leur largeur.
+
+\series bold
+
+\backslash
+vphantom
+\series default
+ crée de l'espace seulement pour la largeur du contenu de la boîte.
+ C'est pour cela que les boîtes qui se trouvent sur les boutons des deux
+ commandes n'ont qu'une seule flèche rouge.
+\end_layout
+
+\begin_layout Standard
+Par exemple
+\series bold
+
+\backslash
+vphantom
+\series default
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\series bold
+a
+\backslash
+int
+\series default
+ crée de l'espace pour la hauteur du signe intégral
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+La commande
+\series bold
+
+\backslash
+int
+\series default
+ insère le signe de l'intégrale, voir
+\begin_inset LatexCommand ref
+reference "sub:Grands-opérateurs"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+, vu que c'est le plus haut caractère.
+ Voir un exemple d'application dans
+\begin_inset LatexCommand ref
+reference "sub:Crochets-multilignes"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Lignes
+\begin_inset LatexCommand index
+name "Lignes"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formules ! soulignées"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox est seulement utilisée pour faire de la place
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+overline
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A+B
+\begin_inset LatexCommand index
+name "Commandes ! O ! \\textbackslash overline"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+underline
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A+B
+\begin_inset LatexCommand index
+name "Commandes ! U ! \\textbackslash underline"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+overline
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\backslash
+underline
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Dans le dernier exemple, il importe peu que
+\series bold
+
+\backslash
+overline
+\series default
+ ou
+\series bold
+
+\backslash
+underline
+\series default
+ soit inséré en premier.
+\end_layout
+
+\begin_layout Standard
+Pour souligner deux fois, par exemple des résultats, on utilise
+\backslash
+underline deux fois.
+\end_layout
+
+\begin_layout Standard
+Il est possible de mettre jusqu'à 6 lignes au dessus ou en dessous de caractères.
+\end_layout
+
+\begin_layout Subsection
+Points de suspension
+\begin_inset LatexCommand index
+name "Points de suspension"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Différents types de points de suspension sont disponibles.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Dans la barre d'outils mathématique dans le sous-menu du bouton
+\begin_inset Graphics
+ filename ../../images/math/ldots.png
+ scale 85
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ Les points utilisés pour les listes et qui se trouvent sur la ligne de
+ base, on utilise (
+\series bold
+
+\backslash
+ldots
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! L ! \\textbackslash ldots"
+
+\end_inset
+
+), alors que pour les points utilisé pour les opérations et qui se trouvent
+ à la même hauteur que les opérateurs, on utilise (
+\series bold
+
+\backslash
+cdots
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! C ! \\textbackslash cdots"
+
+\end_inset
+
+).
+ Quand on utilise la commande
+\series bold
+
+\backslash
+dots
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! D ! \\textbackslash dots"
+
+\end_inset
+
+, LaTeX décide en fonction du caractère qui suit, quel type utiliser.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A_1
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+,
+\backslash
+dots
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+,A_n
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A_{1},\dots,A_{n}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A_1
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
++
+\backslash
+dots
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
++A_n
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A_{1}+\dots+A_{n}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A_1
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+,
+\backslash
+ldots
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+,A_n
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A_{1},\ldots,A_{n}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A_1
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
++
+\backslash
+cdots
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
++A_n
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A_{1}+\cdots+A_{n}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+vdots
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\vdots$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ddots
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\ddots$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+matrice 3×3\InsetSpace \thinspace{}
+avec les différents types de points
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\begin{array}{ccc}
+A_{11} & \cdots & A_{1m}\\
+\vdots & \ddots & \vdots\\
+A_{n1} & \cdots & A_{nm}\end{array}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Les points de suspension accessibles avec le menu
+\family sans
+Insérer\SpecialChar \menuseparator
+Caractère\InsetSpace ~
+spécial
+\family default
+ sont des
+\series bold
+
+\backslash
+ldots
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Spécialement pour les matrices, il y a des points de suspension qui peuvent
+ couvrir plusieurs colonnes.
+ Il sont créés avec la commande
+\series bold
+
+\backslash
+hdotsfor
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! H ! \\textbackslash hdotsfor"
+
+\end_inset
+
+, qui a la syntaxe suivante:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+hdotsfor[distance]{nombre de colonnes}
+\end_layout
+
+\begin_layout Standard
+Le nombre de colonnes précise combien de colonnes doivent être couvertes.
+ La distance est un facteur donnant la distance entre les points.
+\end_layout
+
+\begin_layout Standard
+Dans la matrice suivante, on a inséré la commande
+\series bold
+
+\backslash
+hdotsfor[2]{4}
+\series default
+ dans la première colonne de le deuxième ligne, pour avoir une ligne de
+ points de suspension avec une distance entre points double de celle obtenue
+ avec la commande
+\series bold
+
+\backslash
+dots
+\series default
+:
+\begin_inset Formula \[
+\left(\begin{array}{cccc}
+A & B & C & D\\
+\hdotsfor[2]{4}\\
+a & z & e & r\end{array}\right)\]
+
+\end_inset
+
+Notez que les cases de la matrice qui doivent être couvertes doivent être
+ vides, sinon vous aurez des erreurs LaTeX.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Pour aller plus loin, vous pouvez utiliser la commande
+\series bold
+
+\backslash
+dotfill
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! D ! \\textbackslash dotfill"
+
+\end_inset
+
+ pour remplir le reste d'une ligne avec des points.
+ L'effet de ces commandes est le même que celui de
+\series bold
+
+\backslash
+hfill
+\series default
+, voir
+\begin_inset LatexCommand ref
+reference "sub:Espace-variable"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+Par exemple, la commande
+\series bold
+A
+\backslash
+dotfill
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+B
+\series default
+ produit
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $A\dotfill B$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Comme
+\series bold
+
+\backslash
+dotfill
+\series default
+ avec des points, il existe la commande
+\series bold
+
+\backslash
+hrulefill
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! H ! \\textbackslash hrulefill"
+
+\end_inset
+
+ avec un filet:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $A\hrulefill B$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Pour utiliser ces commandes dans le texte, elles doivent être insérées en
+ mode TeX.
+\end_layout
+
+\begin_layout Section
+Matrices
+\begin_inset LatexCommand label
+name "sec:Matrices"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Matrices"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+On peut insérer des matrices avec le bouton
+\begin_inset Graphics
+ filename ../../images/dialog-show_mathmatrix.png
+ scale 85
+
+\end_inset
+
+ de la barre d'outils mathématique ou en utilisant le menu
+\family sans
+ Insérer\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Matrice\InsetSpace ~
+mathématique
+\family default
+.
+ On vous demande alors le nombre de lignes et de colonnes de la matrice
+ et leur alignement.
+ L'alignement vertical n'est en fait important que pour les matrices qui
+ se trouvent dans une formule en ligne:
+\end_layout
+
+\begin_layout Standard
+L'alignement de la première matrice est haut
+\begin_inset Formula $\begin{array}[t]{cccc}
+A & D & G & J\\
+B & E & H & K\\
+C & F & I & L\end{array}$
+\end_inset
+
+, la seconde milieu
+\begin_inset Formula $\begin{array}{cccc}
+A & D & G & J\\
+B & E & H & K\\
+C & F & I & L\end{array}$
+\end_inset
+
+, et la troisième bas
+\begin_inset Formula $\begin{array}[b]{cccc}
+A & D & G & J\\
+B & E & H & K\\
+C & F & I & L\end{array}$
+\end_inset
+
+ .
+\end_layout
+
+\begin_layout Standard
+L'alignement horizontal précise comment le contenu des colonnes doit être
+ aligné.
+ On le choisit en entrant une lettre pour chaque colonne.
+
+\emph on
+l
+\emph default
+ pour un alignement à gauche (left) ,
+\emph on
+c
+\emph default
+ centré, et
+\emph on
+ r
+\emph default
+ à droite (right).
+ Par exemple, pour créer une matrice\InsetSpace ~
+4
+\series bold
+×
+\series default
+4 où la première colonne est alignée à gauche, la deuxième et la troisième
+ sont centrées et la dernière est alignée à gauche, on va entrer
+\series bold
+lccr
+\series default
+ pour l'alignement horizontal.
+ En principe, toutes les colonnes d'une matrice sont centrées, ce qui fait
+ que l'alignement par défaut pour toutes les colonnes est un
+\series bold
+c
+\series default
+.
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+pagebreak
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Alignement horizontal:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+lll
+\series default
+ :
+\begin_inset Formula $\begin{array}{lll}
+10000 & D & G\\
+B & 10000 & H\\
+C & F & 10000\end{array}$
+\end_inset
+
+ ,
+\series bold
+ccc
+\series default
+ :
+\begin_inset Formula $\begin{array}{ccc}
+10000 & D & G\\
+B & 10000 & H\\
+C & F & 10000\end{array}$
+\end_inset
+
+ ,
+\series bold
+rrr
+\series default
+ :
+\begin_inset Formula $\begin{array}{rrr}
+10000 & D & G\\
+B & 10000 & H\\
+C & F & 10000\end{array}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Pour ajouter ou supprimer des lignes ou des colonnes après coup, on peut
+ utiliser les boutons
+\begin_inset Graphics
+ filename ../../images/tabular-feature_append-row.png
+ scale 85
+
+\end_inset
+
+,
+\begin_inset Graphics
+ filename ../../images/tabular-feature_delete-row.png
+ scale 85
+
+\end_inset
+
+, etc.\InsetSpace \thinspace{}
+de la barre d'outils mathématique, ou le menu
+\family sans
+Éditer\SpecialChar \menuseparator
+Lignes\InsetSpace \thinspace{}
+&\InsetSpace \thinspace{}
+colonnes
+\family default
+.
+ On peut aussi ajouter de nouvelles lignes avec
+\family sans
+Ctrl-Entrée
+\family default
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+On peut ajouter des parenthèses autour d'une matrice, soit avec les commandes
+
+\series bold
+
+\backslash
+left
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! L ! \\textbackslash left"
+
+\end_inset
+
+ et
+\series bold
+
+\backslash
+right
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! R ! \\textbackslash right"
+
+\end_inset
+
+ (raccourci
+\family sans
+Alt-m\InsetSpace ~
+parenthèse
+\family default
+), voir
+\begin_inset LatexCommand ref
+reference "sub:Taille-parenthèses-automatique"
+
+\end_inset
+
+, ou en utilisant les commandes suivantes:
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox est seulement utilisée pour faire de la place
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bmatrix
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+matrice\InsetSpace \thinspace{}
+2×2
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
+0 & \textrm{-}\mathrm{i}\\
+\mathrm{i} & 0\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Bmatrix
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+matrice\InsetSpace \thinspace{}
+2×2
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
+0 & \textrm{-}\mathrm{i}\\
+\mathrm{i} & 0\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+pmatrix
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+matrice\InsetSpace \thinspace{}
+2×2
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
+0 & \textrm{-}\mathrm{i}\\
+\mathrm{i} & 0\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+vmatrix
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+matrice\InsetSpace \thinspace{}
+2×2
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
+0 & \textrm{-}\mathrm{i}\\
+\mathrm{i} & 0\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Vmatrix
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+matrice\InsetSpace \thinspace{}
+2×2
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
+0 & \textrm{-}\mathrm{i}\\
+\mathrm{i} & 0\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+matrix
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+matrice\InsetSpace \thinspace{}
+2×2
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
+0 & \textrm{-}\mathrm{i}\\
+\mathrm{i} & 0\end{array}\end{matrix}\raisebox{-5.3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Quand on insère par exemple
+\series bold
+
+\backslash
+vmatrix,
+\series default
+ une boîte bleue apparaît entre deux lignes verticales où la matrice est
+ insérée.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Comme toutes les formules multi-lignes sont en fait des matrices, la longueur
+
+\series bold
+
+\backslash
+arraycolsep
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! A ! \\textbackslash arraycolsep"
+
+\end_inset
+
+ qui est décrite dans
+\begin_inset LatexCommand ref
+reference "sub:Séparation-des-colonnes"
+
+\end_inset
+
+ peut aussi être utilisée pour changer la distance qui sépare les colonnes
+ dans les matrices.
+\end_layout
+
+\begin_layout Standard
+Pour changer l'espacement des lignes, on utilise la commande
+\series bold
+
+\backslash
+arraystretch
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! A ! \\textbackslash arraystretch"
+
+\end_inset
+
+ de la façon suivante:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+renewcommand{
+\backslash
+arraystretch}{facteur d'étirement}
+\begin_inset LatexCommand index
+name "Commandes ! R ! \\textbackslash renewcommand"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+La commande
+\series bold
+
+\backslash
+renewcommand
+\series default
+ affecte le facteur d'étirement à la commande prédéfinie
+\series bold
+
+\backslash
+arraystretch
+\series default
+.
+ Par exemple, pour doubler l'espacement des lignes, utilisez un facteur
+ 2.
+ Ce facteur sera utilisé pour toutes les matrices qui suivent.
+ Pour revenir à l'espacement initial, affectez un facteur 1 à
+\series bold
+
+\backslash
+arraystretch
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+Pour insérer une matrice dans une ligne de texte, on utilise la commande
+
+\series bold
+
+\backslash
+smallmatrix
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! S ! \\textbackslash smallmatrix"
+
+\end_inset
+
+.
+ Quand elle est insérée, une boîte bleue avec deux lignes en pointillé apparaît
+ où la matrice est insérée.
+\end_layout
+
+\begin_layout Standard
+Voici une matrice
+\begin_inset Formula $\left(\begin{smallmatrix}A & B\\
+C & D\end{smallmatrix}\right)$
+\end_inset
+
+ dans une ligne de texte.
+\end_layout
+
+\begin_layout Section
+Parenthèses et autres délimiteurs
+\begin_inset LatexCommand index
+name "Parenthèses"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Accolades"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Crochets"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Délimiteurs"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Parenthèses verticales et délimiteurs
+\begin_inset LatexCommand index
+name "Accolades ! verticales"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\lang english
+
+\hfill
+
+\lang french
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="9" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+(
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $($
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+{
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\{$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+[
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $[$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+langle
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\langle$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+lceil
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\lceil$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+lfloor
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\lfloor$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+/
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $/$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+|
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $|$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="9" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $)$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+}
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+]
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $]$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+rangle
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\rangle$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+rceil
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\rceil$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+rfloor
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\rfloor$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+
+\backslash
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\backslash$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+|
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\|$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\lang english
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Standard
+
+\series bold
+Note:
+\series default
+ En mode TeX, on doit utiliser la commande
+\series bold
+
+\backslash
+textbackslash
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! T ! \\textbackslash textbackslash"
+
+\end_inset
+
+ pour la barre de fraction inverse (backslash), puisque la commande
+\backslash
+
+\backslash
+ produit un saut de ligne.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+On peut ajuster la taille de tous les caractères listés ci-dessus avec les
+ commandes décrites dans les deux sous-sections qui suivent.
+ Quand on utilise ces commandes, on peut utiliser directement les caractères
+ < et > , plutôt que les commandes
+\series bold
+
+\backslash
+langle
+\series default
+ et
+\series bold
+
+\backslash
+rangle
+\series default
+.
+\end_layout
+
+\begin_layout Subsubsection
+Taille de parenthèse manuelle
+\begin_inset LatexCommand label
+name "sub:Taille-parenthèses-manuelle"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Taille parenthèses ! manuelle"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+La taille des parenthèses peut être précisée manuellement en utilisant les
+ commandes LaTeX
+\series bold
+
+\backslash
+big
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! B ! \\textbackslash big"
+
+\end_inset
+
+,
+\series bold
+
+\backslash
+Big
+\series default
+,
+\series bold
+
+\backslash
+bigg
+\series default
+, et
+\series bold
+
+\backslash
+Bigg
+\series default
+.
+
+\series bold
+
+\backslash
+big
+\series default
+ indique la plus petite taille et
+\series bold
+
+\backslash
+Bigg
+\series default
+ la plus grande.
+\end_layout
+
+\begin_layout Standard
+Ces commandes sont utilisées pour mettre en évidence les différents niveaux
+ de parenthèses:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="2">
+<features>
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+toutes les parenthèses de la même taille:
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+c'est mieux comme cela:
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+\lang english
+
+\backslash
+raisebox
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Pour la deuxième formule, on a utilisé la commande
+\backslash
+Big((A+B)(A-B)
+\backslash
+Big)^
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+C.
+\end_layout
+
+\begin_layout Standard
+Voici un aperçu de toutes les tailles de parenthèses:
+\end_layout
+
+\begin_layout Standard
+\align center
+
+\backslash
+Bigg(
+\backslash
+exp
+\backslash
+bigg<
+\backslash
+Big[
+\backslash
+big{
+\backslash
+ln(3x)
+\backslash
+big}^2
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\backslash
+sin(x)
+\backslash
+Big]^
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\backslash
+bigg>
+\backslash
+Bigg)^0,5
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\newpage
+En plus des commandes
+\series bold
+
+\backslash
+big
+\series default
+, il y a la variante
+\series bold
+
+\backslash
+bigm
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! B ! \\textbackslash bigm"
+
+\end_inset
+
+ qui ajoute un peu plus d'espace entre la parenthèse et son contenu, et
+ la variante
+\series bold
+
+\backslash
+bigl
+\series default
+-
+\series bold
+
+\backslash
+bigr
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! B ! \\textbackslash bigl - \\textbackslash bigr"
+
+\end_inset
+
+, qui n'ajoute pas d'espace.
+ Le
+\emph on
+l
+\emph default
+ à la fin de la commande
+\series bold
+
+\backslash
+bigl
+\series default
+ est pour la parenthèse gauche; pour la parenthèse droite, il est remplacé
+ par un
+\emph on
+r
+\emph default
+.
+ Une parenthèse droite ou gauche peut être aussi bien une parenthèse fermante
+ ou ouvrante.
+\end_layout
+
+\begin_layout Standard
+Dans le tableau qui suit il y a une comparaison des différentes variantes:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features>
+<column alignment="center" valignment="middle" leftline="true" width="0">
+<column alignment="center" valignment="middle" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox est seulement utilisée pour faire de la place
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Bigm(
+\backslash
+bigm(
+\backslash
+ln(3x)
+\backslash
+bigm)^2
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\backslash
+Bigm)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Big(
+\backslash
+big(
+\backslash
+ln(3x)
+\backslash
+big)^2
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\backslash
+Big)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Bigl(
+\backslash
+bigl(
+\backslash
+ln(3x)
+\backslash
+bigr)^2
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\backslash
+Bigr)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigl)
+\backslash
+ln(3x)
+\backslash
+bigr(
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsubsection
+Taille de parenthèse automatique
+\begin_inset LatexCommand label
+name "sub:Taille-parenthèses-automatique"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Taille parenthèses ! automatique"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+On peut insérer des parenthèses à taille variable avec les commandes
+\series bold
+
+\backslash
+left
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! L ! \\textbackslash left"
+
+\end_inset
+
+ et
+\series bold
+
+\backslash
+right
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! R ! \\textbackslash right"
+
+\end_inset
+
+ ou avec le bouton\InsetSpace ~
+
+\begin_inset Graphics
+ filename ../../images/dialog-show_mathdelimiter.png
+ scale 85
+
+\end_inset
+
+ de la barre d'outils mathématique.
+ On doit insérer la parenthèse voulue juste après la commande
+\series bold
+
+\backslash
+left
+\series default
+ ou
+\series bold
+
+\backslash
+right
+\series default
+.
+ La taille de la parenthèse sera alors calculée automatiquement pour la
+ sortie.
+\end_layout
+
+\begin_layout Standard
+\align center
+parenthèse normale: La commande
+\series bold
+
+\backslash
+ln(
+\backslash
+frac
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+C
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+)
+\series default
+ donne
+\begin_inset Formula \[
+\ln(\frac{A}{C})\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+parenthèse adaptable: La commande
+\series bold
+
+\backslash
+ln
+\backslash
+left(
+\backslash
+frac
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+C
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\backslash
+right)
+\series default
+ donne
+\begin_inset Formula \[
+\ln\left(\frac{A}{C}\right)\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+À la place des commandes
+\series bold
+
+\backslash
+left
+\series default
+ et
+\series bold
+
+\backslash
+right
+\series default
+ on peut utiliser le raccourci
+\family sans
+Alt-m\InsetSpace ~
+parenthèse
+\family default
+.
+ Ceci a l'avantage que vous pouvez voir immédiatement dans LyX la taille
+ réelle des parenthèses et que la parenthèse droite associée est aussi créée
+ en même temps.
+\newline
+La commande pour le dernier exemple serait alors:
+\series bold
+
+\backslash
+ln Alt-m
+\series default
+
+\series bold
+(
+\backslash
+frac
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+C
+\end_layout
+
+\begin_layout Standard
+Pour omettre une parenthèse gauche ou droite, on met un point à la place
+ de la parenthèse omise.
+ Par exemple, la commande
+\series bold
+
+\backslash
+left.
+\backslash
+frac
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+B
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\backslash
+right}
+\series default
+ donne:
+\series bold
+
+\begin_inset Formula \[
+\left.\frac{A}{B}\right\} \]
+
+\end_inset
+
+
+\series default
+Les commandes
+\series bold
+
+\backslash
+left
+\series default
+ et
+\series bold
+
+\backslash
+right
+\series default
+ seront converties par LyX en parenthèses de taille appropriée quand le
+ document sera rechargé et une parenthèse omise apparaîtra sous la forme
+ d'une ligne en pointillé.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Parce que toutes les distributions LaTeX courantes utilisent eTeX, une extension
+ de LaTeX, la commande
+\series bold
+
+\backslash
+middle
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! M ! \\textbackslash middle"
+
+\end_inset
+
+ est aussi disponible pour toutes les parenthèses et limites.
+ Avec cette commande la taille du caractère suivant est adaptée à la taille
+ des parenthèses voisines, ce qui est nécessaire par exemple, pour les vecteurs
+ de la physique quantique:
+\begin_inset Formula \[
+\left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
+
+\end_inset
+
+Pour les vecteurs physiques, il existe un paquetage LaTeX spécialisé décrit
+ en
+\begin_inset LatexCommand ref
+reference "sub:Vecteurs-physiques"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Accolades horizontales
+\begin_inset LatexCommand index
+name "Accolades ! horizontales"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\begin_inset Note Note
+status open
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox est seulement utilisée pour faire de la place
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+raisebox{2.3mm}{
+\end_layout
+
+\end_inset
+
+
+\backslash
+overbrace
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A+B
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+^
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+3
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Commandes ! O ! \\textbackslash overbrace"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\overbrace{A+B}^{3}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+raisebox{-2.2mm}{
+\end_layout
+
+\end_inset
+
+
+\backslash
+underbrace
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A+B
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+_5
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Commandes ! U ! \\textbackslash underbrace"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\underbrace{A+B}_{5}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+overbrace
+\backslash
+underbrace
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A+B_w
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+_7
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+^
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+C
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Dans le dernier exemple, il importe peu que
+\series bold
+
+\backslash
+overbrace
+\series default
+ ou
+\series bold
+
+\backslash
+underbrace
+\series default
+ soit inséré en premier.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Quand des accolades doivent se chevaucher les unes les autres, on doit utiliser
+ des formules multi-lignes, comme c'est décrit en :
+\begin_inset Formula \begin{eqnarray*}
+A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
+ & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*}
+
+\end_inset
+
+Dans la première ligne la formule est insérée avec l'accolade.
+ Dans celle-ci, il est important que la commande d'espacement
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Les commandes concernant les espaces sont expliquées dans
+\begin_inset LatexCommand ref
+reference "sub:Espace-prédéfini"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\backslash
+:
+\series default
+ soit insérée avant le premier
+\begin_inset Formula $d$
+\end_inset
+
+, parce que l'accolade qui se termine après le dernier
+\begin_inset Formula $q$
+\end_inset
+
+ empêche que le
+\begin_inset Quotes eld
+\end_inset
+
++
+\begin_inset Quotes erd
+\end_inset
+
+ qui suit soit entouré par des espaces
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+parce que l'accolade n'est pas traitée comme un caractère, voir
+\begin_inset LatexCommand ref
+reference "sub:Opérateurs-binaires"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+ On insère la deuxième accolade dans la deuxième ligne.
+ Comme elle doit commencer juste avant le premier
+\begin_inset Formula $b$
+\end_inset
+
+, on insère d'abord la commande
+\series bold
+
+\backslash
+hphantom{gggg+
+\backslash
+:}
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+plus au sujet de
+\series bold
+
+\backslash
+hphantom
+\series default
+, voir
+\begin_inset LatexCommand ref
+reference "sub:Garnitures"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+ Cet espace est nécessaire puisque le
+\begin_inset Quotes eld
+\end_inset
+
++
+\begin_inset Quotes erd
+\end_inset
+
+ est aussi entouré d'espace dans la formule.
+ L'accolade est placée sous la commande
+\series bold
+
+\backslash
+hphantom{bbqq+dddd}
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+Cela devient plus compliqué quand les deux accolades se chevauchent comme
+ dans l'exemple suivant:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+setlength{
+\backslash
+jot}{-6pt}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{eqnarray*}
+ & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
+A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\end{eqnarray*}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+setlength{
+\backslash
+jot}{3pt}
+\end_layout
+
+\end_inset
+
+La première ligne de la formule est la même que la deuxième ligne de l'exemple
+ précédent, à la différence que l'accolade se trouve maintenant au dessus.
+ La seconde ligne contient la formule avec la deuxième accolade.
+ Pour éviter qu'il y ait trop d'espace entre l'accolade de la première ligne
+ et la formule, on doit réduire l'espacement entre les lignes.
+ Ce n'est pas facile à cause d'un bug de LyX
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://bugzilla.lyx.org/show_bug.cgi?id=1505}{
+\end_layout
+
+\end_inset
+
+LyX-bug #1505
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+ Comme solution à ce problème, on peut mettre à -6\InsetSpace \thinspace{}
+pt la formule globale
+ pour l'espacement des lignes
+\series bold
+
+\backslash
+jot
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! J ! \\textbackslash jot"
+
+\end_inset
+
+, juste avant la formule en utilisant la commande
+\series bold
+
+\backslash
+setlength{
+\backslash
+jot}{-6pt}
+\series default
+ en mode TeX.
+
+\series bold
+
+\backslash
+jot
+\series default
+ est remise à sa valeur initiale de 3\InsetSpace \thinspace{}
+pt juste après la formule, en utilisant
+ la même commande.
+ Vous trouverez plus d'explications sur la séparation des lignes dans les
+ formules dans
+\begin_inset LatexCommand ref
+reference "sub:Séparation-des-lignes"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Section
+Flèches
+\begin_inset LatexCommand index
+name "Flèches"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+On peut insérer des flèches avec le bouton
+\begin_inset Graphics
+ filename ../../images/math/leftarrow.png
+ scale 85
+
+\end_inset
+
+ de la barre d'outils mathématique ou en insérant une des commandes listées
+ dans les sous-sections qui suivent.
+\end_layout
+
+\begin_layout Subsection
+Flèches horizontales
+\begin_inset LatexCommand index
+name "Flèches ! horizontales"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+gets
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\gets$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Leftarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Leftarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+longleftarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\longleftarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Longleftarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Longleftarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+leftharpoonup
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\leftharpoonup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+leftharpoondown
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\leftharpoondown$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+hookleftarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\hookleftarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+to
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\to$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Rightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Rightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+longrightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\longrightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Longrightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Longrightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+rightharpoonup
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\rightharpoonup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+rightharpoondown
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\rightharpoondown$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+hookrightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\hookrightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="6" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+leftrightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\leftrightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Leftrightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Leftrightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+longleftrightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\longleftrightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Longleftrightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Longleftrightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+rightleftharpoons
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\rightleftharpoons$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+hspace{25pt}
+\end_layout
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mapsto
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mapsto$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+longmapsto
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\longmapsto$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+leadsto
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\leadsto$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+dasharrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\dasharrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Les flèches qui sont utilisées comme accentuation, comme par exemple les
+ flèches des vecteurs, sont listées dans
+\begin_inset LatexCommand ref
+reference "sec:Accents"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Il y a aussi les flèches avec étiquette
+\begin_inset LatexCommand index
+name "Flèches ! avec étiquette"
+
+\end_inset
+
+
+\series bold
+
+\backslash
+xleftarrow
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! X ! \\textbackslash xleftarrow"
+
+\end_inset
+
+ et
+\series bold
+
+\backslash
+xrightarrow
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! X ! \\textbackslash xrightarrow\\vspace{4mm}"
+
+\end_inset
+
+.
+ Quand on insère une de ces commandes dans une formule, une flèche avec
+ deux boîtes bleues apparaît, dans lesquelles on peut mettre les étiquettes.
+ La longueur de la flèche s'adapte à la largeur de l'étiquette.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox est seulement utilisée pour faire de la place
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+F(a)
+\backslash
+xleftarrow
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+x=a
+\begin_inset Formula $\downarrow$
+\end_inset
+
+x>0
+\begin_inset Formula $\to$
+\end_inset
+
+F(x)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+F(x)
+\backslash
+xrightarrow
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+x=a
+\begin_inset Formula $\downarrow$
+\end_inset
+
+x>0
+\begin_inset Formula $\to$
+\end_inset
+
+F(a)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Flèches verticales et diagonales
+\begin_inset LatexCommand index
+name "Flèches ! diagonales"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Flèches ! verticales"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="7" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+uparrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\uparrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Uparrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Uparrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+updownarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\updownarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Updownarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Updownarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Downarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Downarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+downarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\downarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+nearrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\nearrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+searrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\searrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+swarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\swarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+nwarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\nwarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Les flèches verticales peuvent aussi être utilisées comme séparateurs en
+ même temps que les commandes décrites dans
+\begin_inset LatexCommand ref
+reference "sub:Taille-parenthèses-manuelle"
+
+\end_inset
+
+ et
+\begin_inset LatexCommand ref
+reference "sub:Taille-parenthèses-automatique"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+
+\newpage
+
+\end_layout
+
+\begin_layout Section
+Accents
+\begin_inset LatexCommand label
+name "sec:Accents"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Accents"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+On peut ajouter des accents avec le bouton\InsetSpace ~
+
+\begin_inset Graphics
+ filename ../../images/math/hat.png
+ scale 85
+
+\end_inset
+
+ de la barre d'outils mathématique ou en utilisant les commandes listées
+ dans les sous-sections qui suivent.
+\end_layout
+
+\begin_layout Subsection
+Accents pour un caractère
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+texorpdfstring{
+\end_layout
+
+\end_inset
+
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+pour les accents dans le texte, voir
+\begin_inset LatexCommand ref
+reference "sub:Accents-dans-le-texte"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}{}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\backslash
+texorpdfstring est utilisé pour éviter que la note de bas de page apparaisse
+ dans les signets PDF.
+\end_layout
+
+\begin_layout Standard
+Plus au sujet de
+\backslash
+texorpdfstring dans la section
+\begin_inset LatexCommand ref
+reference "sub:formules-dans-les-entêtes"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand label
+name "sub:Accents-sur-un-caractère"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Accents ! pour un caractère"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox est seulement utilisée pour faire de la place
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+dot
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\dot{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ddot
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+dddot
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ddddot{A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+vec
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\begin_inset LatexCommand index
+name "Vecteurs"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\vec{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bar
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\bar{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mathring
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="7" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+tilde
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+hat
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\hat{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+check
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\check{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+acute
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\acute{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+grave
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\grave{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+breve
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\breve{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Pour créer des trémas (umlauts en allemand)
+\begin_inset LatexCommand index
+name "Umlauts | see{Trémas}"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Trémas"
+
+\end_inset
+
+ dans des formules, on insère des guillemets devant une voyelle.
+ Ces deux caractères sont alors traités comme
+\emph on
+un seul
+\emph default
+caractère par LaTeX si la portion de formule avec le tréma est marqué comme
+ étant en allemand.
+ Avec cette méthode, contrairement à
+\series bold
+
+\backslash
+ddot
+\series default
+, on crée de
+\begin_inset Quotes eld
+\end_inset
+
+vrais
+\begin_inset Quotes erd
+\end_inset
+
+ umlauts, comme le montre l'exemple suivant:
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace -2mm
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox est seulement utilisée pour faire de la place
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Quotes grd
+\end_inset
+
+i
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\lang german
+\begin_inset Formula $"i$
+\end_inset
+
+
+\lang french
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+il faut que cette formule soit en allemand (NdT)
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ddot
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+i
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Un autre avantage par rapport à
+\series bold
+
+\backslash
+ddot
+\series default
+ est que les trémas peuvent être convertis directement en texte mathématique,
+ parce que les accents vus plus haut
+\emph on
+ne sont pas autorisés
+\emph default
+en texte mathématique.
+ Quand on convertit un caractère accentué en texte mathématique, seul le
+ caractère qui est sous l'accent est converti.
+ Ceci s'applique aussi à toutes les autres conversions comme par exemple
+ l'italique ou le gras.
+\end_layout
+
+\begin_layout Standard
+En texte mathématique, les trémas et autres caractères accentués peuvent
+ être insérés directement.
+\end_layout
+
+\begin_layout Subsection
+Accents pour les opérateurs
+\begin_inset LatexCommand index
+name "Accents ! pour les opérateurs"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Avec les commandes
+\series bold
+
+\backslash
+overset
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! O ! \\textbackslash overset"
+
+\end_inset
+
+ et
+\series bold
+
+\backslash
+underset
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! U ! \\textbackslash underset"
+
+\end_inset
+
+ on peut placer des caractères respectivement au dessus ou en dessous d'un
+ opérateur, pour l'accentuer.
+ Avec la commande
+\series bold
+
+\backslash
+sideset
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! S ! \\textbackslash sideset"
+
+\end_inset
+
+, on peut placer des caractères avant ou après un opérateur.
+ La syntaxe de la commande est:
+\series bold
+
+\newline
+
+\backslash
+sideset{caractère avant}{caractère après}
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+sideset
+\series default
+ doit toujours se trouver avant l'opérateur qui est accentué.
+ Vous pouvez utiliser pour l'accentuation plusieurs caractères et même
+ d'autres opérateurs ou des symboles.
+ Pour placer avec
+\series bold
+
+\backslash
+sideset,
+\series default
+ par exemple seulement des caractères derrière un opérateur, ne mettez rien
+ entre les deux premières accolades, mais ne les omettez pas.
+\end_layout
+
+\begin_layout Standard
+Par exemple la commande
+\series bold
+
+\backslash
+sideset{
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{
+\series default
+'
+\series bold
+
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+sum_k=1
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\series default
+^
+\series bold
+n
+\series default
+ donne:
+\begin_inset Formula \[
+\sideset{}{'}\sum_{k=1}^{n}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+La commande
+\series bold
+
+\backslash
+overset
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\backslash
+maltese
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\series default
+
+\begin_inset Formula $\uparrow$
+\end_inset
+
+
+\series bold
+a
+\series default
+ donne:
+\begin_inset Formula \[
+\overset{a}{\maltese}\]
+
+\end_inset
+
+Comme on peut le voir dans le dernier exemple, avec
+\series bold
+
+\backslash
+overset
+\series default
+ et
+\series bold
+
+\backslash
+underset
+\series default
+ on peut aussi accentuer des symboles et des caractères; avec
+\series bold
+
+\backslash
+sideset
+\series default
+ ce n'est pas possible.
+\end_layout
+
+\begin_layout Subsection
+Accents pour plusieurs caractères
+\begin_inset LatexCommand label
+name "sub:Accents-pour-plusieurs"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Accents ! pour plusieurs caractères"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox est seulement utilisée pour faire de la place
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+overleftarrow
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+underleftarrow
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+overleftrightarrow
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+underleftrightarrow
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+overrightarrow
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+underrightarrow
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+widetilde
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+widehat
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Avec ces commandes, vous pouvez accentuer autant de caractères que vous
+ voulez.
+ Mais les accents
+\series bold
+
+\backslash
+widetilde
+\series default
+ et
+\series bold
+
+\backslash
+widehat
+\series default
+apparaîtront dans la sortie finale avec une longueur de seulement trois
+ caractères, comme on le voit dans l'exemple suivant:
+\begin_inset Formula \[
+\widetilde{A+B=C-D}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Avec les commandes
+\series bold
+
+\backslash
+overset
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! O ! \\textbackslash overset"
+
+\end_inset
+
+ et
+\series bold
+
+\backslash
+underset
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! U ! \\textbackslash underset"
+
+\end_inset
+
+ décrites dans la sous-section précédente, il est aussi possible d'accentuer
+ plusieurs caractères.
+
+\series bold
+
+\series default
+La commande
+\series bold
+
+\backslash
+underset
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A=B
+\begin_inset Formula $\downarrow$
+\end_inset
+
+***
+\series default
+ donne:
+\begin_inset Formula \[
+\underset{***}{A=B}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Espace
+\begin_inset LatexCommand label
+name "sub:Espace"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Espace ! horizontal"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Espace prédéfini
+\begin_inset LatexCommand label
+name "sub:Espace-prédéfini"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Espace ! horizontal ! prédéfini"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Il es parfois nécessaire d'insérer un espace horizontal dans une formule.
+ On le fait en utilisant une espace insécable (raccourci
+\family sans
+Ctrl-Espace
+\family default
+).
+ Un
+\begin_inset Quotes eld
+\end_inset
+
+
+\series bold
+\color blue
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\series default
+\color inherit
+
+\begin_inset Quotes erd
+\end_inset
+
+ apparaît et en appuyant plusieurs fois sur
+\family sans
+Espace
+\family default
+ on peut choisir l'une des huit différentes tailles d'espaces disponibles.
+ On peut aussi insérer ces espaces en utilisant le bouton
+\begin_inset Graphics
+ filename ../../images/math/space.png
+ scale 85
+
+\end_inset
+
+ de la barre d'outils mathématique.
+ Indépendemment de la commande insérée, on peut toujours changer de taille
+ après en appuyant sur
+\family sans
+Espace
+\family default
+.
+
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset VSpace -5mm
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="7">
+<features>
+<column alignment="center" valignment="middle" leftline="true" width="6.8cm">
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+,
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+:
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+;
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+quad
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+qquad
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+!
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Nombre de fois où on a appuyé sur la barre d'
+\family sans
+Espace
+\family default
+après avoir inséré l'espace insécable
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+1
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+2
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+3
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+4
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+5
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\, B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\: B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\; B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\quad B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\qquad B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\! B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+La dernière taille n'a pas l'air de produire une espace.
+ Elle est affichée en rouge dans LyX, contrairement aux autres espaces,
+ parce que c'est une espace négative.
+ Il y a deux autres espaces négatives:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="3">
+<features>
+<column alignment="center" valignment="middle" leftline="true" width="6.8cm">
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+negmedspace
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+negthickspace
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Nombre de fois où on a appuyé sur la barre d'
+\family sans
+Espace
+\family default
+après avoir inséré l'espace insécable
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+6
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+7
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell multicolumn="1" alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\negmedspace B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\negthickspace B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Les espaces négatives peuvent faire que les caractères se chevauchent.
+ Elles peuvent être utilisée pour forcer des ligatures, par exemple pour
+ les opérateurs de somme:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\begin_inset Note Note
+status open
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox est seulement utilisée pour faire de la place
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sum
+\backslash
+sum
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+f_kl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sum
+\backslash
+negmedspace
+\backslash
+sum
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+f_kl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Les opérateur de relations comme par exemple le signe égal, sont toujours
+ entourés par des espaces.
+ Pour les supprimer, le signe égal est mis entre deux accolades TeX.
+ L'exemple suivant donne une illustration:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="2">
+<features>
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+équation normale
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A=B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+\lang english
+
+\backslash
+raisebox
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula $\raisebox{5mm}{}$
+\end_inset
+
+équation sans espace
+\end_layout
+
+\end_inset
+</cell>
+<cell multicolumn="1" alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A{=}B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\noindent
+La commande utilisée pour la dernière formule est:
+\series bold
+A
+\backslash
+{=
+\begin_inset Formula $\to$
+\end_inset
+
+B
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Les espaces sont nécessaires pour les unités physiques, parce que l'espace
+ insérée entre la valeur et l'unité est une espace fine et pas une espace
+ normale.
+ Pour les unités dans le texte, l'espace fine est insérée avec le menu
+\family sans
+Insérer\SpecialChar \menuseparator
+Typographie\InsetSpace ~
+spéciale\SpecialChar \menuseparator
+Espace\InsetSpace ~
+fine
+\family default
+ (raccourci
+\family sans
+Ctrl-Shift-Espace
+\family default
+).
+\end_layout
+
+\begin_layout Standard
+Un exemple pour voir la différence:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="2">
+<features>
+<column alignment="left" valignment="top" width="0">
+<column alignment="left" valignment="top" width="0">
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+24 kW
+\begin_inset Formula $\cdot$
+\end_inset
+
+h
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+espace normale entre l'unité est la valeur
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+24\InsetSpace \thinspace{}
+kW
+\begin_inset Formula $\cdot$
+\end_inset
+
+h
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+espace fine entre l'unité et la valeur
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Espace variable
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+texorpdfstring{
+\end_layout
+
+\end_inset
+
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+pour les espacements verticaux dans les formules, voir
+\begin_inset LatexCommand ref
+reference "sub:Séparation-des-lignes"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}{}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\backslash
+texorpdfstring est utilisé pour éviter que la note de bas de page apparaisse
+ dans les signets PDF.
+\end_layout
+
+\begin_layout Standard
+Plus au sujet de
+\backslash
+texorpdfstring dans la section
+\begin_inset LatexCommand ref
+reference "sub:formules-dans-les-entêtes"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand label
+name "sub:Espace-variable"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Espace ! horizontal ! variable"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Dans LyX, on peut insérer une espace de longueur définie avec la commande
+\newline
+
+\series bold
+
+\backslash
+hspace{length}
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! H ! \\textbackslash hspace"
+
+\end_inset
+
+.
+
+\end_layout
+
+\begin_layout Standard
+Pour la longueur toutes les unités qui sont listées dans
+\begin_inset LatexCommand ref
+reference "tab:Unités-utilisées"
+
+\end_inset
+
+ sont utilisables à l'exception de l'unité
+\begin_inset Quotes eld
+\end_inset
+
+mu
+\begin_inset Quotes erd
+\end_inset
+
+.
+ La longueur peut aussi être négative.
+ Pour insérer suffisamment d'espace pour que la formule utilise tout l'espace
+ disponible, on utilise la commande
+\series bold
+
+\backslash
+hfill
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! H ! \\textbackslash hfill"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace -1mm
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A=B
+\backslash
+hspace{3cm
+\begin_inset Formula $\to$
+\end_inset
+
+A
+\backslash
+not=C
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A=B\hspace{3cm}A\not=C$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A
+\backslash
+hspace{-1mm
+\begin_inset Formula $\to$
+\end_inset
+
+A
+\backslash
+not=A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\hspace{-1mm}A\not=A$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A=A
+\backslash
+hfill
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+B=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A=A\hfill B=B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Dans le dernier exemple, l'espace disponible est déterminé par le contenu
+ de colonne le plus long du tableau.
+ Dans une formule en ligne l'espace dépend de la longueur de la ligne dans
+ laquelle
+\series bold
+
+\backslash
+hfill
+\series default
+ est inséré.
+ Ce qui fait que si la formule prend toute la largeur de la ligne, aucun
+ espace ne sera ajouté.
+
+\series bold
+
+\backslash
+hfill
+\series default
+ a un effet sur les formules hors ligne uniquement si on utilise le style
+ de formule
+\series bold
+Indenté
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Les styles de formules sont expliqués dans
+\begin_inset LatexCommand ref
+reference "sec:Styles-de-formules"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+On peut aussi insérer les commandes
+\series bold
+
+\backslash
+hspace
+\series default
+ et
+\series bold
+
+\backslash
+hfill
+\series default
+ en mode TeX pour les utiliser avec du texte:
+\end_layout
+
+\begin_layout Standard
+Ceci est une ligne avec un espace de
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+hspace{2cm}
+\end_layout
+
+\end_inset
+
+2\InsetSpace \thinspace{}
+cm.
+\end_layout
+
+\begin_layout Standard
+Ceci est une ligne avec un
+\hfill
+espace maximum.
+\end_layout
+
+\begin_layout Standard
+Dans le dernier exemple, on a inséré
+\series bold
+
+\backslash
+hfill
+\series default
+ avec le menu
+\family sans
+Insérer\SpecialChar \menuseparator
+Typographie\InsetSpace ~
+spéciale\SpecialChar \menuseparator
+Ressort\InsetSpace ~
+horizontal
+\family default
+, ce qui n'est pas possible dans les formules.
+ Cette méthode a l'avantage que l'on peut voir dans LyX que c'est un espace
+ étirable.
+\end_layout
+
+\begin_layout Standard
+Quand ces commandes se trouvent au début d'un texte qui n'est pas au début
+ d'un paragraphe, elle sont ignorée par LaTeX.
+ Pour éviter cela, on utilise la commande
+\series bold
+
+\backslash
+hspace*
+\series default
+ à la place de
+\series bold
+
+\backslash
+hspace
+\series default
+.
+ Pour obtenir la même chose avec
+\series bold
+
+\backslash
+hfill
+\series default
+, on insère un saut de ligne et une garniture vide
+\series bold
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+pour les garnitures, voir
+\begin_inset LatexCommand ref
+reference "sub:Garnitures"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series default
+ en mode TeX avec la commande
+\series bold
+
+\backslash
+vphantom{}
+\series default
+avant
+\series bold
+
+\backslash
+hfill
+\series default
+.
+
+\end_layout
+
+\begin_layout Subsection
+Espace après les formules en ligne
+\begin_inset LatexCommand index
+name "Espace ! après les formules en ligne"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+L'espace qui entoure les formules en ligne peut être ajusté avec la longueur
+
+\series bold
+
+\backslash
+mathsurround
+\begin_inset LatexCommand index
+name "Commandes ! M ! \\textbackslash mathsurround"
+
+\end_inset
+
+
+\series default
+.
+ La valeur d'une longueur est modifiée avec la commande
+\series bold
+
+\backslash
+setlength
+\begin_inset LatexCommand index
+name "Commandes ! S ! \\textbackslash setlength"
+
+\end_inset
+
+
+\series default
+ qui a la syntaxe suivante:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+setlength{nom de la longueur}{valeur}
+\end_layout
+
+\begin_layout Standard
+Pour mettre
+\series bold
+
+\backslash
+mathsurround
+\series default
+ à une valeur de 5\InsetSpace \thinspace{}
+mm, on insère la commande
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+setlength{
+\backslash
+mathsurround}{5mm}
+\end_layout
+
+\begin_layout Standard
+en mode TeX.
+ Une espace de 5\InsetSpace \thinspace{}
+mm va maintenant être placée autour de toutes les formules
+ en ligne:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+setlength{
+\backslash
+mathsurround}{5mm}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Voici une formule en ligne
+\begin_inset Formula $A=B$
+\end_inset
+
+ avec une espace de 5\InsetSpace \thinspace{}
+mm autour.
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+setlength{
+\backslash
+mathsurround}{0pt}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Pour revenir à la valeur prédéfinie, on met
+\series bold
+
+\backslash
+mathsurround
+\series default
+ à 0\InsetSpace \thinspace{}
+pt.
+\end_layout
+
+\begin_layout Section
+Boîtes et cadres
+\begin_inset LatexCommand index
+name "Boîtes"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Cadres | see {Boîtes}"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Les boîtes utilisées pour le texte sont décrites dans le chapitre
+\emph on
+Boîtes
+\emph default
+du manuel
+\emph on
+Objets Insérés.
+
+\end_layout
+
+\begin_layout Subsection
+Boîtes avec cadre
+\begin_inset LatexCommand label
+name "sub:Boîtes-avec-cadre"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Boîtes ! avec cadre"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Il es possible d'encadrer des formules ou des portions de formules avec
+ la commande
+\series bold
+
+\backslash
+fbox
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! F ! \\textbackslash fbox"
+
+\end_inset
+
+ et
+\series bold
+
+\backslash
+boxed
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! B ! \\textbackslash boxed"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+Quand on insère une de ces commandes dans un formule, une boîte bleue apparaît
+ à l'intérieur d'un cadre pour que l'on puisse entrer des portions de formules.
+ Pour
+\series bold
+
+\backslash
+fbox
+\series default
+ on doit créer à l'intérieur de cette boîte, une formule supplémentaire
+ avec
+\family sans
+Ctrl-m
+\family default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+À cause d'un bug de LyX, il est impossible de créer une nouvelle formule
+ avec
+\family sans
+Ctrl-m
+\family default
+, voir
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
+\end_layout
+
+\end_inset
+
+LyX-bug #1435
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+, sinon le contenu de la boîte sera considéré comme du texte mathématique.
+ Quand on utilise
+\series bold
+
+\backslash
+boxed
+\series default
+, une nouvelle formule est automatiquement créée à l'intérieur du cadre.
+\end_layout
+
+\begin_layout Standard
+La commande
+\series bold
+
+\backslash
+fbox
+\series default
+ n'est pas utilisable pour encadrer des formules hors ligne, parce que la
+ formule serait alors toujours mise à la taille du texte.
+
+\series bold
+
+\backslash
+boxed
+\series default
+, au contraire, n'est pas utilisable pour les formules en ligne, parce que
+ la formule serait alors toujours mise à la taille des formules hors ligne.
+\end_layout
+
+\begin_layout Standard
+Comme extension à
+\series bold
+
+\backslash
+fbox
+\series default
+ il y a la commande
+\series bold
+
+\backslash
+framebox
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! F ! \\textbackslash framebox"
+
+\end_inset
+
+ où on peut en plus spécifier la largeur du cadre et l'alignement.
+ La syntaxe de la commande
+\series bold
+
+\backslash
+framebox
+\series default
+ est la suivante:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+framebox[Largeur du cadre][position]{contenu de la boîte}
+\end_layout
+
+\begin_layout Standard
+La position peut être soit
+\emph on
+l
+\emph default
+ soit
+\emph on
+r
+\emph default
+.
+
+\emph on
+l
+\emph default
+ aligne la formule à gauche dans la boîte,
+\emph on
+r
+\emph default
+ à droite.
+ Quand on ne précise pas la position, la formule est centrée.
+\newline
+Si on ne donne
+ pas de largeur, on ne peut pas donner d'indication de position.
+ Dans ce cas, la largeur du cadre est ajustée au contenu de la boîte, comme
+ c'est le cas avec
+\series bold
+
+\backslash
+fbox
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+Quand on insère la commande
+\series bold
+
+\backslash
+framebox
+\series default
+, une boîte apparaît contenant trois boîtes bleues.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+À cause d'un bug de LyX, le curseur doit être placé à gauche, à côté des
+ boîtes bleues pour pouvoir les remplir, voir
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://bugzilla.lyx.org/show_bug.cgi?id=2461}{
+\end_layout
+
+\end_inset
+
+LyX-bug #2461
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+ Les deux premières sont entourées de crochets pour signales des arguments
+ optionnels.
+ La troisième boîte est là pour contenir les portions de formules, comme
+ pour
+\series bold
+
+\backslash
+fbox
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+Le tableau a été placé dans une minipage pour que la note de bas de page
+ apparaisse.
+ Sinon le texte de la note n'aurait pas été affiché.
+\end_layout
+
+\end_inset
+
+
+\begin_inset Box Frameless
+position "c"
+hor_pos "c"
+has_inner_box 1
+inner_pos "c"
+use_parbox 0
+width "100col%"
+special "none"
+height "1in"
+height_special "totalheight"
+status open
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+À cause d'un bug de LyX, il n'est pas possible de créer une nouvelle formule
+ avec
+\family sans
+Ctrl-m
+\family default
+, voir
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
+\end_layout
+
+\end_inset
+
+LyX-bug #1435
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+\lang english
+
+\backslash
+raisebox
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+fbox
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\family sans
+Ctrl-m
+\family default
+
+\backslash
+int
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula \raisebox{6mm}{}\fbox{$\int A=B$}\raisebox{-4mm}{}
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+boxed
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\backslash
+int
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A+
+\backslash
+fbox
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+framebox
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+20mm
+\begin_inset Formula $\to$
+\end_inset
+
+
+\begin_inset Formula $\to$
+\end_inset
+
+
+\family sans
+Ctrl-m
+\family default
+
+\backslash
+frac
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}$
+\end_inset
+
+
+\begin_inset Formula $\framebox[20mm]{$\frac{A}{B}$}$
+\end_inset
+
+
+\begin_inset Formula $\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+On peut aussi ajuster l'épaisseur du cadre.
+ Pour cela, il faut insérer les commandes suivantes en mode TeX avant la
+ formule
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+fboxrule
+\series default
+
+\series bold
+
+\begin_inset Quotes eld
+\end_inset
+
+épaisseur
+\begin_inset Quotes erd
+\end_inset
+
+
+\series default
+
+\series bold
+
+\backslash
+fboxsep
+\series default
+
+\series bold
+
+\begin_inset Quotes eld
+\end_inset
+
+distance
+\begin_inset Quotes erd
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Quotes eld
+\end_inset
+
+distance
+\begin_inset Quotes erd
+\end_inset
+
+ précise la distance minimale entre le cadre et le premier caractère de
+ la boîte.
+ Un exemple pour illustrer ceci avec la formule encadrée suivante:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+fboxrule 2mm
+\backslash
+fboxsep 3mm
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \[
+\boxed{A+B=C}\]
+
+\end_inset
+
+Avant cette formule, on a inséré en mode TeX les commandes
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+fboxrule
+\series default
+
+\series bold
+2mm
+\series default
+
+\series bold
+
+\backslash
+fboxsep
+\series default
+
+\series bold
+3mm
+\end_layout
+
+\begin_layout Standard
+Les valeurs indiquées sont utilisées pour toutes les boîtes qui suivent.
+\end_layout
+
+\begin_layout Standard
+Pour revenir à la taille de cadre standard, on insère la commande
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+fboxrule
+\series default
+
+\series bold
+0.4pt
+\series default
+
+\series bold
+
+\backslash
+fboxsep
+\series default
+
+\series bold
+3pt
+\series default
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+fboxrule 0.4pt
+\backslash
+fboxsep 3pt
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+avant la formule suivante.
+\end_layout
+
+\begin_layout Subsection
+Boîtes sans cadre
+\begin_inset LatexCommand label
+name "sub:Boîtes-sans-cadre"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Boîtes ! sans cadre"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Pour obtenir des boîtes sans cadre, on utilise les commandes suivantes:
+
+\series bold
+
+\backslash
+mbox
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! M ! \\textbackslash mbox"
+
+\end_inset
+
+,
+\series bold
+
+\backslash
+makebox
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! M ! \\textbackslash makebox"
+
+\end_inset
+
+, et
+\series bold
+
+\backslash
+raisebox
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! R ! \\textbackslash raisebox"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Avec
+\series bold
+
+\backslash
+raisebox
+\series default
+ une boîte peut être mise en exposant ou en indice.
+ Mais contrairement aux indices et aux exposants normaux, les caractères
+ conservent leur taille de police initiale.
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ est utilisée avec la syntaxe suivante:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox{hauteur}{contenu de la boîte}
+\end_layout
+
+\begin_layout Standard
+Quand la boîte doit contenir une formule, il faut une formule supplémentaire
+ comme pour
+\series bold
+
+\backslash
+fbox
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+H
+\backslash
+raisebox{2mm
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{al
+\begin_inset Formula $\to$
+\end_inset
+
+ lo
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $H\raisebox{2mm}{al}lo$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+H
+\backslash
+raisebox{-2mm
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{al
+\begin_inset Formula $\to$
+\end_inset
+
+lo
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $H\raisebox{-2mm}{al}lo$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A=
+\backslash
+raisebox{-2mm
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{
+\family sans
+Ctrl-m
+\family default
+
+\backslash
+sqrt
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+$A=
+\backslash
+raisebox{-2mm}{$
+\backslash
+sqrt{B}$}$
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+La dernière formule ne peut actuellement être créée qu'en mode TeX, parce
+ que LyX insère une boîte plutôt que la formule supplémentaire qui est nécessair
+e
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+voir
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
+\end_layout
+
+\end_inset
+
+LyX-bug #1435
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+La commande
+\series bold
+
+\backslash
+mbox
+\series default
+ est équivalente à
+\series bold
+
+\backslash
+fbox
+\series default
+ et
+\series bold
+
+\backslash
+makebox
+\series default
+ est équivalente à
+\series bold
+
+\backslash
+framebox
+\series default
+, avec la différence qu'il n'y a pas de cadre.
+\end_layout
+
+\begin_layout Subsection
+Boîtes colorées
+\begin_inset LatexCommand label
+name "sub:Boîtes-colorées"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Boîtes ! colorées"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Pour pouvoir utiliser les commandes de cette section il faut que le paquetage
+ LaTeX
+\series bold
+color
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+La paquetage LaTeX
+\series bold
+color
+\series default
+ fait partie de toutes les installations LaTeX standard.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Paquetages ! color"
+
+\end_inset
+
+ soit chargé dans le préambule LaTeX avec la ligne
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Dès que du texte est coloré avec une couleur prédéfinie quelque part dans
+ le document, LyX charge automatiquement le paquetage LaTeX
+\series bold
+color
+\series default
+.
+ Il est donc possible que le paquetage soit chargé deux fois, mais cela
+ ne doit pas poser de problème.
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+Pour éviter que le paquetage soit chargé deux fois, une macro a été insérée
+ dans le préambule LaTeX.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{color}
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Pour colorer des boîtes, on utilise la commande
+\series bold
+
+\backslash
+colorbox
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! C ! \\textbackslash colorbox"
+
+\end_inset
+
+ avec la syntaxe suivante
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+colorbox{couleur}{contenu de la boîte}
+\end_layout
+
+\begin_layout Standard
+Le contenu de la boîte peut être une autre boîte et une
+\series bold
+
+\backslash
+colorbox
+\series default
+ peut aussi être une partie d'une autre boîte (voir le deuxième et le troisième
+ exemple).
+ Quand une boîte est destinée à contenir une formule, on doit insérer une
+ boîte supplémentaire, comme avec
+\series bold
+
+\backslash
+fbox
+\series default
+.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Ceci s'applique aussi à la commande
+\series bold
+
+\backslash
+fcolorbox
+\series default
+.
+ D'où la note
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
+\end_layout
+
+\end_inset
+
+LyX-bug #1435
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+On peut choisir une des couleurs prédéfinies suivantes:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+black
+\series default
+ (noir),
+\series bold
+blue
+\series default
+ (bleu),
+\series bold
+cyan
+\series default
+,
+\series bold
+green
+\series default
+ (vert),
+\series bold
+magenta
+\series default
+,
+\series bold
+red
+\series default
+ (rouge),
+\series bold
+white
+\series default
+ (blanc), et
+\series bold
+yellow (jaune)
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox est seulement utilisée pour faire de la place
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+colorbox{yellow
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+colorbox{green
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{
+\backslash
+fbox
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+fbox
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\backslash
+colorbox{green
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}\fbox{\colorbox{green}{A=B}}\raisebox{-3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+colorbox
+\series default
+ colorie uniquement la boîte, pas les caractères qui se trouvent dedans.
+ Pour colorer tous les caractères, on sélectionne toute la formule et on
+ choisit la couleur voulue avec la fenêtre de dialogue
+\family sans
+Style\InsetSpace ~
+de\InsetSpace ~
+texte
+\family default
+.
+ Cette fenêtre de dialogue peut être appelée avec le bouton
+\begin_inset Graphics
+ filename ../../images/dialog-show_character.png
+ scale 85
+
+\end_inset
+
+ de la barre d'outils, ou avec le menu
+\family sans
+Éditer\SpecialChar \menuseparator
+Style\InsetSpace ~
+de\InsetSpace ~
+texte\SpecialChar \menuseparator
+Personnalisé
+\family default
+.
+ Le numéro de la formule prendra la même couleur que la formule.
+ Si le numéro doit avoir une couleur différente de celle des caractères
+ de la formule, la couleur doit être changée à l'intérieur de la formule.
+\end_layout
+
+\begin_layout Standard
+Un exemple:
+\end_layout
+
+\begin_layout Standard
+
+\color red
+\begin_inset Formula \begin{equation}
+\int A=B\label{eq:rouge}\end{equation}
+
+\end_inset
+
+
+\color green
+
+\begin_inset Formula \begin{equation}
+\textcolor{red}{\int A=B}\label{eq:rougevert}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+La formule
+\begin_inset LatexCommand eqref
+reference "eq:rouge"
+
+\end_inset
+
+ est complètement colorée en rouge.
+\newline
+La formule
+\begin_inset LatexCommand eqref
+reference "eq:rougevert"
+
+\end_inset
+
+ a d'abord été complètement colorée en vert pour mettre le numéro en vert.
+ Ensuite, les caractères de la formule ont été colorés en rouge.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Pour colorer le cadre d'une couleur différente du reste de la boîte, on
+ utilise la commande
+\series bold
+
+\backslash
+fcolorbox
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! F ! \\textbackslash fcolorbox"
+
+\end_inset
+
+ avec la syntaxe suivante:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+fcolorbox{couleur du cadre}{couleur}{contenu de la boîte}
+\end_layout
+
+\begin_layout Standard
+Donc
+\series bold
+
+\backslash
+fcolorbox
+\series default
+ est une extension de la commande
+\series bold
+
+\backslash
+colorbox
+\series default
+.
+ L'épaisseur du cadre est déterminée comme avec
+\series bold
+
+\backslash
+framebox
+\series default
+, avec
+\series bold
+
+\backslash
+fboxrule
+\series default
+ et
+\series bold
+
+\backslash
+fboxsep
+\series default
+.
+ Un exemple:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+fboxrule 1mm
+\backslash
+fboxsep 1mm
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \[
+\fcolorbox{cyan}{magenta}{A=B}\]
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+fboxrule 0.4pt
+\backslash
+fboxsep 3pt
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Cette formule a été créée avec la commande
+\newline
+
+\series bold
+
+\backslash
+fcolorbox{cyan
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{magenta
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{A=B
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Si on veut utiliser d'autres couleurs que celles qui sont prédéfinies, il
+ faut d'abord les définir.
+\end_layout
+
+\begin_layout Standard
+On peut par exemple définir la couleur
+\begin_inset Quotes eld
+\end_inset
+
+vertfonce
+\begin_inset Quotes erd
+\end_inset
+
+ avec la ligne suivante dans le préambule LaTeX:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+definecolor{vertfonce}{cmyk}{0.5,
+\series default
+
+\series bold
+0,
+\series default
+
+\series bold
+1,
+\series default
+
+\series bold
+0.5}
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! D ! \\textbackslash definecolor"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+cmyk
+\series default
+ est l'espace colorimétrique basé sur les couleurs
+\series bold
+cyan
+\series default
+,
+\series bold
+magenta
+\series default
+, jaune
+\series bold
+ (yellow
+\series default
+), et noir
+\series bold
+(black
+\series default
+).
+ Les quatre nombres séparés par des virgules sont les proportions des couleurs
+ correspondantes dans l'espace colorimétrique.
+ Ces facteurs prennent des valeurs entre 0 et 1.
+ À la place de
+\series bold
+cmyk
+\series default
+on peut aussi utiliser l'espace
+\series bold
+rgb
+\series default
+basé sur les couleurs rouge (
+\series bold
+red
+\series default
+), vert (
+\series bold
+green
+\series default
+) et bleu (
+\series bold
+blue
+\series default
+).
+ On a dans ce cas trois facteurs qui donnent les proportions de ces trois
+ couleurs.
+ Il y a aussi l'espace de couleur
+\series bold
+gray
+\series default
+(dégradé de gris) avec un facteur donnant la proportion de gris.
+\end_layout
+
+\begin_layout Standard
+Comme exemple, une boîte encadrée avec la couleur
+\series bold
+vertfonce
+\series default
+que l'on vient de définir et des caractères colorés en jaune (
+\series bold
+yellow
+\series default
+):
+\begin_inset Formula \begin{equation}
+\colorbox{vertfonce}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+On peut aussi utiliser ces couleurs personnalisées avec du texte à l'aide
+ de la commande
+\series bold
+
+\backslash
+textcolor
+\series default
+:
+\begin_inset LatexCommand index
+name "Texte ! coloré"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+textcolor{vertfonce}{
+\end_layout
+
+\end_inset
+
+cette phrase est en
+\begin_inset Quotes eld
+\end_inset
+
+vertfonce
+\begin_inset Quotes erd
+\end_inset
+
+.
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+textcolor
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! T ! \\textbackslash textcolor"
+
+\end_inset
+
+ utilise la syntaxe
+\series bold
+
+\backslash
+textcolor{couleur}{caractères à colorer}
+\series default
+.
+\end_layout
+
+\begin_layout Subsection
+Boîtes de paragraphe
+\begin_inset LatexCommand label
+name "sub:Boîtes-de-paragraphes"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Boîtes ! comme paragraphe"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+On peut créer une boîte qui peut contenir plusieurs lignes, voir des paragraphes
+ entiers, c'est ce que l'on nomme une boîte de paragraphe (parbox en anglais).
+ On la crée avec le menu
+\family sans
+Insérer\SpecialChar \menuseparator
+Boîte
+\family default
+ ou le bouton
+\begin_inset Graphics
+ filename ../../images/box-insert.png
+ scale 85
+
+\end_inset
+
+ de la barre d'outils.
+\end_layout
+
+\begin_layout Standard
+L'exemple qui suit montre une boîte de paragraphe encadrée incluse dans
+ une ligne:
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Ceci est une ligne
+\begin_inset Box Boxed
+position "c"
+hor_pos "c"
+has_inner_box 1
+inner_pos "t"
+use_parbox 1
+width "5cm"
+special "none"
+height "1in"
+height_special "totalheight"
+status open
+
+\begin_layout Standard
+Ceci est une boîte de paragraphe.
+ Elle a exactement 5\InsetSpace \thinspace{}
+cm de large et peut aussi contenir des formules:
+\begin_inset Formula $\int A\,\mathrm{d}s=C$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ avec une boîte de paragraphe.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Une telle boîte est créée en faisant un clic droit sur la boîte d'insert
+ grise.
+ Une fenêtre de dialogue apparaît montrant les propriétés de la boîte.
+ Dans notre cas, on met:
+\emph on
+Décoration:
+\emph default
+ Boîte rectangulaire,
+\emph on
+Boîte intérieure:
+\emph default
+ Parbox,
+\emph on
+Largeur
+\emph default
+: 5\InsetSpace \thinspace{}
+cm,
+\emph on
+Alignement vertical boîte
+\emph default
+: milieu
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Dans LaTeX, une boîte de paragraphe est créée avec la commande
+\series bold
+
+\backslash
+parbox
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! P ! \\textbackslash parbox"
+
+\end_inset
+
+ qui a la syntaxe suivante:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+parbox[position]{largeur}{contenu de la boîte}
+\end_layout
+
+\begin_layout Standard
+Les positions
+\emph on
+b
+\emph default
+ et
+\emph on
+t
+\emph default
+ sont possibles.
+
+\emph on
+b
+\emph default
+ pour bas (bottom) signifie que la boîte est alignée au sein du texte qui
+ l'entoure, au niveau de sa dernière ligne.
+ Avec
+\emph on
+t
+\emph default
+ pour haut (top) l'alignement se fait avec la première ligne.
+ Si aucune position n'est précisée, la boîte est centrée verticalement,
+ voir la section
+\emph on
+Boîtes
+\emph default
+du manuel
+\emph on
+Objets insérés
+\emph default
+pour des exemples.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Pour encadrer une formule complètement, y compris le numéro de la formule,
+ il faut la placer dans une boîte de paragraphe.
+ Pour le faire, on insère la commande
+\series bold
+
+\backslash
+fbox{
+\backslash
+parbox{
+\backslash
+linewidth-2
+\backslash
+fboxsep-2
+\backslash
+fboxrule}{
+\series default
+ en mode TeX avant la formule.
+ Dans cette commande
+\series bold
+
+\backslash
+linewidth
+\begin_inset LatexCommand index
+name "Commandes ! L ! \\textbackslash linewidth"
+
+\end_inset
+
+
+\series default
+ est l'épaisseur de ligne qui est active pour tout le document.
+ Puisque le cadre se trouve à l'extérieur de la boîte de paragraphe, on
+ doit soustraire de l'épaisseur de ligne deux fois la séparation du cadre
+ et l'épaisseur du cadre.
+ Comme cela n'est pas fait automatiquement par LyX, à cause d'un bug
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://bugzilla.lyx.org/show_bug.cgi?id=4483}{
+\end_layout
+
+\end_inset
+
+LyX-bug #4483
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+, on doit utiliser le mode TeX.
+ Pour pouvoir effectuer des multiplications et des additions dans les arguments,
+ on doit charger le paquetage LaTeX
+\series bold
+calc
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+calc
+\series default
+ fait partie de toutes les installations standard de LaTeX.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Paquetages ! calc"
+
+\end_inset
+
+ dans le préambule LaTeX avec la ligne
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{calc}
+\end_layout
+
+\begin_layout Standard
+Après la formule, les deux boîtes sont refermées en entrant
+\series bold
+}}
+\series default
+ en mode TeX.
+ Voici un exemple:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+fboxsep 5mm
+\backslash
+fboxrule 5mm
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+fbox{
+\backslash
+parbox{
+\backslash
+linewidth-2
+\backslash
+fboxsep-2
+\backslash
+fboxrule}{
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{equation}
+\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}}
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+fboxrule 0.4pt
+\backslash
+fboxsep 3pt
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Comme on utilise une boîte de paragraphe comme argument de
+\series bold
+
+\backslash
+fbox
+\series default
+, il n'y a dans ce cas pas de différence entre
+\series bold
+
+\backslash
+fbox
+\series default
+ et
+\series bold
+
+\backslash
+boxed
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Les boîtes de paragraphes sont très utiles pour commenter directement des
+ formules.
+ Pour faire cela, on utilise la commande
+\series bold
+
+\backslash
+parbox
+\series default
+ en combinaison avec la commande
+\series bold
+
+\backslash
+tag
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+plus au sujet de la commande
+\series bold
+
+\backslash
+tag
+\series default
+, voir
+\begin_inset LatexCommand ref
+reference "sub:Numérotation-personnalisée"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+Un exemple de formule commentée avec
+\series bold
+
+\backslash
+parbox
+\series default
+:
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+[5x-7b=3b
+\backslash
+tag*{
+\backslash
+parbox{5cm}{
+\end_layout
+
+\end_inset
+
+Ceci est une description.
+ Elle est clairement séparée de la formule et est multi-ligne.
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}}
+\backslash
+]
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Une telle formule doit être complètement insérée en mode TeX, parce que
+ LyX ne supporte pas encore la commande
+\series bold
+
+\backslash
+parbox
+\series default
+ dans les formules.
+ On crée la formule avec la suite de commandes suivante:
+\end_layout
+
+\begin_layout Standard
+On insère la commande
+\series bold
+
+\backslash
+[5x-7b=3b
+\backslash
+tag*
+\backslash
+{
+\backslash
+parbox{5cm}{
+\series default
+ en mode TeX.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Quand on utilise le style de formule
+\series bold
+Indenté
+\series default
+, on peut aussi remplacer
+\series bold
+
+\backslash
+tag*
+\backslash
+{
+\series default
+ par
+\series bold
+
+\backslash
+hfill
+\series default
+.
+ (pour les styles de formules, voir
+\begin_inset LatexCommand ref
+reference "sec:Styles-de-formules"
+
+\end_inset
+
+).
+\end_layout
+
+\end_inset
+
+ Ensuite la description suit en texte normal et enfin on insère
+\series bold
+}}
+\backslash
+]
+\series default
+ en mode TeX.
+ Dans ces commandes,
+\series bold
+
+\backslash
+[
+\series default
+ et
+\series bold
+
+\backslash
+]
+\series default
+ créent une formule hors ligne.
+\end_layout
+
+\begin_layout Standard
+On peut voir les avantages de
+\series bold
+
+\backslash
+parbox
+\series default
+ dans cet exemple qui a été commenté en utilisant du texte mathématique:
+\begin_inset Formula \[
+5x-7b=3b\textrm{Ceci est une description. Elle n'est pas séparée de la formule ...}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Opérateurs
+\begin_inset LatexCommand index
+name "Opérateurs"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Grands Opérateurs
+\begin_inset LatexCommand label
+name "sub:Grands-opérateurs"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Opérateurs ! grands"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Sommes"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Intégrales"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Pour pouvoir utiliser tous les opérateurs intégraux listés ici, on doit
+ activer l'option
+\family sans
+Utiliser\InsetSpace ~
+automatiquement le paquetage\InsetSpace ~
+esint
+\family default
+ dans les
+\family sans
+Options du mode math.
+\end_layout
+
+\begin_layout Standard
+
+\lang english
+
+\hfill
+
+\lang french
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="11" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sum
+\begin_inset LatexCommand index
+name "Commandes ! S ! \\textbackslash sum"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\sum$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+int
+\begin_inset LatexCommand index
+name "Commandes ! I ! \\textbackslash int"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\int$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+intop
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\intop$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+oint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\oint$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ointop
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\ointop$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ointctrclockwise
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\ointctrclockwise$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ointclockwise
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\ointclockwise$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sqint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\sqint$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigcap
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bigcap$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigcup
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bigcup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="10" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+prod
+\begin_inset LatexCommand index
+name "Commandes ! P ! \\textbackslash prod"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\prod$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+coprod
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\coprod$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigodot
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bigodot$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigotimes
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bigotimes$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigoplus
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bigoplus$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigwedge
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bigwedge$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigvee
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bigvee$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigsqcup
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bigsqcup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+biguplus
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\biguplus$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\lang english
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+Tous les grands opérateurs peuvent aussi être insérés en utilisant le bouton
+
+\begin_inset Graphics
+ filename ../../images/math/intop.png
+ scale 85
+
+\end_inset
+
+ de la barre d'outils mathématique.
+\end_layout
+
+\begin_layout Standard
+On nomme ces opérateurs
+\begin_inset Quotes eld
+\end_inset
+
+grands
+\begin_inset Quotes erd
+\end_inset
+
+ parce qu'ils sont plus grands que les opérateurs binaires qui leur ressemblent
+ parfois.
+ Tous les grands opérateur peuvent avoir des limites comme c'est décrit
+ dans la section qui suit.
+\end_layout
+
+\begin_layout Standard
+Les opérateurs
+\series bold
+
+\backslash
+intop
+\series default
+ et
+\series bold
+
+\backslash
+ointop
+\series default
+ sont différents de respectivement
+\series bold
+
+\backslash
+int
+\series default
+ et
+\series bold
+
+\backslash
+oint
+\series default
+, dans la manière dont sont affichés les limites, voir
+\begin_inset LatexCommand ref
+reference "sub:Limites-des-opérateurs"
+
+\end_inset
+
+.
+
+\end_layout
+
+\begin_layout Subsubsection*
+Conseils pour les intégrales
+\end_layout
+
+\begin_layout Standard
+La lettre
+\emph on
+d
+\emph default
+ dans une intégrale est un opérateur, elle doit donc être en lettres droites.
+ On le fait en sélectionnant le
+\emph on
+d
+\emph default
+et en utilisant le raccourci clavier
+\family sans
+Alt-c\InsetSpace ~
+r
+\family default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Pour les styles de polices, voir
+\begin_inset LatexCommand ref
+reference "sub:Styles-de-polices"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+ Pour finir, on insère une espace fine avant le
+\emph on
+d
+\emph default
+puisque c'est l'habitude avec les opérateurs.
+ Un exemple:
+\end_layout
+
+\begin_layout Standard
+incorrect:
+\begin_inset Formula $\int A(x)dx$
+\end_inset
+
+
+\newline
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+hphantom{in}
+\end_layout
+
+\end_inset
+
+correct:
+\begin_inset Formula $\int A(x)\,\mathrm{d}x$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Pour les intégrales multiples, il y a les commandes suivantes:
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox est seulement utilisée pour faire de la place
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+iint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+oiint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sqiint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+iiint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+iiiint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+dotsint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Subsection
+Limites des opérateurs
+\begin_inset LatexCommand label
+name "sub:Limites-des-opérateurs"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Opérateurs ! Limites"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Les limites sont créées avec les indices et les exposants:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox est seulement utilisée pour faire de la place
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+prod^
+\backslash
+infty
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula $\to$
+\end_inset
+
+_0
+\begin_inset Formula $\to$
+\end_inset
+
+A(x)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Pour les formules en lignes, les limites sont placées juste après l'opérateur.
+ Pour les formules hors ligne, les limites sont placées au dessus ou en
+ dessous de l'opérateur, sauf pour les limites des intégrales.
+\end_layout
+
+\begin_layout Standard
+Pour forcer les limites à être après l'opérateur, on place le curseur juste
+ après l'opérateur et on change le type de limite avec le menu
+\family sans
+Éditer\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Changer\InsetSpace ~
+le\InsetSpace ~
+type\InsetSpace ~
+de\InsetSpace ~
+limites
+\family default
+ pour
+\family sans
+En\InsetSpace ~
+ligne
+\family default
+ (raccourci
+\family sans
+Alt-m\InsetSpace ~
+l
+\family default
+).
+ Un exemple:
+\end_layout
+
+\begin_layout Standard
+Par défaut les limites ont ce type:
+\begin_inset Formula \[
+\sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
+
+\end_inset
+
+Voici à quoi elles ressemblent si on change le type des limites à
+\family sans
+En\InsetSpace ~
+ligne
+\family default
+:
+\begin_inset Formula \[
+\sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
+
+\end_inset
+
+Pour les intégrales, à part pour
+\series bold
+
+\backslash
+intop
+\series default
+ et
+\series bold
+
+\backslash
+ointop
+\series default
+, les limites sont placées par défaut après l'opérateur.
+ Mais pour les intégrales multiples les limites sont souvent placées sous
+ l'opérateur.
+ Dans l'exemple suivant, le type de limites a donc été mis à
+\series bold
+Hors\InsetSpace ~
+ligne
+\series default
+et elles sont donc placées sous les intégrales:
+\begin_inset Formula \begin{equation}
+\iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Pour préciser des conditions pour les limites, on utilise les commandes
+
+\series bold
+
+\backslash
+subarray
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! S ! \\textbackslash subarray"
+
+\end_inset
+
+ et
+\series bold
+
+\backslash
+substack
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! S ! \\textbackslash substack"
+
+\end_inset
+
+.
+ Par exemple, pour obtenir cette expression
+\begin_inset Formula \begin{equation}
+\sum_{\begin{subarray}{c}
+0<k<1000\\
+\\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+on doit faire ceci:
+\newline
+D'abord taper la commande
+\series bold
+
+\backslash
+sum
+\series default
+^
+\series bold
+n
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+_
+\series default
+ .
+ On se trouve alors dans une boîte bleue sous l'opérateur de sommation et
+ on y insère la commande
+\series bold
+
+\backslash
+subarray
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\series default
+.
+ La boîte bleue se trouve maintenant dans une boîte violette et on peut
+ écrire plusieurs lignes les unes au dessus des autres.
+ On crée une nouvelle ligne en insérant un saut de ligne (
+\family sans
+Ctrl-Entrée
+\family default
+).
+ Maintenant, quand on tape
+\newline
+
+\series bold
+0<k<1000 Ctrl-Entrée
+\newline
+
+\series default
+une nouvelle boîte apparaît en dessous pour une nouvelle ligne.
+\end_layout
+
+\begin_layout Standard
+L'alignement des lignes peut être modifié en alignement à gauche avec la
+ barre d'outils
+\family sans
+Tableaux
+\family default
+ ou avec le menu
+\family sans
+Éditer\SpecialChar \menuseparator
+Lignes\InsetSpace ~
+&\InsetSpace ~
+colonnes
+\family default
+.
+ Pour avoir un alignement à droite, on insère un
+\series bold
+
+\backslash
+hfill
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\series default
+ au début de la ligne.
+\end_layout
+
+\begin_layout Standard
+La commande
+\series bold
+
+\backslash
+substack
+\series default
+ est équivalente à
+\series bold
+
+\backslash
+subarray
+\series default
+ avec la différence que les lignes sont toujours centrées.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Comme dans le cas de la formule
+\begin_inset LatexCommand eqref
+reference "eq:substack"
+
+\end_inset
+
+, il se peut qu'il y ait trop d'espace après un opérateur, puisque les caractère
+s qui suivent l'opérateur se trouvent après la limite.
+\end_layout
+
+\begin_layout Standard
+Pour éviter cela, on peut utiliser la macro suivante dans le préambule LaTeX:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+def
+\backslash
+clap#1{
+\backslash
+hbox to 0pt{
+\backslash
+hss #1
+\backslash
+hss}}
+\newline
+
+\backslash
+def
+\backslash
+mathclap {
+\backslash
+mathpalette
+\backslash
+mathclapinternal}
+\newline
+
+\backslash
+def
+\backslash
+mathclapinternal #1#2{
+\backslash
+clap{$
+\backslash
+mathsurround =0pt #1{#2}$}}
+\end_layout
+
+\begin_layout Standard
+Elle définit la commande
+\series bold
+
+\backslash
+mathclap
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! M ! \\textbackslash mathclap"
+
+\end_inset
+
+ qui met la largeur de la limite à 0\InsetSpace \thinspace{}
+pt.
+ La syntaxe de la commande est:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+mathclap{limite}
+\end_layout
+
+\begin_layout Standard
+où la limite peut être composée de plusieurs conditions.
+\end_layout
+
+\begin_layout Standard
+Appliqué à la formule
+\begin_inset LatexCommand eqref
+reference "eq:substack"
+
+\end_inset
+
+, on utilise la commande
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+sum_
+\backslash
+mathclap{
+\backslash
+substack
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+0<k<1000 Ctrl-Enter
+\end_layout
+
+\begin_layout Standard
+pour créer la limite inférieure.
+ L'opérande est maintenant juste après l'opérateur de sommation:
+\begin_inset Formula \[
+\sum_{\mathclap{\substack{0<k<1000\\
+\\k\,\in\,\mathbb{N}}
+}}^{n}k^{-2}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+On décrit comment utiliser une limite pour plusieurs opérateurs dans
+\begin_inset LatexCommand ref
+reference "sub:Opérateurs-personnalisés"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Opérateurs binaires
+\begin_inset LatexCommand label
+name "sub:Opérateurs-binaires"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Opérateurs ! binaires"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Les opérateurs binaires sont entourés d'espaces quand il y a un caractère
+ avant et après eux.
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\lang english
+
+\hfill
+
+\lang french
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="13" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox est seulement utilisée pour faire de la place
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
++
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $+$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+-
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $-$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+pm
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\pm$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mp
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mp$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+cdot
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\cdot$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+times
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\times$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+div
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\div$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+raisebox{-1.2mm}{
+\end_layout
+
+\end_inset
+
+*
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $*$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+star
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\star$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+circ
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\circ$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+diamond
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\diamond$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bullet
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bullet$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="13" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+nabla
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\nabla$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigtriangledown
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bigtriangledown$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigtriangleup
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bigtriangleup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Box
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Box$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+cap
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\cap$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+cup
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\cup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+dagger
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\dagger$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ddagger
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\ddagger$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+wr
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\wr$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigcirc
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bigcirc$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+wedge
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\wedge$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+vee
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\vee$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="13" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+oplus
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\oplus$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ominus
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\ominus$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+otimes
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\otimes$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+oslash
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\oslash$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+odot
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\odot$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+amalg
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\amalg$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+uplus
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\uplus$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+setminus
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\setminus$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sqcap
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\sqcap$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sqcup
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\sqcup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+triangleleft
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\triangleleft$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+triangleright
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\triangleright$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+Tous les opérateurs binaires peuvent être insérés avec le bouton
+\begin_inset Graphics
+ filename ../../images/math/pm.png
+ scale 85
+
+\end_inset
+
+ de la barre d'outils mathématique.
+\end_layout
+
+\begin_layout Standard
+Pour obtenir l'opérateur Laplacien, on peut utiliser
+\series bold
+
+\backslash
+Delta
+\series default
+ ou
+\series bold
+
+\backslash
+nabla
+\series default
+^
+\series bold
+2
+\series default
+ (
+\begin_inset Formula $\nabla^{2}$
+\end_inset
+
+) à la place de
+\series bold
+
+\backslash
+bigtriangleup
+\series default
+ .
+\end_layout
+
+\begin_layout Standard
+Le caractère
+\family sans
+Séparateur\InsetSpace ~
+de\InsetSpace ~
+menu
+\family default
+ du menu
+\family sans
+Insérer\SpecialChar \menuseparator
+Caractères\InsetSpace ~
+spécial
+\family default
+ est en fait l'opérateur
+\series bold
+
+\backslash
+triangleright
+\series default
+.
+\end_layout
+
+\begin_layout Subsection
+Opérateurs personnalisés
+\begin_inset LatexCommand label
+name "sub:Opérateurs-personnalisés"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Opérateurs ! personnalisés"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Avec l'aide de la commande
+\series bold
+
+\backslash
+DeclareMathOperator
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! D ! \\textbackslash dbinom@\\textbackslash DeclareMathOperator"
+
+\end_inset
+
+, on peut définir des opérateurs personnalisés dans le préambule LaTeX.
+ La syntaxe de la commande est:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+DeclareMathOperator{nouvelle commande}{affichage}
+\end_layout
+
+\begin_layout Standard
+L'affichage peut être composé de caractères ou de symboles qui définissent
+ comment l'opérateur doit apparaître dans la sortie finale.
+ Pour définir un grand opérateur, on met une * après la commande.
+ Tous les grands opérateurs personnalisés peuvent avoir des limites comme
+ c'est décrit dans
+\begin_inset LatexCommand ref
+reference "sub:Limites-des-opérateurs"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+Par exemple la ligne
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+DeclareMathOperator*{
+\backslash
+Losange}{
+\backslash
+blacklozenge}
+\end_layout
+
+\begin_layout Standard
+dans le préambule LaTeX définit la commande
+\series bold
+
+\backslash
+Losange
+\series default
+, qui insère un grand opérateur qui consiste en un symbole losange venant
+ de
+\begin_inset LatexCommand ref
+reference "sub:Symboles-divers"
+
+\end_inset
+
+:
+\begin_inset Formula \[
+\Losange_{n=1}^{\infty}\]
+
+\end_inset
+
+La commande utilisée pour cette formule est:
+\series bold
+
+\backslash
+Losange
+\series default
+^
+\series bold
+
+\backslash
+infty
+\begin_inset Formula $\to$
+\end_inset
+
+_n=1
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Quand un opérateur personnalisé n'est pas utilisé plusieurs fois dans le
+ document, on peut aussi le définir avec les commandes
+\series bold
+
+\backslash
+mathop
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! M ! \\textbackslash mathop"
+
+\end_inset
+
+ et
+\series bold
+
+\backslash
+mathbin
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! M ! \\textbackslash mathbin"
+
+\end_inset
+
+, qui ont les syntaxes suivantes:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+mathop{affichage}
+\series default
+ et
+\series bold
+
+\backslash
+mathbin{affichage}
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+mathop
+\series default
+ définit des grands opérateurs et
+\series bold
+
+\backslash
+mathbin
+\series default
+ des opérateurs binaires.
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+mathop
+\series default
+ peut par exemple servir à mettre une limite à plusieurs opérateurs:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+\mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+La commande pour la formule précédente est:
+\newline
+
+\series bold
+
+\backslash
+mathop{
+\backslash
+sum
+\backslash
+negmedspace
+\backslash
+sum
+\series default
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\begin_inset Formula $\to$
+\end_inset
+
+^N
+\series default
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\series bold
+_i,j=1
+\end_layout
+
+\begin_layout Section
+Polices de caractères
+\begin_inset LatexCommand index
+name "Polices de caractères"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Fontes| see{Polices de caractères}"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Styles de polices
+\begin_inset LatexCommand label
+name "sub:Styles-de-polices"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Polices de caractères ! style"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Dans les formules on peut affecter aux lettres latines un des styles de
+ police suivant:
+\begin_inset VSpace -2mm
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="6" columns="3">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Raccourci
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mathbb
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+ABC
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mathbb{ABC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Alt-z k
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mathbf
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+AbC
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mathbf{AbC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Alt-z f
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+boldsymbol
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+AbC
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\boldsymbol{AbC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+-
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mathcal
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+ABC
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mathcal{ABC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Alt-z h
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mathfrak
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+AbC
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mathfrak{AbC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+-
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="3">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Raccourci
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mathit
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+AbC
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mathit{AbC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+-
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mathrm
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+AbC
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mathrm{AbC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Alt-z r
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mathsf
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+AbC
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mathsf{AbC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Alt-z s
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mathtt
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+AbC
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mathtt{AbC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+-
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Standard
+
+\series bold
+Note:
+\series default
+ Les styles
+\series bold
+
+\backslash
+mathbb
+\series default
+ et
+\series bold
+
+\backslash
+mathcal
+\series default
+ ne peuvent être utilisés que pour les lettres majuscules.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Le style prédéfini est
+\series bold
+
+\backslash
+mathnormal
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+Les commandes de style fonctionnent aussi pour des caractères dans des construct
+ions mathématiques:
+\begin_inset Formula \[
+\mathfrak{A=\frac{b}{C}}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Les caractères en texte mathématique n'apparaissent pas avec un style de
+ police mathématique mais avec le style de police texte
+\series bold
+
+\backslash
+textrm
+\series default
+.
+ Le fait que l'on ne puisse pas changer leur style avec la fenêtre de dialogue
+ de style est un bug de LyX.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://bugzilla.lyx.org/show_bug.cgi?id=4091}{
+\end_layout
+
+\end_inset
+
+LyX-bug #4091
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+À la place des commandes de style, on peut utiliser le menu
+\family sans
+Éditer\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Style\InsetSpace ~
+de\InsetSpace ~
+Texte
+\family default
+ ou le bouton
+\begin_inset Graphics
+ filename ../../images/math/font.png
+ scale 85
+
+\end_inset
+
+ de la barre d'outils mathématique.
+\end_layout
+
+\begin_layout Subsection
+Formules en gras
+\begin_inset LatexCommand label
+name "sub:Formules-en-gras"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formules ! en gras"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Pour mettre toute une formule en gras, on ne peut pas utiliser la commande
+
+\series bold
+
+\backslash
+mathbf
+\series default
+ de la sous-section précédente, parce qu'elle ne marche pas avec les lettres
+ grecques minuscules.
+ En plus elle affiche toujours les lettres latines en caractères droits,
+ comme dans l'équation suivante:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+\mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{équation avec \textbackslash mathbf}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Pour afficher cette formule correctement; on utilise la commande
+\series bold
+
+\backslash
+boldsymbol
+\series default
+:
+\begin_inset Formula \[
+\boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{équation avec \textbackslash boldsymbol}}\]
+
+\end_inset
+
+Il est aussi possible de mettre l'équation dans un environnement
+\series bold
+boldmath
+\series default
+.
+ On crée cet environnement en insérant la commande
+\series bold
+
+\backslash
+boldmath
+\begin_inset LatexCommand index
+name "Commandes ! B ! \\textbackslash boldmath"
+
+\end_inset
+
+
+\series default
+ en mode TeX.
+ Pour terminer l'environnement, on insère la commande
+\series bold
+
+\backslash
+unboldmath
+\begin_inset LatexCommand index
+name "Commandes ! U ! \\textbackslash unboldmath"
+
+\end_inset
+
+
+\series default
+ toujours en mode TeX.
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+boldmath
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \[
+\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{équation dans un environnement boldmath}\]
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+unboldmath
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Tailles de polices
+\begin_inset LatexCommand label
+name "sub:Tailles-polices"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Polices ! tailles"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Pour les caractères qui se trouvent dans des formules, il y a, comme pour
+ les caractères qui sont dans le texte, les commandes de changement de taille
+ suivantes:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+Huge
+\series default
+,
+\series bold
+
+\backslash
+huge
+\series default
+,
+\series bold
+
+\backslash
+LARGE
+\series default
+,
+\series bold
+
+\backslash
+Large
+\series default
+,
+\series bold
+
+\backslash
+large
+\series default
+,
+\series bold
+
+\backslash
+normalsize
+\series default
+,
+\series bold
+
+\backslash
+small
+\series default
+,
+\newline
+
+\series bold
+
+\backslash
+footnotesize
+\series default
+,
+\series bold
+
+\backslash
+scriptsize
+\series default
+, et
+\series bold
+
+\backslash
+tiny
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Qui correspondent respectivement aux tailles Énorme, Très très grand, Très
+ grand, Grand, Normal, Petit, Très petit, Tout petit et Minuscule (NdT).
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+La taille des caractères produits par ces commandes dépend de la taille
+ de police du document, qui correspond à la commande
+\series bold
+
+\backslash
+normalsize
+\series default
+.
+ Les autres commandes produisent des tailles plus ou moins grandes que
+\series bold
+
+\backslash
+normalsize
+\series default
+.
+ La taille de la police ne peut donc pas dépasser une certaine valeur.
+ Par exemple, pour un document dans une police de taille 12\InsetSpace \thinspace{}
+pt, la commande
+
+\series bold
+
+\backslash
+Huge
+\series default
+ va donner la même taille que
+\series bold
+
+\backslash
+huge
+\series default
+.
+
+\end_layout
+
+\begin_layout Standard
+Une commande de changement de taille est insérée en mode TeX avant la formule
+ et fixe la taille de toutes les formules qui suivent ainsi que celle des
+ caractères du texte.
+ Pour revenir à la taille initiale, on doit insérer la commande
+\series bold
+
+\backslash
+normalsize
+\series default
+ en mode TeX après la formule.
+\end_layout
+
+\begin_layout Standard
+À l'intérieur de la formule, on ne peut changer la taille que des caractères
+ ou des symboles qui sont en mode texte mathématique.
+ Pour le faire, on insère la commande de changement de taille en mode texte
+ mathématique.
+ Tous les caractères qui suivent jusqu'à la fin du texte mathématique ou
+ jusqu'à ce que la taille soit de nouveau modifiée, auront la taille choisie.
+ Deux exemples:
+\begin_inset VSpace -2mm
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+huge
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \[
+A=\frac{B}{c}\cdot\maltese\]
+
+\end_inset
+
+
+\begin_inset Formula \[
+\maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+normalsize
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Avant les deux formules, on a inséré la commande
+\series bold
+
+\backslash
+huge
+\series default
+.
+ La commande utilisée pour la deuxième formule est:
+\newline
+
+\series bold
+
+\backslash
+maltese
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A Alt-m m
+\backslash
+Large
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\backslash
+maltese
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\backslash
+textit
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\begin_inset Formula $\to$
+\end_inset
+
+
+\begin_inset Formula $\to$
+\end_inset
+
+
+\newline
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+hspace*{1cm}
+\end_layout
+
+\end_inset
+
+Alt-m
+\series default
+
+\series bold
+m
+\backslash
+tiny
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\backslash
+maltese
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\backslash
+textit
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\begin_layout Standard
+Si un symbole ne peut pas être affiché dans plusieurs tailles, il sera toujours
+ affiché dans la taille par défaut
+\end_layout
+
+\begin_layout Section
+Les lettres grecques
+\begin_inset LatexCommand index
+name "Lettres grecques"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+On peut insérer toutes les lettres grecques avec le bouton
+\begin_inset Graphics
+ filename ../../images/math/alpha.png
+ scale 85
+
+\end_inset
+
+ de la barre d'outils mathématiques.
+\end_layout
+
+\begin_layout Subsection
+Lettres minuscules
+\begin_inset LatexCommand label
+name "sub:Minuscules"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Lettres grecques ! minuscules"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\lang english
+
+\hfill
+
+\lang french
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="11" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+alpha
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\alpha$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+beta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\beta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+gamma
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\gamma$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+delta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\delta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+epsilon
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\epsilon$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+varepsilon
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\varepsilon$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+zeta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\zeta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+eta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\eta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+theta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\theta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+vartheta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\vartheta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="12" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+iota
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\iota$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+kappa
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\kappa$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+varkappa
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\varkappa$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+lambda
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\lambda$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mu
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mu$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+nu
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\nu$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+xi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\xi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+o
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $o$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+pi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\pi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+varpi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\varpi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+rho
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\rho$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="11" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+varrho
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\varrho$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sigma
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\sigma$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+varsigma
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\varsigma$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+tau
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\tau$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+upsilon
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\upsilon$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+phi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\phi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+varphi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\varphi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+chi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\chi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+psi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\psi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+omega
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\omega$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\lang english
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+On explique comment obtenir des lettres grecques droites dans
+\begin_inset LatexCommand ref
+reference "sub:minuscules-grecques-droites"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Lettres majuscules
+\begin_inset LatexCommand index
+name "Lettres grecques ! majuscules"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\lang english
+
+\hfill
+
+\lang french
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="7" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Gamma
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Gamma$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Delta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Delta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Theta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Theta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Lambda
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Lambda$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Xi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Xi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Pi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Pi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="6" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Sigma
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Sigma$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Upsilon
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Upsilon$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Phi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Phi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Psi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Psi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Omega
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Omega$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\lang english
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Le fait que les lettres grecques majuscules apparaissent droites provient
+ d'un défaut de conception quand TeX a été développé.
+ Pour obtenir des lettres majuscules italiques correctes, commencez chaque
+ commande par
+\series bold
+var
+\series default
+.
+ Par exemple, la commande
+\series bold
+
+\backslash
+varGamma
+\series default
+ produit:
+\begin_inset Formula $\varGamma$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Lettres grasses
+\begin_inset LatexCommand index
+name "Lettres grecques ! grasses"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Les lettres grecques ne peuvent être mise dans différents styles de polices
+ comme les lettres latines.
+ Elles peuvent seulement être mises en gras avec la commande
+\series bold
+
+\backslash
+boldsymbol
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! B ! \\textbackslash boldsymbol"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Upsilon
+\backslash
+boldsymbol
+\backslash
+Upsilon
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+theta
+\backslash
+boldsymbol
+\backslash
+theta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\theta\boldsymbol{\theta}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Symboles
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+texorpdfstring{
+\end_layout
+
+\end_inset
+
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Une liste avec tous les symboles de la plupart des paquetages LaTeX peut
+ être trouvée dans
+\begin_inset LatexCommand cite
+key "Symbole"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}{}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\backslash
+texorpdfstring est utilisée pour éviter que la note de bas de page n'apparaisse
+ dans les signets PDF.
+\end_layout
+
+\begin_layout Standard
+Plus au sujet de
+\backslash
+texorpdfstring dans la section
+\begin_inset LatexCommand ref
+reference "sub:formules-dans-les-entêtes"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Symboles"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Plusieurs symboles listés dans cette section peuvent aussi être insérés
+ grâce aux boutons
+\begin_inset Graphics
+ filename ../../images/math/nabla.png
+ scale 85
+
+\end_inset
+
+ et
+\begin_inset Graphics
+ filename ../../images/math/digamma.png
+ scale 85
+
+\end_inset
+
+ de la barre d'outils mathématique.
+\end_layout
+
+\begin_layout Subsection
+Symboles mathématiques
+\begin_inset LatexCommand label
+name "sub:Symboles-mathématiques"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Symboles ! mathématiques"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="10" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+neg
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\neg$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Im
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Im$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Re
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Re$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+aleph
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\aleph$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+partial
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\partial$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+infty
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\infty$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+wp
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\wp$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+imath
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\imath$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+jmath
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\jmath$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="10" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox est seulement utilisée pour faire de la place
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+forall
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\forall$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+exists
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\exists$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+nexists
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\nexists$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+emptyset
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\emptyset$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+varnothing
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\varnothing$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+dag
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\dag$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ddag
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\ddag$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+complement
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+raisebox{-0.8mm}{
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula $\complement$
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Bbbk
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Bbbk$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="10" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+prime
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\prime$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+backprime
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\backprime$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mho
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mho$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+triangle
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\triangle$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+angle
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\angle$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+measuredangle
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\measuredangle$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sphericalangle
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\sphericalangle$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+top
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\top$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bot
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bot$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+
+\newpage
+
+\end_layout
+
+\begin_layout Subsection
+Symboles divers
+\begin_inset LatexCommand label
+name "sub:Symboles-divers"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Symboles ! divers"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="10" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+flat
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\flat$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+natural
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\natural$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sharp
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\sharp$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+surd
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\surd$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+checkmark
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\checkmark$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+yen
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\yen$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+pounds
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\pounds$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+$
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\$$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+§
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $§$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="10" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+hbar
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\hbar$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+hslash
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\hslash$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+clubsuit
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\clubsuit$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+spadesuit
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\spadesuit$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigstar
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bigstar$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+blacklozenge
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\blacklozenge$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+blacktriangle
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\blacktriangle$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+blacktiangledown
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\blacktriangledown$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bullet
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bullet$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="10" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+diamondsuit
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\diamondsuit$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Diamond
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Diamond$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+heartsuit
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\heartsuit$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+P
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\P$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+copyright
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\copyright$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+circledR
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\circledR$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+maltese
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\maltese$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+diagup
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\diagup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+diagdown
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\diagdown$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+D'autres symboles sont listés dans
+\begin_inset LatexCommand ref
+reference "sub:Caractères-spéciaux-divers"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+Certains symboles peuvent être affichés dans plusieurs tailles, voir
+\begin_inset LatexCommand ref
+reference "sub:Tailles-polices"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Le symbole de l'Euro €
+\begin_inset LatexCommand index
+name "Symboles ! symbole de l'Euro"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "\\textcent@\\officialeuro"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Pour utiliser le symbole de l'Euro dans une formule, il faut installer le
+ paquetage LaTeX
+\series bold
+eurosym
+\series default
+
+\begin_inset LatexCommand index
+name "Paquetages ! eurosym"
+
+\end_inset
+
+ et le charger avec la ligne suivante dans le préambule LaTeX
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage[gennarrow]{eurosym}
+\end_layout
+
+\begin_layout Standard
+Le symbole de l'Euro peut alors être inséré avec la commande
+\series bold
+
+\backslash
+euro
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! E ! \\textbackslash euro"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+On peut aussi insérer le symbole de l'Euro directement en mode texte mathématiqu
+e avec la touche €, sans avoir à installer le paquetage
+\series bold
+eurosym
+\series default
+.
+ Quand
+\series bold
+eurosym
+\series default
+ est installé, on peut aussi insérer la commande
+\series bold
+
+\backslash
+euro
+\series default
+ en mode TeX.
+ Le symbole monétaire officiel de l'Euro peut être inséré avec la commande
+
+\series bold
+
+\backslash
+officialeuro
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! O ! \\textbackslash officialeuro"
+
+\end_inset
+
+, qui n'est utilisable qu'en mode TeX.
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+ifeurosym
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Standard
+Le tableau suivant ne sera affiché que si le paquetage LaTeX
+\series bold
+eurosym
+\series default
+ est installé.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Un aperçu des différents symboles de l'Euro:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="3">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+formule
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+euro
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\euro$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+texte mathématique
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+€
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mbox{€}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+mode TeX
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+officialeuro
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+officialeuro
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+else
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Standard
+Ce qui suit sera affiché si le paquetage LaTeX
+\series bold
+eurosym
+\series default
+ n'est pas installé:
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Vous devez installer le paquetage LaTeX
+\series bold
+eurosym
+\series default
+ pour voir le reste de cette section dans la sortie imprimée.
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+fi
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Opérateurs de relation
+\begin_inset LatexCommand label
+name "sec:Relations"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Relations"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Comparaisons|see{Relations}"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Tous les opérateurs de relation peuvent aussi être insérés en passant par
+ le bouton
+\begin_inset Graphics
+ filename ../../images/math/leq.png
+ scale 85
+
+\end_inset
+
+ de la barre d'outils.
+\end_layout
+
+\begin_layout Standard
+
+\lang english
+
+\hfill
+
+\lang french
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="17" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+<
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $<$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+le
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\le$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ll
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\ll$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+prec
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\prec$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+preceq
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\preceq$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+subset
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\subset$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+subseteq
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\subseteq$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sqsubseteq
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\sqsubseteq$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+in
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\in$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+vdash
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\vdash$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+smile
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\smile$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+lhd
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\lhd$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+unlhd
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\unlhd$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+gtrless
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\gtrless$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mid
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mid$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+nmid
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\nmid$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="17" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+=
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $=$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+not=
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\not=$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+equiv
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\equiv$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sim
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\sim$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+simeq
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\simeq$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+approx
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\approx$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+cong
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\cong$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bowtie
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bowtie$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+notin
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\notin$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+perp
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\perp$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+propto
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\propto$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+asymp
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\asymp$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+doteq
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\doteq$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+circeq
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\circeq$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+models
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\models$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+widehat=
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\widehat{=}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="17" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+>
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $>$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ge
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\ge$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+gg
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\gg$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+succ
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\succ$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+succeq
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\succeq$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+supset
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\supset$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+supseteq
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\supseteq$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sqsupseteq
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\sqsupseteq$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ni
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\ni$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+dashv
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\dashv$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+frown
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\frown$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+rhd
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\rhd$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+unrhd
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\unrhd$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+lessgtr
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\lessgtr$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+parallel
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\parallel$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+nparallel
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\nparallel$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\lang english
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Les caractères
+\series bold
+
+\backslash
+lhd
+\series default
+ et
+\series bold
+
+\backslash
+rhd
+\series default
+ sont plus gros que les opérateurs
+\series bold
+
+\backslash
+triangleleft
+\series default
+ et
+\series bold
+
+\backslash
+triangleright
+\series default
+ auxquels ils ressemblent.
+\end_layout
+
+\begin_layout Standard
+Les opérateurs de relation sont, contrairement aux symboles, toujours entourés
+ par des espaces.
+\end_layout
+
+\begin_layout Standard
+Les opérateurs de relation avec des étiquettes peuvent être créés avec la
+ commande
+\series bold
+
+\backslash
+stackrel
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! S ! \\textbackslash stackrel"
+
+\end_inset
+
+:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox est seulement utilisée pour faire de la place
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A(r)
+\backslash
+stackrel
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+r
+\backslash
+to
+\backslash
+infty
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula $\downarrow$
+\end_inset
+
+
+\backslash
+approx
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Fonctions
+\end_layout
+
+\begin_layout Subsection
+Fonctions prédéfinies
+\begin_inset LatexCommand label
+name "sub:Fonctions-prédéfinies"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Fonctions ! prédéfinies"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+En général, les variables sont écrites en
+\emph on
+italiques
+\emph default
+ dans les expressions mathématiques, mais pas les noms des fonctions, puisque
+
+\begin_inset Formula $sin$
+\end_inset
+
+ pourrait être confondue avec le produit
+\begin_inset Formula $s\cdot i\cdot n$
+\end_inset
+
+.
+ Il y a donc des fonctions prédéfinies qui sont en plus séparées de leurs
+ arguments par un peu d'espace.
+ Elles sont insérées comme des commandes commençant par une barre de fraction
+ inverse avant leur nom.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="4">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Asin(x)+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $Asin(x)+B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A
+\backslash
+sin(x)+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\sin(x)+B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+pagebreak
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Les fonctions suivantes sont prédéfinies:
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace -2mm
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="9" columns="4">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sin
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sinh
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+arcsin
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sup
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+cos
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+cosh
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+arccos
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+inf
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+tan
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+tanh
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+arctan
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+lim
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+cot
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+coth
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+arg
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+liminf
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sec
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+min
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+deg
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+limsup
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+csc
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+max
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+det
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Pr
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ln
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+exp
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+dim
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+hom
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+lg
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+log
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ker
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+gcd
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Elles peuvent aussi être insérées en utilisant le bouton
+\begin_inset Graphics
+ filename ../../images/math/functions.png
+ scale 85
+
+\end_inset
+
+ de la barre d'outils mathématique.
+\end_layout
+
+\begin_layout Subsection
+Fonctions définies par l'utilisateur
+\begin_inset LatexCommand index
+name "Fonctions ! définies par l'utilisateur"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Pour utiliser une fonction qui n'est pas prédéfinie, comme par exemple la
+ fonction sgn(x), il y a deux possibilités:
+\end_layout
+
+\begin_layout Itemize
+Définir la fonction en insérant la ligne suivante dans le préambule LaTeX
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Pour en savoir plus sur la commande
+\series bold
+
+\backslash
+DeclareMathOperator
+\series default
+ voir
+\begin_inset LatexCommand ref
+reference "sub:Opérateurs-personnalisés"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\newline
+
+\begin_inset VSpace -3mm
+\end_inset
+
+
+\newline
+
+\series bold
+
+\backslash
+DeclareMathOperator{
+\backslash
+sgn}{sgn}
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! D ! \\textbackslash dbinom@\\textbackslash DeclareMathOperator"
+
+\end_inset
+
+
+\newline
+
+\begin_inset VSpace -2mm
+\end_inset
+
+
+\newline
+Maintenant la fonction qui vient d'être définie peut être appelée avec la
+ commande
+\series bold
+
+\backslash
+sgn
+\series default
+.
+\end_layout
+
+\begin_layout Itemize
+Écrire la formule comme d'habitude, marquer le nom de la fonction -- dans
+ notre exemple les lettres
+\emph on
+sgn
+\emph default
+ -- et les changer en texte mathématique.
+ Pour finir, on insère une espace entre le préfacteur et la fonction.
+\end_layout
+
+\begin_layout Standard
+Le résultat avec les deux méthodes est le même qu'avec les fonctions prédéfinies
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Dans LyX, les fonctions prédéfinies sont en noir, celles définies par l'utilisat
+eur en rouge.
+\end_layout
+
+\end_inset
+
+:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A
+\backslash
+sgn(x)+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\sgn(x)+B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A
+\backslash
+,
+\begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt-m}\,\textrm{m}}$
+\end_inset
+
+(x)+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\,\textrm{sgn}(x)+B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+La première méthode est recommandée quand la fonction définie doit être
+ utilisée plusieurs fois dans le document.
+\end_layout
+
+\begin_layout Subsection
+Les limites
+\begin_inset LatexCommand index
+name "Limites"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Pour les limites, en plus des commandes
+\series bold
+
+\backslash
+lim
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! L ! \\textbackslash lim"
+
+\end_inset
+
+,
+\series bold
+
+\backslash
+liminf
+\series default
+ et
+\series bold
+
+\backslash
+limsup
+\series default
+ on a aussi les fonctions suivantes:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox est seulement utilisée pour faire de la place
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+varliminf
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\varliminf$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+varlimsup
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\varlimsup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+varprojlim
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\varprojlim$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+varinjlim
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\varinjlim$
+\end_inset
+
+
+\begin_inset Formula $\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+La valeur de la limite est créée en ajoutant un indice.
+ Il est placé juste à la droite de la fonction dans le cas d'une formule
+ en ligne:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="2">
+<features>
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+hspace{1cm}
+\end_layout
+
+\end_inset
+
+Résultat
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+hspace
+\series default
+
+\series bold
+et
+\backslash
+raisebox sont seulement utilisées pour faire de la place
+\series default
+\lang english
+.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+lim_x
+\backslash
+to
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+x=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Dans une formule hors ligne la valeur de la limite est placée comme d'habitude,
+ en dessous de la fonction:
+\begin_inset Formula \[
+\lim_{x\to A}x=B\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Les fonctions modulo-
+\begin_inset LatexCommand index
+name "Fonctions ! modulo"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+La fonction modulo est un peu spéciale, vu qu'il en existe quatre variantes.
+\end_layout
+
+\begin_layout Standard
+Les variantes pour une formule hors ligne:
+\begin_inset Formula \begin{align*}
+\underline{\textrm{Commande}\raisebox{-0.9mm}{}} & & \underline{\textrm{Résultat}}\\
+\mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
+\mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
+\mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
+\mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Dans une formule en ligne, il y a moins d'espace inséré avant le nom de
+ la fonction, quelque soit la variante.
+\end_layout
+
+\begin_layout Section
+Caractères spéciaux
+\begin_inset LatexCommand index
+name "Caractères spéciaux"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Caractères spéciaux en texte mathématique
+\end_layout
+
+\begin_layout Standard
+Les commandes suivantes ne peuvent être utilisées qu'en texte mathématique
+ ou en mode TeX:
+\end_layout
+
+\begin_layout Standard
+
+\lang english
+
+\hfill
+
+\lang french
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="2">
+<features>
+<column alignment="block" valignment="top" leftline="true" width="0">
+<column alignment="block" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+oe
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{\oe}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+OE
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{\OE}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ae
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{\ae}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+AE
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{\AE}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+aa
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{\aa}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+AA
+\begin_inset LatexCommand index
+name "\\@\\textrm{\\AA}"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{\AA}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+i
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{\i}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="2">
+<features>
+<column alignment="block" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+commande
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+la commande
+\series bold
+
+\backslash
+hspace{0mm}
+\series default
+ est utilisée pour faire une séparation invisible, sinon la sortie finale
+ serait respectivement ¡ et ¿.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+o
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{\o}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+O
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{\O}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+l
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{\l}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+L
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{\L}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+!
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+hspace{0mm}
+\end_layout
+
+\end_inset
+
+`
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{!`}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+?
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+hspace{0mm}
+\end_layout
+
+\end_inset
+
+`
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{?`}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+j
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{\j}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\lang english
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+Les caractères
+\begin_inset Formula $\textrm{\textrm{Å}}$
+\end_inset
+
+ et
+\begin_inset Formula $\textrm{\textrm{Ø}}$
+\end_inset
+
+ peuvent aussi être insérés avec le bouton
+\begin_inset Graphics
+ filename ../../images/math/digamma.png
+ scale 85
+
+\end_inset
+
+ de la barre d'outils mathématique.
+\end_layout
+
+\begin_layout Standard
+Les commandes
+\series bold
+!
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+hspace{0mm}
+\end_layout
+
+\end_inset
+
+`
+\series default
+ et
+\series bold
+?
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+hspace{0mm}
+\end_layout
+
+\end_inset
+
+`
+\series default
+ sont des exceptions puisqu'elles peuvent être insérées directement dans
+ le texte dans LyX.
+\end_layout
+
+\begin_layout Subsection
+Les accents dans le texte
+\begin_inset LatexCommand label
+name "sub:Accents-dans-le-texte"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Accents ! dans le texte"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Avec les commandes suivantes, on peut accentuer toutes les lettres.
+ Ces commandes doivent être insérées en mode TeX.
+\end_layout
+
+\begin_layout Standard
+
+\lang english
+
+\hfill
+
+\lang french
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="2">
+<features>
+<column alignment="block" valignment="top" leftline="true" width="0">
+<column alignment="block" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+
+\begin_inset Quotes grd
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+"e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+`e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+`e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+^
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+^e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+=e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+=e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+u
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+u e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+b
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+b e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+t
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+ee
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+t ee
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="2">
+<features>
+<column alignment="block" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+H
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+H e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+'e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+'e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+~e
+\begin_inset LatexCommand index
+name "Tilde"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+~e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+.e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+.e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+v
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+v e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+d
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+d e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+c
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+c e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Avec la commande
+\series bold
+
+\backslash
+t
+\series default
+ on peut aussi accentuer deux caractères différents.
+ La commande
+\series bold
+
+\backslash
+t
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+sz
+\series default
+ va donner:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+t sz
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Les accents
+\series bold
+`
+\series default
+ ,
+\series bold
+'
+\series default
+ , et
+\series bold
+^
+\series default
+ peuvent être insérés directement avec le clavier, sans utiliser le mode
+ TeX, quand ils sont utilisés avec des voyelles.
+ La même chose s'applique au tilde
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Ceci s'applique uniquement aux claviers où le tilde est défini comme un
+ accent.
+\end_layout
+
+\end_inset
+
+
+\series bold
+~
+\series default
+ en combinaison avec
+\emph on
+a
+\emph default
+ ,
+\emph on
+n
+\emph default
+ , ou
+\emph on
+o
+\emph default
+.
+\end_layout
+
+\begin_layout Standard
+Les commandes
+\series bold
+
+\backslash
+b
+\series default
+ ,
+\series bold
+
+\backslash
+c
+\series default
+ ,
+\series bold
+
+\backslash
+d
+\series default
+ ,
+\series bold
+
+\backslash
+H
+\series default
+ ,
+\series bold
+
+\backslash
+t
+\series default
+ ,
+\series bold
+
+\backslash
+u
+\series default
+ ,
+\series bold
+
+\backslash
+v
+\series default
+, et les accents qui sont insérés directement au clavier sont aussi disponibles
+ en texte mathématique.
+ Pour les autres accents, il y a des commandes mathématiques spéciales à
+ utiliser dans les formules, voir
+\begin_inset LatexCommand ref
+reference "sub:Accents-sur-un-caractère"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+En plus, avec la commande
+\series bold
+
+\backslash
+textcircled
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! T ! \\textbackslash textcircled"
+
+\end_inset
+
+ tous les nombres et toutes les lettres peuvent être mises dans un cercle,
+ comme pour le symbole du copyright.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox est seulement utilisée pour faire de la place
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+textcircled{w}
+\end_layout
+
+\end_inset
+</cell>
+<cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+textcircled{w}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Large
+\backslash
+textcircled{
+\backslash
+normalsize
+\backslash
+protect
+\backslash
+raisebox{-1.5pt}{W}}
+\end_layout
+
+\end_inset
+</cell>
+<cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}$
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+Large
+\backslash
+textcircled{
+\backslash
+normalsize
+\backslash
+protect
+\backslash
+raisebox{-1.5pt}W}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula $\raisebox{-2mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+On doit faire attentions à ce que le caractère tienne dans le cercle.
+
+\series bold
+
+\backslash
+Large
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+voir
+\begin_inset LatexCommand ref
+reference "sub:Tailles-polices"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ donne ici la taille du cercle.
+ On peut centrer le caractère avec l'aide de la commande
+\series bold
+
+\backslash
+raisebox
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+voir
+\begin_inset LatexCommand ref
+reference "sub:Boîtes-sans-cadre"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ .
+\end_layout
+
+\begin_layout Subsection
+Nombres en minuscules
+\begin_inset LatexCommand index
+name "Minuscules pour les nombres"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Les nombres en minuscule sont créés avec la commande
+\series bold
+
+\backslash
+oldstylenums
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! O ! \\textbackslash oldstylenums"
+
+\end_inset
+
+.
+ Cette commande peut être utilisée dans des formules et aussi en mode TeX.
+ La syntaxe de la commande est:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+oldstylenums{nombre}
+\end_layout
+
+\begin_layout Standard
+La commande
+\series bold
+
+\backslash
+oldstylenums{0123456789
+\series default
+ donne:
+\begin_inset Formula $\oldstylenums{0123456789}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Caractères spéciaux divers
+\begin_inset LatexCommand label
+name "sub:Caractères-spéciaux-divers"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Caractères spéciaux ! divers"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Les caractères suivants ne peuvent être insérés que dans des formules en
+ utilisant les commandes suivantes:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+^
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mathcircumflex$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+_
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\_$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+^
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\backslash
+circ
+\begin_inset LatexCommand index
+name "°"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $^{\circ}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Le symbole degré ° peut être inséré directement à condition que le préambule
+ LaTeX contienne la ligne suivante
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Plus d'information à ce sujet dans
+\begin_inset LatexCommand ref
+reference "sub:Caractères-texte"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+DeclareInputtext{176}{
+\backslash
+ifmmode^
+\backslash
+circ
+\backslash
+else
+\backslash
+textdegree
+\backslash
+f\SpecialChar \textcompwordmark{}
+i}
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Le tilde
+\begin_inset LatexCommand index
+name "Tilde"
+
+\end_inset
+
+ est conçu pour être un accent, il semble un peu déplacé quand il est seul:
+ ~
+\newline
+Mais pour les adresses internet (les URLs), on a parfois besoin d'un tilde
+ tout seul.
+ Dans ce cas on peut utiliser l'opérateur de relation
+\series bold
+
+\backslash
+sim
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+voir
+\begin_inset LatexCommand ref
+reference "sec:Relations"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series default
+ dans une formule.
+ Comme on ne peut pas insérer une formule dans une boîte d'URL (menu
+\family sans
+Insérer\SpecialChar \menuseparator
+URL
+\family default
+), l'URL est insérée comme du texte normal en police '
+\family typewriter
+machine à écrire
+\family default
+'.
+ Si l'URL doit être un hyperlien dans la sortie DVI ou PDF, il faut utiliser
+ la commande
+\series bold
+
+\backslash
+href
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+href
+\series default
+ peut être utilisé uniquement avec le paquetage LaTeX
+\series bold
+hyperref
+\series default
+
+\begin_inset LatexCommand index
+name "Paquetages ! hyperref"
+
+\end_inset
+
+.
+ Plus d'information sur
+\series bold
+
+\backslash
+href
+\series default
+ est donné dans la section
+\family typewriter
+URL
+\family default
+ du manuel
+\family typewriter
+Objets\InsetSpace ~
+insérés
+\family default
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Commandes ! H ! \\textbackslash href"
+
+\end_inset
+
+ .
+\end_layout
+
+\begin_layout Standard
+Un exemple d'URL avec un tilde:
+\end_layout
+
+\begin_layout Standard
+en tant que texte:
+\family typewriter
+http://www.lyx.org/
+\begin_inset Formula $\sim$
+\end_inset
+
+mustermann
+\end_layout
+
+\begin_layout Standard
+avec
+\series bold
+
+\backslash
+href
+\series default
+:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://www.lyx.org/~mustermann}{
+\end_layout
+
+\end_inset
+
+http://www.lyx.org/
+\begin_inset Formula $\sim$
+\end_inset
+
+mustermann
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Styles de formules
+\begin_inset LatexCommand label
+name "sec:Styles-de-formules"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formules ! styles"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+Il y a deux styles d'alignements différents:
+\end_layout
+
+\begin_deeper
+\begin_layout Description
+Centré est le standard prédéfini
+\end_layout
+
+\begin_layout Description
+Indenté pour ce style, l'option
+\series bold
+fleqn
+\series default
+ doit être insérée dans la fenêtre de dialogue
+\family sans
+Document\SpecialChar \menuseparator
+Paramètres
+\family default
+ dans la rubrique
+\family sans
+Classe\InsetSpace ~
+de\InsetSpace ~
+Document
+\end_layout
+
+\begin_layout Standard
+Quand on utilise
+\series bold
+Indenté
+\series default
+, la profondeur de l'indentation peut être ajustée en modifiant la longueur
+
+\series bold
+
+\backslash
+mathindent
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! M ! \\textbackslash mathindent"
+
+\end_inset
+
+.
+ Par exemple, pour une distance de 15\InsetSpace \thinspace{}
+mm, on insère la ligne de commande
+ suivante dans le préambule LaTeX
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+setlength{
+\backslash
+mathindent}{15mm}
+\end_layout
+
+\begin_layout Standard
+Si on ne spécifie pas de distance, la valeur prédéfinie de 30\InsetSpace \thinspace{}
+pt est utilisée.
+\end_layout
+
+\end_deeper
+\begin_layout Itemize
+Et deux styles différents de numérotation:
+\end_layout
+
+\begin_deeper
+\begin_layout Description
+Droite est le standard prédéfini
+\end_layout
+
+\begin_layout Description
+Gauche pour ce style, l'option
+\series bold
+leqno
+\series default
+ doit être insérée dans la fenêtre de dialogue
+\family sans
+Document\SpecialChar \menuseparator
+Paramètres
+\family default
+ dans la rubrique
+\family sans
+Classe\InsetSpace ~
+de\InsetSpace ~
+Document
+\end_layout
+
+\end_deeper
+\begin_layout Standard
+
+\series bold
+fleqn
+\series default
+ et
+\series bold
+leqno
+\series default
+ peuvent être utilisés ensembles.
+ Dans ce cas les deux options sont insérées, séparées par une virgule.
+\end_layout
+
+\begin_layout Standard
+Les styles choisis sont utilisés par toutes les formules du document.
+ Quand il faut créer à la fois des formules centrées et des formules alignées,
+ on utilise le style
+\series bold
+Centré
+\series default
+.
+ Les formules indentées sont alors placées dans un environnement
+\series bold
+falign,
+\series default
+voir
+\begin_inset LatexCommand ref
+reference "sub:environnement-Flalign"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Section
+Formules multi-lignes
+\begin_inset LatexCommand label
+name "sec:Formules-multilignes"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formules ! multi-lignes"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Généralités
+\end_layout
+
+\begin_layout Standard
+Dans LyX, on crée les formules multi-lignes en appuyant sur
+\family sans
+\series bold
+Ctrl-Entrée
+\family default
+\series default
+ à l'intérieur d'une formule.
+ Cela crée un environnement
+\series bold
+align
+\series default
+qui est décrit dans
+\begin_inset LatexCommand ref
+reference "sub:environnement-align-standard"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+Il y a d'autres environnement de formules multi-lignes qui peuvent être
+ créés en passant par le menu
+\family sans
+Insérer\SpecialChar \menuseparator
+Math
+\family default
+.
+ Ces environnements sont décrits dans les sections qui suivent.
+\end_layout
+
+\begin_layout Standard
+Dans tous les environnements de formules multi-ligne, une nouvelle ligne
+ est créée en appuyant sur
+\family sans
+Ctrl-Entrée
+\family default
+.
+ Pour ajouter ou supprimer des lignes, on peut utiliser respectivement les
+ boutons
+\begin_inset Graphics
+ filename ../../images/tabular-feature_append-row.png
+ scale 85
+
+\end_inset
+
+ ou
+\begin_inset Graphics
+ filename ../../images/tabular-feature_delete-row.png
+ scale 85
+
+\end_inset
+
+ de la barre d'outils mathématique ou bien le menu
+\family sans
+Éditer\SpecialChar \menuseparator
+Lignes\InsetSpace \thinspace{}
+&\InsetSpace \thinspace{}
+Colonnes
+\family default
+.
+\end_layout
+
+\begin_layout Subsubsection
+Séparation des lignes
+\begin_inset LatexCommand label
+name "sub:Séparation-des-lignes"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formules ! multi-lignes ! Séparation des lignes"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Il n'y a parfois pas assez d'espace entre les lignes d'une formule multi-lignes:
+\begin_inset Formula \begin{eqnarray*}
+B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD & = & \textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}\\
+4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right) & = & 0\end{eqnarray*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+En LaTeX l'espacement supplémentaire entre deux lignes est spécifié en tant
+ qu'argument optionnel de la commande de saut de ligne.
+ Ce n'est pas encore possible avec LyX
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+voir
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://bugzilla.lyx.org/show_bug.cgi?id=1505}{
+\end_layout
+
+\end_inset
+
+LyX-bug #1505
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+, ce qui fait que la totalité de la formule doit être insérée en mode TeX.
+ Pour ajouter de l'espace dans notre exemple, on insère la commande
+\series bold
+
+\backslash
+
+\backslash
+[3mm]
+\series default
+ à la fin de la première ligne et on obtient:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+begin{eqnarray*}
+\end_layout
+
+\begin_layout Standard
+
+B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
+ = &
+\backslash
+textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
+\backslash
+
+\backslash
+[3mm]
+\end_layout
+
+\begin_layout Standard
+
+4x^{2}
+\backslash
+left(B^{2}+x_{0}^{2}
+\backslash
+right)+4x_{0}x
+\backslash
+left(D-B^{2}
+\backslash
+right)+B^{2}
+\backslash
+left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
+\backslash
+right) & = & 0
+\end_layout
+
+\begin_layout Standard
+
+
+\backslash
+end{eqnarray*}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+On obtient alors:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+setlength{
+\backslash
+jot}{3mm+3pt}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{eqnarray*}
+B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD & = & \textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}\\
+4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right) & = & 0\end{eqnarray*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+setlength{
+\backslash
+jot}{3pt}
+\end_layout
+
+\end_inset
+
+ Pour revenir à l'espacement par défaut, on remet la valeur de
+\series bold
+
+\backslash
+jot
+\series default
+ à 3\InsetSpace \thinspace{}
+pt.
+\end_layout
+
+\begin_layout Subsubsection
+Séparation des colonnes
+\begin_inset LatexCommand label
+name "sub:Séparation-des-colonnes"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formules ! multi-lignes ! Séparation des colonnes"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Les formules multi-lignes forment une matrice.
+ Une formule dans un environnement eqnarray est par exemple une matrice
+ à trois colonnes.
+ En changeant l'espacement des colonnes de cet environnement, on peut modifier
+ l'espace à côté du symbole de relation.
+\end_layout
+
+\begin_layout Standard
+L'espacement des colonnes est spécifié avec la longueur
+\series bold
+
+\backslash
+arraycolsep
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! A ! \\textbackslash arraycolsep"
+
+\end_inset
+
+ selon la relation:
+\newline
+séparation des colonnes = 2\InsetSpace \thinspace{}
+
+\series bold
+
+\backslash
+arraycolsep
+\series default
+
+\newline
+Donc, la commande
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+setlength{
+\backslash
+arraycolsep}{1cm}
+\end_layout
+
+\begin_layout Standard
+insérée en mode TeX, met pour toutes les formules qui la suivent, l'espacement
+ des colonnes à 2\InsetSpace \thinspace{}
+cm.
+ Pour revenir à la valeur par défaut, on met
+\series bold
+
+\backslash
+arraycolsep
+\series default
+ à 5\InsetSpace \thinspace{}
+pt.
+\end_layout
+
+\begin_layout Standard
+Une formule avec des colonnes séparées de 2\InsetSpace \thinspace{}
+cm:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+setlength{
+\backslash
+arraycolsep}{1cm}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{eqnarray*}
+A & = & B\\
+C & \ne & A\end{eqnarray*}
+
+\end_inset
+
+Une formule avec la séparation de colonne prédéfinie de 10\InsetSpace \thinspace{}
+pt:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+setlength{
+\backslash
+arraycolsep}{5pt}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{eqnarray*}
+A & = & B\\
+C & \ne & A\end{eqnarray*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsubsection
+Formules longues
+\begin_inset LatexCommand index
+name "Formules ! longues"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Les formules longues peuvent être mises en forme en utilisant une de ces
+ méthodes:
+\end_layout
+
+\begin_layout Itemize
+Quand un des membres de l'équation est beaucoup plus court que la largeur
+ de la ligne, c'est lui qui est choisi comme membre de gauche et le membre
+ de droite est écrit sur deux lignes:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+medskip
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{eqnarray}
+H & = & W_{SB}+W_{mv}+W_{D}-\frac{\hbar^{2}}{2m_{0}}\Delta-\frac{\hbar^{2}}{2m_{1}}\Delta_{1}-\frac{\hbar^{2}}{2m_{2}}\Delta_{2}-\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{1}|}\nonumber \\
+ & & -\hspace{3pt}\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{2}|}+\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{R}_{1}-\mathbf{R}_{2}|}\label{eq:kurzlang}\end{eqnarray}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+smallskip
+\end_layout
+
+\end_inset
+
+
+\newline
+Le signe moins au début de la deuxième ligne n'apparaît normalement pas
+ comme un opérateur puisqu'il est le premier caractère de la ligne.
+ À cause de cela, il ne devrait pas être entouré d'espace ce qui le rendrait
+ difficile à distinguer de la barre de fraction.
+ Pour éviter cela, une espace a été insérée après les signe moins avec la
+ commande
+\series bold
+
+\backslash
+hspace{3pt}
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+plus au sujet de la commande
+\series bold
+
+\backslash
+hspace
+\series default
+, voir
+\begin_inset LatexCommand ref
+reference "sub:Espace-variable"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Commandes ! H ! \\textbackslash hspace"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Itemize
+Quand les deux membre de l'équation sont trop longs, on utilise la commande
+
+\series bold
+
+\backslash
+lefteqn
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! L ! \\textbackslash lefteqn"
+
+\end_inset
+
+.
+ Elle est insérée dans la première colonne de la première ligne et a comme
+ effet que tout ce qui sera inséré après va recouvrir les colonnes qui suivent:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+medskip
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{eqnarray}
+\lefteqn{4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right)+D^{2}}\nonumber \\
+ & & -\hspace{3pt}B^{2}-2B\sqrt{r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}+r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}\nonumber \\
+ & & =B^{2}+2\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)+\frac{\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)^{2}}{B^{2}}\label{eq:lefteqn}\end{eqnarray}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+smallskip
+\end_layout
+
+\end_inset
+
+
+\newline
+Après l'insertion de la commande
+\series bold
+
+\backslash
+lefteqn
+\series default
+, le curseur se trouve dans une boîte violette qui est légèrement décalée
+ vers la gauche par rapport à la boîte bleue.
+ C'est dans cette dernière que l'on insère la formule.
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+medskip
+\end_layout
+
+\end_inset
+
+
+\newline
+Le contenu des lignes suivantes est inséré dans la deuxième colonne ou dans
+ celles d'après.
+ Plus le numéro de la colonne sera élevé, plus l'indentation sera importante.
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+medskip
+\end_layout
+
+\end_inset
+
+
+\newline
+
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Standard
+Notez les points suivants quand vous utilisez
+\series bold
+
+\backslash
+lefteqn
+\series default
+:
+\end_layout
+
+\begin_layout Itemize
+La formule n'utilise pas la totalité de la largeur de la page.
+ Quand par exemple on a ajouté le terme
+\begin_inset Formula $-B^{2}$
+\end_inset
+
+ à la première ligne de l'exemple ci-dessus, il aurait dû être en dehors
+ de la marge.
+ Pour mieux utiliser la largeur disponible, on peut insérer un espacement
+ négatif en début de la première ligne.
+\end_layout
+
+\begin_layout Itemize
+À cause d'un bug dans LyX le curseur ne peut pas être positionné sur la
+ première ligne avec la souris
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://bugzilla.lyx.org/show_bug.cgi?id=1429}{
+\end_layout
+
+\end_inset
+
+LyX-bug #1429
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+ On peut seulement placer le curseur au début de la ligne et ensuite le
+ déplacer avec les flèches du clavier.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+D'autres méthodes pour créer des formules longues sont offertes par les
+ environnements décrits dans
+\begin_inset LatexCommand ref
+reference "sub:Environnement-Multline"
+
+\end_inset
+
+ et
+\begin_inset LatexCommand ref
+reference "sub:Portions-de-formules-en-multiligne"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsubsection
+Crochets sur plusieurs lignes
+\begin_inset LatexCommand label
+name "sub:Crochets-multilignes"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Crochets ! pour expressions multi-lignes"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Pour des parenthèses ou des crochets entourant des expressions réparties
+ sur plusieurs lignes, on rencontre le problème suivant:
+\begin_inset Formula \begin{eqnarray*}
+A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
+ & & \left.\cdots+B-D\right]\end{eqnarray*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Le crochet de fermeture est plus petit que celui d'ouverture parce que les
+ crochets à taille variable ne peuvent pas couvrir plusieurs lignes.
+\end_layout
+
+\begin_layout Standard
+Pour donner la bonne taille au crochet de la deuxième ligne, la première
+ ligne doit se terminer par la commande
+\series bold
+
+\backslash
+right.
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! R ! \\textbackslash right"
+
+\end_inset
+
+ et la seconde commencer par
+\series bold
+
+\backslash
+left.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+pour plus au sujet des commandes
+\series bold
+
+\backslash
+left
+\series default
+ et
+\series bold
+
+\backslash
+right
+\series default
+ voir
+\begin_inset LatexCommand ref
+reference "sub:Taille-parenthèses-automatique"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! L ! \\textbackslash left"
+
+\end_inset
+
+.
+ Après le
+\series bold
+
+\backslash
+left.
+
+\series default
+ on insère la commande
+\series bold
+
+\backslash
+vphantom
+\series default
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\backslash
+prod
+\series default
+^
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\backslash
+infty
+\series default
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\begin_inset Formula $\downarrow$
+\end_inset
+
+_R=1}
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! V ! \\textbackslash vphantom"
+
+\end_inset
+
+ , puisque l'opérateur produit avec ses limites est le symbole le plus grand
+ de la première ligne, c'est donc lui qui doit imposer la taille du crochet
+ de la deuxième ligne.
+\end_layout
+
+\begin_layout Standard
+On obtient ceci:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \begin{eqnarray*}
+A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
+ & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Les environnements align
+\end_layout
+
+\begin_layout Standard
+Les environnements align peuvent être utilisés pour tous les cas de formules
+ multi-lignes.
+ Ils sont particulièrement utiles pour positionner plusieurs formules côte-à-côt
+e.
+\end_layout
+
+\begin_layout Standard
+Les environnement Align sont composés de colonnes.
+ Les colonnes impaires sont alignées à gauche alors que les colonnes paires
+ sont alignées à droite.
+ Chaque ligne d'un environnement Align peut être numérotée.
+\end_layout
+
+\begin_layout Standard
+Les environnement Align sont créés avec le menu
+\family sans
+Insérer\SpecialChar \menuseparator
+Math
+\family default
+.
+ Avec le menu
+\family sans
+Éditer\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Change le type de formule
+\family default
+ on peut convertir des formules existantes en environnement Align.
+\end_layout
+
+\begin_layout Standard
+Pour ajouter ou supprimer des colonnes, on peut utiliser soit les boutons
+
+\begin_inset Graphics
+ filename ../../images/tabular-feature_append-column.png
+ scale 85
+
+\end_inset
+
+ ou
+\begin_inset Graphics
+ filename ../../images/tabular-feature_delete-column.png
+ scale 85
+
+\end_inset
+
+, respectivement, soit le menu
+\family sans
+Éditer\SpecialChar \menuseparator
+Lignes & colonnes
+\family default
+.
+\end_layout
+
+\begin_layout Subsubsection
+L'environnement align standard
+\begin_inset LatexCommand label
+name "sub:environnement-align-standard"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formules ! multi-lignes ! environnement align"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Cet environnement align est créé en appuyant sur
+\family sans
+Ctrl-Entrée
+\family default
+ dans une formule ou en utilisant le menu
+\family sans
+Insérer\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Environnement\InsetSpace ~
+AMS\InsetSpace ~
+align
+\family default
+.
+\end_layout
+
+\begin_layout Standard
+Un exemple avec deux formules mises côte-à-côte, créé avec un environnement
+ align à quatre colonnes:
+\begin_inset Formula \begin{align*}
+A & =\sin(B) & C & =D\\
+C & \ne A & B & \ne D\end{align*}
+
+\end_inset
+
+Comme on peut le voir, dans cet environnement les formules sont placées
+ comme s'il y avait un
+\series bold
+
+\backslash
+hfill
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+pour plus d'information au sujet de
+\series bold
+
+\backslash
+hfill
+\series default
+ voir
+\begin_inset LatexCommand ref
+reference "sub:Espace-variable"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series default
+ avant la première colonne et après chaque colonne paire.
+ Quand on utilise le style
+\series bold
+Indenté
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+pour les styles de formules, voir
+\begin_inset LatexCommand ref
+reference "sec:Styles-de-formules"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series default
+la formule est écrite sans le
+\series bold
+
+\backslash
+hfill
+\series default
+ avant la première colonne.
+\end_layout
+
+\begin_layout Subsubsection
+L'environnement alignat
+\begin_inset LatexCommand index
+name "Formules ! multi-lignes ! environnement alignat"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+L'environnement alignat n'a pas d'espacement de colonne prédéfini.
+ Il peut être inséré manuellement avec les espaces qui sont décrits en
+\begin_inset LatexCommand ref
+reference "sub:Espace"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+Voici l'exemple précédent dans un environnement alignat où on a inséré une
+ espace de 1\InsetSpace \thinspace{}
+cm au début de la deuxième formule:
+\begin_inset Formula \begin{alignat*}{2}
+A & =\sin(B) & \hspace{1cm}C & =D\\
+C & \ne A & B & \ne D\end{alignat*}
+
+\end_inset
+
+Puisque l'espacement des colonnes peut être choisi séparément pour chaque
+ colonne, cet environnement est particulièrement adapté aux cas où on a
+ trois colonnes ou plus côte-à-côte.
+
+\end_layout
+
+\begin_layout Subsubsection
+Environnement falign
+\begin_inset LatexCommand label
+name "sub:environnement-Flalign"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formules ! multi-lignes ! environnement flalign"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Dans cet environnement les deux premières colonnes sont placées le plus
+ à gauche possible et les deux dernière le plus à droite possible.
+ Un exemple:
+\begin_inset Formula \begin{flalign*}
+A & =1 & B & =2 & C & =3\\
+X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+En créant un environnement flalign avec un nombre impair de colonnes et
+ en insérant des accolades TeX vides dans la dernière colonne, plusieurs
+ formules d'un document peuvent être mises à gauche, bien que le style de
+ formules
+\series bold
+Centré
+\series default
+soit utilisé.
+ Comme exemple la formule
+\begin_inset LatexCommand eqref
+reference "eq:VolInt"
+
+\end_inset
+
+ indentée:
+\begin_inset Formula \begin{flalign}
+\hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
+
+\end_inset
+
+Les deux premières colonnes contiennent la formule.
+ Pour l'indenter comme avec le style de formule
+\series bold
+Indenté,
+\series default
+ on a inséré une espace de 30\InsetSpace \thinspace{}
+pt au début de la première colonne.
+\end_layout
+
+\begin_layout Subsection
+Environnement eqnarray
+\begin_inset LatexCommand index
+name "Formules ! multi-lignes ! environnement eqnarray"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Quand on créé cet environnement, trois boîtes bleues apparaissent.
+ Le contenu de la première boîte est aligné à droite, celui de la dernière
+ est aligné à gauche.
+ Le contenu de la boîte du milieu est centré et apparaît un peu plus petit,
+ parce qu'il est prévu pour y mettre seulement des opérateurs de relation.
+\begin_inset Formula \begin{eqnarray*}
+\frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
+AB & AB & AB\\
+A & = & A\end{eqnarray*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Environnement gather
+\begin_inset LatexCommand index
+name "Formules ! multi-lignes ! environnement gather"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Cet environnement consiste seulement en une colonne centrée.
+ Chaque ligne peut être numérotée.
+\begin_inset Formula \begin{gather}
+A=1\\
+X=\textrm{-}1\end{gather}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Environnement multline
+\begin_inset LatexCommand label
+name "sub:Environnement-Multline"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formules ! multi-lignes ! environnement multline"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+L'environnement multline consiste, comme l'environnement gather en une seule
+ colonne.
+ Mais la première ligne est alignée à gauche, la dernière est alignée à
+ droite et toutes les autres sont centrées.
+ Cet environnement est donc particulièrement adapté aux formules très longues.
+ Comme exemple, voici la formule
+\begin_inset LatexCommand eqref
+reference "eq:lefteqn"
+
+\end_inset
+
+ dans un environnement multline:
+\begin_inset Formula \begin{multline}
+4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right)+D^{2}\\
+-B^{2}-2B\sqrt{r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}+r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}\\
+=B^{2}+2\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)+\frac{\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)^{2}}{B^{2}}\end{multline}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Dans la sortie finale, seule la dernière ligne d'un environnement multline
+ apparaît numérotée si le document est numéroté à droite, la première s'il
+ est numéroté à gauche
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+pour les styles de numérotation, voir
+\begin_inset LatexCommand ref
+reference "sec:Styles-de-formules"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+ C'est aussi le cas dans LyX quand il y a un numéro de formule affiché après
+ chaque ligne
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+C'est
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://bugzilla.lyx.org/show_bug.cgi?id=518}{
+\end_layout
+
+\end_inset
+
+LyX-bug #518
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+Avec les commandes
+\series bold
+
+\backslash
+shoveright
+\begin_inset LatexCommand index
+name "Commandes ! S ! \\textbackslash shoveright"
+
+\end_inset
+
+
+\series default
+ et
+\series bold
+
+\backslash
+shoveleft
+\begin_inset LatexCommand index
+name "Commandes ! S ! \\textbackslash shoveleft"
+
+\end_inset
+
+
+\series default
+ une ligne centrée peut être alignée respectivement à droite ou à gauche.
+ Les commandes sont utilisées de la façon suivante:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+shoveright{contenu de la ligne}
+\series default
+ et
+\series bold
+
+\backslash
+shoveleft{contenu de la ligne}
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+La longueur
+\series bold
+
+\backslash
+multlinegap
+\begin_inset LatexCommand index
+name "Commandes ! M ! \\textbackslash multlinegap"
+
+\end_inset
+
+
+\series default
+ précise la distance entre le début de la première ligne et la marge de
+ gauche.
+ La valeur prédéfinie est 0\InsetSpace \thinspace{}
+pt.
+\end_layout
+
+\begin_layout Standard
+Comme exemple, la formule précédente en ajoutant avant en mode TeX
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+setlength{
+\backslash
+multlinegap}{2cm}
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+setlength{
+\backslash
+multlinegap}{2cm}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{multline}
+4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right)+D^{2}\\
+\shoveleft{-B^{2}-2B\sqrt{r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}+r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}\\
+=B^{2}+2\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)+\frac{\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)^{2}}{B^{2}}\end{multline}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+setlength{
+\backslash
+multlinegap}{0pt}
+\end_layout
+
+\end_inset
+
+La deuxième ligne a été alignée à gauche en utilisant
+\series bold
+
+\backslash
+shoveleft
+\series default
+.
+\end_layout
+
+\begin_layout Subsection
+Portions de formules en multi-ligne
+\begin_inset LatexCommand label
+name "sub:Portions-de-formules-en-multiligne"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formules ! multi-lignes ! portions de formules"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Pour afficher seulement une partie d'une formule avec plusieurs lignes,
+ on peut utiliser l'un des environnements suivants:
+\series bold
+aligned
+\series default
+,
+\series bold
+alignedat
+\series default
+,
+\series bold
+gathered
+\series default
+ or
+\series bold
+split
+\series default
+.
+ Ils peuvent être insérés en utilisant le menu
+\family sans
+Insérer\SpecialChar \menuseparator
+Math
+\family default
+ ou en utilisant les commandes décrites dans cette section.
+\end_layout
+
+\begin_layout Standard
+Les trois premier ont les mêmes propriétés que les environnements de formules
+ correspondants, à part le fait que l'on peut ajouter d'autres portions
+ de formules après eux.
+ Un exemple:
+\begin_inset Formula \[
+\left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
+\Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
+\right\} \textrm{Relations d'incertitude}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Pour obtenir cette formule, on crée une formule hors-ligne dans laquelle
+ on insère la commande
+\series bold
+
+\backslash
+aligned
+\begin_inset LatexCommand index
+name "Commandes ! A ! \\textbackslash aligned"
+
+\end_inset
+
+
+\series default
+.
+ Une boîte violette apparaît autour de la boîte de formule dans laquelle
+ on peut ajouter des lignes et des colonnes.
+ En dehors de l'environnement multiligne, on peut mettre d'autres portions
+ de formules, comme des accolades.
+\end_layout
+
+\begin_layout Standard
+L'environnement aligned est aussi utilisable pour de longues formules dont
+ les lignes sont alignées horizontalement.
+ Un avantage d'utiliser l'environnement aligned avec des formules hors-lignes
+ est que le numéro des formules est centré verticalement après les formules.
+ Un exemple, la formule
+\begin_inset LatexCommand eqref
+reference "eq:kurzlang"
+
+\end_inset
+
+ dans l'environnement aligned:
+\begin_inset Formula \begin{equation}
+\begin{aligned}H=\; & W_{SB}+W_{mv}+W_{D}-\frac{\hbar^{2}}{2m_{0}}\Delta-\frac{\hbar^{2}}{2m_{1}}\Delta_{1}-\frac{\hbar^{2}}{2m_{2}}\Delta_{2}-\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{1}|}\\
+ & -\hspace{3pt}\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{2}|}+\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{R}_{1}-\mathbf{R}_{2}|}\end{aligned}
+\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Pour utiliser les environnements
+\series bold
+alignedat
+\series default
+,
+\series bold
+gathered
+\series default
+, ou
+\series bold
+split
+\series default
+, on doit insérer respectivement, les commandes
+\series bold
+
+\backslash
+alignedat
+\series default
+,
+\begin_inset LatexCommand index
+name "Commandes ! A ! \\textbackslash alignedat"
+
+\end_inset
+
+
+\series bold
+
+\backslash
+gathered
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! G ! \\textbackslash gathered"
+
+\end_inset
+
+, ou
+\series bold
+
+\backslash
+split
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! S ! \\textbackslash split"
+
+\end_inset
+
+.
+ L'environnement split a les mêmes propriétés que l'environnement aligned,
+ mais il ne peut avoir que deux colonnes.
+\end_layout
+
+\begin_layout Subsection
+Texte dans les formules multi-lignes
+\begin_inset LatexCommand label
+name "sub:Texte-dans-multi-lignes"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Texte ! dans les formules"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formules ! multi-lignes ! texte"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Dans les environnements align, multline et gather, on peut insérer du texte
+ qui apparaîtra sur une ligne séparée et donc, n'affectera pas l'alignement
+ des colonnes.
+ Pour faire cela, on utilise la commande
+\series bold
+
+\backslash
+intertext
+\begin_inset LatexCommand index
+name "Commandes ! I ! \\textbackslash intertext"
+
+\end_inset
+
+
+\series default
+ avec la syntaxe suivante:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+intertext{texte}
+\end_layout
+
+\begin_layout Standard
+Le texte ne doit pas être plus long qu'une ligne puisqu'il ne pourra pas
+ subir de césure.
+ Comme LyX ne supporte pas directement
+\series bold
+
+\backslash
+intertext
+\series default
+, le texte doit être écrit comme du texte mathématique.
+ Le texte inséré avec
+\series bold
+
+\backslash
+intertext
+\series default
+ doit être au début d'une ligne pour se trouver dans la sortie final au
+ dessus de celle-ci.
+ Un exemple où le texte a été inséré au début de la deuxième ligne:
+\begin_inset Formula \begin{align}
+I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
+\intertext{\text{l'intégrande est symétrique autour de $\phi=\pi$, donc}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Numérotation des formules
+\begin_inset LatexCommand index
+name "Numérotation des formules"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formules ! numérotation|see{Numérotation des formules}"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Généralités
+\end_layout
+
+\begin_layout Standard
+On peut créer des formules numérotées avec le menu
+\family sans
+Insérer\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Formule\InsetSpace ~
+numérotée
+\family default
+ (raccourci
+\family sans
+Ctrl-Alt\InsetSpace ~
+n
+\family default
+).
+ On peut aussi numéroter des formules existantes avec le menu
+\family sans
+Éditer\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+(Dés)Activer\InsetSpace ~
+numérotation
+\family default
+ (raccourci
+\family sans
+Alt-m\InsetSpace ~
+n
+\family default
+).
+ Le numéro de la formule est affiché dans LyX après la formule sous la forme
+ d'un dièse entre parenthèse
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+En anglais le dièse est le symbole du numéro (NdT).
+\end_layout
+
+\end_inset
+
+.
+ Le dièse est remplacé dans la sortie finale par le numéro de la formule
+\end_layout
+
+\begin_layout Standard
+Quand on active la numérotation sur des formules multi-lignes, toutes les
+ lignes sont numérotées.
+ La numérotation peut ensuite être contrôlée pour chaque ligne avec le menu
+
+\family sans
+Éditer\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+(Dés)Activer\InsetSpace ~
+Numérotation\InsetSpace ~
+de\InsetSpace ~
+cette\InsetSpace ~
+ligne
+\family default
+ (raccourci
+\family sans
+Alt-m\InsetSpace ~
+N
+\family default
+).
+\end_layout
+
+\begin_layout Standard
+À part pour les formules en ligne, toutes les formules peuvent être numérotées
+ avec deux styles différents, voir
+\begin_inset LatexCommand ref
+reference "sec:Styles-de-formules"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Références croisées
+\begin_inset LatexCommand label
+name "sub:Références-croisées"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Références croisées ! à des formules"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+On peut faire référence à toute formule ayant une étiquette.
+ On ajoute une étiquette avec le menu
+\family sans
+Insérer\SpecialChar \menuseparator
+Étiquette
+\family default
+ ou avec le bouton
+\begin_inset Graphics
+ filename ../../images/label-insert.png
+ scale 85
+
+\end_inset
+
+ de la barre d'outils.
+ Pour cela, le curseur doit se trouver à l'intérieur d'une formule hors
+ ligne.
+ Une fenêtre de dialogue apparaît affichant le préfixe
+\series bold
+eq:
+\series default
+ dans un champ de texte.
+ L'étiquette est insérée à cet endroit, juste après le préfixe.
+ Le préfixe prédéfini signifie
+\begin_inset Quotes eld
+\end_inset
+
+équation
+\begin_inset Quotes erd
+\end_inset
+
+ et rend plus facile la recherche d'une étiquette dans les grand documents
+ en l'identifiant comme une étiquette de formule et pas, par exemple comme
+ une étiquette de section.
+ Pour modifier l'étiquette on doit repasser par le menu
+\family sans
+Insérer\SpecialChar \menuseparator
+Étiquette
+\family default
+.
+\end_layout
+
+\begin_layout Standard
+Le nom de l'étiquette est affiché dans LyX entre deux parenthèses, après
+ la formule.
+ Une formule avec une étiquette est toujours numérotée.
+ L'étiquette est détruite si la numérotation est désactivée.
+ C'est d'ailleurs, pour le moment la seule façon de supprimer une étiquette,
+ voir
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://bugzilla.lyx.org/show_bug.cgi?id=2556}{
+\end_layout
+
+\end_inset
+
+LyX-bug #2556
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+On insère une référence croisée avec le menu
+\family sans
+Insérer\SpecialChar \menuseparator
+Référence\InsetSpace ~
+croisée
+\family default
+ ou avec le bouton
+\begin_inset Graphics
+ filename ../../images/dialog-show-new-inset_ref.png
+ scale 85
+
+\end_inset
+
+ de la barre d'outils.
+ Une référence croisée à une formule apparaît dans la sortie finale comme
+ un numéro de formule.
+ Quand on choisit dans la fenêtre de dialogue de référence croisée le format
+
+\series bold
+(<reference>),
+\series default
+ la référence croisée apparaît dans la sortie finale comme un numéro de
+ formule entre parenthèses.
+\newline
+En faisant un clic droit sur une référence croisée
+ dans LyX, on saute à la formule qui est référencée.
+\end_layout
+
+\begin_layout Standard
+Voici comme exemples des références croisées à des formules qui se trouvent
+ dans les sous-sections qui suivent:
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+Noter les différents types de références croisées.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Les équations
+\begin_inset LatexCommand eqref
+reference "eq:tag"
+
+\end_inset
+
+ et
+\begin_inset LatexCommand eqref
+reference "eq:c"
+
+\end_inset
+
+ sont équivalentes.
+ Dans (
+\begin_inset LatexCommand ref
+reference "eq:Lat"
+
+\end_inset
+
+) on a utilisé de grosses lettres latines pour la numérotation, contrairement
+ à (
+\begin_inset LatexCommand ref
+reference "eq:Rom"
+
+\end_inset
+
+).
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Quand l'argument de
+\series bold
+
+\backslash
+tag
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+tag
+\series default
+ est décrit dans
+\begin_inset LatexCommand ref
+reference "sub:Numérotation-personnalisée"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\series default
+ contient une boîte comme dans
+\begin_inset LatexCommand ref
+reference "sub:Boîtes-de-paragraphes"
+
+\end_inset
+
+, la formule ne peut pas être référencée.
+\end_layout
+
+\begin_layout Subsection
+Sous-numérotation
+\begin_inset LatexCommand index
+name "Numérotation des formules ! sous-numérotation"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Avec l'aide des commandes
+\series bold
+
+\backslash
+begin{subequations}
+\series default
+ et
+\series bold
+
+\backslash
+end{subequations}
+\series default
+ on peut faire une sous-numérotation de formules.
+ Les deux commandes doivent être insérées en mode TeX.
+\end_layout
+
+\begin_layout Standard
+Un exemple:
+\begin_inset Formula \begin{equation}
+A=C-B\label{eq:a}\end{equation}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+addtocounter{equation}{-1}
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+begin{subequations}
+\end_layout
+
+\end_inset
+
+
+\begin_inset VSpace -5mm
+\end_inset
+
+
+\begin_inset Formula \begin{equation}
+B=C-A\label{eq:b}\end{equation}
+
+\end_inset
+
+
+\begin_inset Formula \begin{equation}
+C=A+B\label{eq:c}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+end{subequations}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Pour créer cet exemple, on fait ce qui suit:
+\end_layout
+
+\begin_layout Enumerate
+on insère la première formule
+\end_layout
+
+\begin_layout Enumerate
+après la première formule on insère
+\newline
+
+\series bold
+
+\backslash
+addtocounter{equation}{-1}
+\backslash
+begin{subequations}
+\begin_inset LatexCommand index
+name "Commandes ! A ! \\textbackslash addtocounter"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Enumerate
+on insère la deuxième formule
+\end_layout
+
+\begin_layout Enumerate
+on insère la troisième formule
+\end_layout
+
+\begin_layout Enumerate
+on insère
+\series bold
+
+\backslash
+end{subequations}
+\series default
+ après la troisième formule
+\end_layout
+
+\begin_layout Standard
+Chaque formule entre les commandes
+\series bold
+
+\backslash
+begin
+\series default
+ et
+\series bold
+
+\backslash
+end
+\series default
+ est sous-numérotée avec a, b,
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+linebreak
+\end_layout
+
+\end_inset
+
+c, \SpecialChar \ldots{}
+ Pour les formules multi-lignes, chaque ligne sera numérotée.
+ Toutes les formules sous-numérotées sont traitées comme
+\emph on
+une seule
+\emph default
+formule.
+ Mais comme chaque formule numérotée incrémente le compteur
+\series bold
+equation
+\series default
+ de un, on a besoin de la commande
+\series bold
+
+\backslash
+addtocounter
+\series default
+ pour le décrémenter.
+ Sinon les formules
+\begin_inset LatexCommand eqref
+reference "eq:a"
+
+\end_inset
+
+,
+\begin_inset LatexCommand eqref
+reference "eq:b"
+
+\end_inset
+
+,
+\begin_inset LatexCommand eqref
+reference "eq:c"
+
+\end_inset
+
+ seraient numérotées comme
+\begin_inset LatexCommand eqref
+reference "eq:a"
+
+\end_inset
+
+,
+\begin_inset LatexCommand eqref
+reference "eq:d"
+
+\end_inset
+
+,
+\begin_inset LatexCommand eqref
+reference "eq:f"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+En insérant les commandes en mode TeX entre les deux premières formules,
+ on crée un espace.
+ Pour le supprimer, on insère un espace vertical négatif de -5\InsetSpace \thinspace{}
+mm après la
+ commande
+\series bold
+
+\backslash
+begin{subequations}
+\series default
+.
+ Quand on utilise le style
+\series bold
+Indenté
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+pour les styles de formules, voir
+\begin_inset LatexCommand ref
+reference "sec:Styles-de-formules"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+,
+\series default
+on insère un espace de -7\InsetSpace \thinspace{}
+mm à la place.
+\end_layout
+
+\begin_layout Standard
+Voici un exemple de formule multi-lignes où on a désactivé la numérotation
+ pour la deuxième ligne::
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+begin{subequations}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{eqnarray}
+A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
+ & = & B^{2}-ZB-BZ+Z^{²}\nonumber \\
+ & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+end{subequations}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Numérotation personnalisée
+\begin_inset LatexCommand label
+name "sub:Numérotation-personnalisée"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Numérotation des formules ! personnalisée"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset LatexCommand index
+name "Numérotation des formules ! délimiteurs personnalisés"
+
+\end_inset
+
+Avec la numérotation standard, on a des parenthèses autour du numéro de
+ formule.
+ Pour, par exemple, remplacer ces parenthèses par des barres verticales,
+ il faut ajouter la lignes suivante dans le préambule LaTeX:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+def
+\backslash
+tagform@#1{
+\backslash
+maketag@@@{|#1|}}
+\series default
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+Cette macro est déjà déclarée dans le préambule LaTeX pour faire des tests.
+ Pour l'activer, il suffit d'enlever le signe pourcent qui se trouve en
+ début de ligne.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Pour utiliser d'autres symboles, il faut remplacer les barres verticales
+ autour du
+\series bold
+#1
+\series default
+ par un caractère ou plus.
+ Pour n'avoir que le numéro de la formule, il suffit d'enlever les barres
+ verticales.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Si vous voulez avoir une expression de votre choix entre parenthèses après
+ la formule au lieu des numéros qui se suivent, vous pouvez utiliser la
+ commande
+\series bold
+
+\backslash
+tag{expression}
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! T ! \\textbackslash tag"
+
+\end_inset
+
+:
+\begin_inset Formula \begin{equation}
+A+B=C\tag{quelquechose}\label{eq:tag}\end{equation}
+
+\end_inset
+
+Dans cet exemple, on a mis la commande
+\series bold
+
+\backslash
+tag
+\backslash
+{quelquechose
+\series default
+ dans la formule.
+\end_layout
+
+\begin_layout Standard
+Quand on insère la commande
+\series bold
+
+\backslash
+tag*
+\backslash
+{quelquechose
+\series default
+ à la place, l'astérisque supprime les parenthèses autour du texte:
+\begin_inset Formula \[
+A+B=C\tag*{quelquechose}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Pour réinitialiser la numérotation des formules à chaque nouvelle partie
+ ou section du document, on utilise les commandes suivantes:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+@addtoreset{equation}{part}
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! \"@\" ! \\textbackslash \"@\"addtoreset"
+
+\end_inset
+
+
+\newline
+ou
+\newline
+
+\series bold
+
+\backslash
+@addtoreset{equation}{section}
+\end_layout
+
+\begin_layout Standard
+Pour pouvoir utiliser ces commandes en mode TeX, le caractère
+\begin_inset Quotes eld
+\end_inset
+
+@
+\begin_inset Quotes erd
+\end_inset
+
+ doit être rendu
+\begin_inset Quotes eld
+\end_inset
+
+actif
+\begin_inset Quotes erd
+\end_inset
+
+ pour LaTeX en utilisant la commande
+\series bold
+
+\backslash
+makeatletter.
+
+\series default
+ La commande
+\series bold
+
+\backslash
+makeatother
+\series default
+ le désactive.
+ La suite de commandes en mode TeX est donc:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+makeatletter
+\newline
+
+\backslash
+@addtoreset{equation}{section}
+\newline
+
+\backslash
+makeatother
+\end_layout
+
+\begin_layout Standard
+Dans le préambule LaTeX on peut omettre les commandes
+\series bold
+
+\backslash
+makeatletter
+\series default
+ et
+\series bold
+
+\backslash
+makeatother
+\series default
+, vu que LyX les insère automatiquement en interne.
+\end_layout
+
+\begin_layout Standard
+Pour supprimer l'effet de
+\series bold
+
+\backslash
+@addtoreset
+\series default
+, on doit charger le fichier
+\series bold
+remreset.sty
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+remreset
+\series default
+ fait partie du paquetage LaTeX
+\series bold
+carlisle
+\series default
+
+\begin_inset LatexCommand index
+name "Paquetages ! carlisle"
+
+\end_inset
+
+ qui est compris dans toutes les installations LaTeX standard.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Paquetages ! remreset"
+
+\end_inset
+
+ dans le préambule LaTeX avec la ligne
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{remreset}
+\end_layout
+
+\begin_layout Standard
+On peut alors utiliser la commande
+\series bold
+
+\backslash
+@removefromreset
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! \"@\" ! \\textbackslash \"@\"removefromreset"
+
+\end_inset
+
+ avec la même syntaxe que
+\series bold
+
+\backslash
+@addtoreset
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+On doit parfois numéroter les formules de la façon suivante
+\end_layout
+
+\begin_layout Standard
+
+\family typewriter
+(numéro de section.numéro de formule)
+\end_layout
+
+\begin_layout Standard
+Le numéro de formule repart à
+\begin_inset Quotes eld
+\end_inset
+
+1
+\begin_inset Quotes erd
+\end_inset
+
+ à chaque nouvelle section
+\end_layout
+
+\begin_layout Standard
+Dans ce cas, on peut utiliser la commande
+\series bold
+
+\backslash
+numberwithin
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! N ! \\textbackslash numberwithin"
+
+\end_inset
+
+, qui a la syntaxe suivante:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+numberwithin{compteur}{sectionnement}
+\end_layout
+
+\begin_layout Standard
+Le compteur indique quelle sorte de numérotation est concernée et le sectionneme
+nt indique quel numéro est placé avant le point.
+\end_layout
+
+\begin_layout Standard
+Donc, dans notre cas, on utilise la commande suivante, soit dans le préambule
+ LaTeX soit en mode TeX:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+numberwithin{equation}{section}
+\end_layout
+
+\begin_layout Standard
+Voici le résultat:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+numberwithin{equation}{section}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{equation}
+A+B=C\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Pour numéroter les tableaux avec le numéro de la partie comme sectionnement,
+ on utilisera
+\newline
+
+\series bold
+
+\backslash
+numberwithin{table}{part}
+\end_layout
+
+\begin_layout Standard
+Pour revenir à la numérotation standard pour éviter ce type de numérotation
+ quand elle est définie par la classe du document, on insère la commande
+ suivante, soit dans le préambule, soit en mode TeX:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+arabic{equation}}
+\begin_inset LatexCommand index
+name "Commandes ! A ! \\textbackslash arabic"
+
+\end_inset
+
+
+\series default
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+arabic{equation}}
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\newline
+
+\series default
+ou
+\series bold
+
+\newline
+
+\backslash
+renewcommand{
+\backslash
+thetable}{
+\backslash
+arabic{table}}
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+numberwithin
+\series default
+ utilise en interne la commande
+\series bold
+
+\backslash
+@addtoreset
+\series default
+, décrite plus haut et qui doit aussi être annulée.
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+makeatletter
+\end_layout
+
+\begin_layout Standard
+
+
+\backslash
+@removefromreset{equation}{section}
+\end_layout
+
+\begin_layout Standard
+
+
+\backslash
+makeatother
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Numérotation avec des chiffres romains ou des lettres
+\begin_inset LatexCommand label
+name "sub:Numérotation-avec-des-chiffres-romains"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Numérotation des formules ! avec des lettres"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Numérotation des formules ! avec des chiffres romains"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+On peut aussi numéroter les formules avec des chiffres romains ou des lettres
+ latines.
+ Par exemple, pour numéroter avec des petits chiffres romains, on insère
+ la commande
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+roman{equation}}
+\end_layout
+
+\begin_layout Standard
+en mode TeX juste avant la formule.
+
+\series bold
+
+\backslash
+renewcommand
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! R ! \\textbackslash renewcommand"
+
+\end_inset
+
+ redéfinit la commande prédéfinie
+\series bold
+
+\backslash
+theequation
+\series default
+ en la commande
+\series bold
+
+\backslash
+roman{equation}
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+La commande
+\series bold
+
+\backslash
+renewcommand
+\series default
+ a la même syntaxe que la commande
+\series bold
+
+\backslash
+newcommand
+\series default
+ qui est décrite dans
+\begin_inset LatexCommand ref
+reference "sec:Commandes-personnalisées"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+.
+
+\series bold
+equation
+\series default
+ est le compteur pour les formules.
+ Quand la commande
+\series bold
+
+\backslash
+the
+\series default
+ est utilisée comme préfixe pour un compteur, la valeur du compteur est
+ écrite en utilisant des chiffres arabes.
+ Quand une formule est numérotée, LaTeX met en interne la commande
+\series bold
+
+\backslash
+theequation
+\series default
+ après la formule.
+
+\series bold
+
+\backslash
+roman{equation}
+\begin_inset LatexCommand index
+name "Commandes ! R ! \\textbackslash roman"
+
+\end_inset
+
+
+\series default
+ écrit la valeur du compteur en utilisant des petits chiffres romains.
+\end_layout
+
+\begin_layout Standard
+Toutes les formules qui suivent
+\series bold
+
+\backslash
+renew
+\series default
+c
+\series bold
+ommand
+\series default
+ sont maintenant numérotées en chiffres romains.
+ Pour passer à une numérotation avec de gros chiffres romains, on insère
+ la même commande, mais avec
+\series bold
+
+\backslash
+roman
+\series default
+ remplacé par
+\series bold
+
+\backslash
+Roman
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! R ! \\textbackslash roman@\\textbackslash Roman"
+
+\end_inset
+
+.
+ Pour numéroter avec des lettres latines minuscules, on a la commande
+\series bold
+
+\backslash
+alph
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! A ! \\textbackslash alphe"
+
+\end_inset
+
+, pour les lettres majuscules, on a
+\series bold
+
+\backslash
+Alph
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! A ! \\textbackslash alph@\\textbackslash Alph"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Standard
+
+\series bold
+Note:
+\series default
+ On peut numéroter au maximum 26 formules avec des lettres latines dans
+ un même document.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+roman{equation}}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \begin{equation}
+A=\textrm{romains minuscules}\label{eq:rom}\end{equation}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+Roman{equation}}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{equation}
+B=\textrm{romains majuscules}\label{eq:Rom}\end{equation}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+alph{equation}}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{equation}
+C=\textrm{latines minuscules}\label{eq:lat}\end{equation}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+Alph{equation}}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{equation}
+D=\textrm{latines majuscules}\label{eq:Lat}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Pour revenir à la numérotation par défaut, on insère la commande:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+arabic{equation}}
+\begin_inset LatexCommand index
+name "Commandes ! A ! \\textbackslash arabic"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+arabic{equation}}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{equation}
+E=\textrm{Arabes}\label{eq:arab}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Comme vous pouvez le voir, les numéros d'équation se suivent, indépendemment
+ du style de numérotation.
+ Si l'on veut que la numérotation reparte à
+\begin_inset Quotes eld
+\end_inset
+
+1
+\begin_inset Quotes erd
+\end_inset
+
+ quand on change de style de numérotation, on doit définir de nouveaux compteurs.
+ On trouvera une description de cette opération dans le fichier
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{Formula-numbering.pdf}{
+\end_layout
+
+\end_inset
+
+Formula-numbering.pdf
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Section
+Commandes personnalisées
+\begin_inset LatexCommand label
+name "sec:Commandes-personnalisées"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Commandes personnalisées"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+De nombreuses commandes LaTeX sont trop longues pour être utilisées fréquemment.
+ Mais on peut définir de nouvelles commandes plus courtes avec la commande
+
+\series bold
+
+\backslash
+newcommand
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! N ! \\textbackslash newcommand"
+
+\end_inset
+
+ .
+\end_layout
+
+\begin_layout Standard
+La syntaxe de
+\series bold
+
+\backslash
+newcommand
+\series default
+ est:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+newcommand{nom de la nouvelle commande}[nombre d'arguments]
+\newline
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+phantom{
+\end_layout
+
+\end_inset
+
+
+\backslash
+newcommand
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+[valeur optionnelle]{définition de la commande}
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Standard
+
+\series bold
+Note:
+\series default
+ Vérifiez que le nom de la nouvelle commande n'est pas déjà utilisé par
+ votre document ou par un des paquetages LaTeX que vous utilisez.
+ Si par exemple, vous tentez de définir la commande
+\series bold
+
+\backslash
+le
+\series default
+ pour
+\series bold
+
+\backslash
+Leftarrow
+\series default
+, vous aurez un message d'erreur puisque
+\series bold
+
+\backslash
+le
+\series default
+ est déjà définie comme étant la commande pour le symbole
+\begin_inset Quotes eld
+\end_inset
+
+
+\begin_inset Formula $\le$
+\end_inset
+
+
+\begin_inset Quotes erd
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Standard
+
+\series bold
+Note:
+\series default
+ Les noms des commandes personnalisées ne peuvent contenir que des lettres
+ latines.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Le nombre d'arguments est un entier entre 0 et 9 et il précise le nombre
+ d'argument que la commande doit avoir.
+ Avec la valeur optionnelle, on peut prédéfinir une valeur pour un argument
+ optionnel.
+ Quand on utilise cette valeur, le
+\emph on
+premier
+\emph default
+argument de la nouvelle commande est automatiquement l'argument optionnel.
+\end_layout
+
+\begin_layout Standard
+Voici quelques exemples:
+\end_layout
+
+\begin_layout Itemize
+Pour définir la commande
+\series bold
+
+\backslash
+gr
+\series default
+ pour
+\series bold
+
+\backslash
+Longrightarrow
+\series default
+, la ligne à insérer dans le préambule LaTeX est:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+medskip
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\newline
+
+\backslash
+newcommand{
+\backslash
+gr}{
+\backslash
+Longrightarrow}
+\end_layout
+
+\begin_layout Itemize
+Pour définir la commande
+\series bold
+
+\backslash
+us
+\series default
+ pour
+\series bold
+
+\backslash
+underline
+\series default
+, l'argument (qui doit être souligné) doit être pris en compte.
+ Pour cela, la ligne à insérer dans le préambule est:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+medskip
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\newline
+
+\backslash
+newcommand{
+\backslash
+us}[1]{
+\backslash
+underline{#1}}
+\series default
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+medskip
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\newline
+
+\series default
+Le caractère
+\series bold
+#
+\series default
+ agit comme un argument formel, le
+\series bold
+1
+\series default
+ derrière lui indique qu'il représente le premier argument.
+\end_layout
+
+\begin_layout Itemize
+Pour remplacer la commande
+\series bold
+
+\backslash
+framebox
+\series default
+ on peut par exemple définir, la commande
+\series bold
+
+\backslash
+fb
+\series default
+:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+medskip
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\newline
+
+\backslash
+newcommand{
+\backslash
+fb}[3]{
+\backslash
+framebox#1#2{$#3$}}
+\series default
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+medskip
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\newline
+
+\series default
+Les deux dollars créent une formule supplémentaire pour la commande
+\series bold
+
+\backslash
+framebox
+\series default
+, voir
+\begin_inset LatexCommand ref
+reference "sub:Boîtes-avec-cadre"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Itemize
+Pour créer une nouvelle commande pour remplacer
+\series bold
+
+\backslash
+fcolorbox
+\series default
+ où la couleur de la boîte n'aurait pas besoin d'être précisée, l'argument
+ pour la couleur est défini comme optionnel:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+medskip
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\newline
+
+\backslash
+newcommand{
+\backslash
+cb}[3][white]{
+\backslash
+fcolorbox{#2}{#1}{$#3$}}
+\series default
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+medskip
+\end_layout
+
+\end_inset
+
+
+\newline
+Quand la couleur n'est pas définie lors d'une utilisation de
+\series bold
+
+\backslash
+cb
+\series default
+, la couleur prédéfinie
+\series bold
+white
+\series default
+ est utilisée par défaut.
+\end_layout
+
+\begin_layout Standard
+Un test des nouvelles commandes:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="6" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox est seulement utilisée pour faire de la place
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A
+\backslash
+gr
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\gr B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+us{ABcd
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+fb{[2cm]
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{
+\backslash
+int
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+cb{red
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{
+\backslash
+int
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+cb[green]
+\backslash
+{red
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{
+\backslash
+int
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Diagrammes
+\begin_inset LatexCommand index
+name "Diagrammes"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Pour créer des diagrammes, on utilise le paquetage LaTeX
+\series bold
+amscd
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+amscd
+\series default
+ fait partie de toutes les installations LateX standard.
+\end_layout
+
+\end_inset
+
+
+\series default
+
+\begin_inset LatexCommand index
+name "Paquetages ! amscd"
+
+\end_inset
+
+.
+ On le charge dans le préambule LaTeX avec la ligne suivante:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{amscd}
+\end_layout
+
+\begin_layout Standard
+Les diagrammes permettent la visualisation de relations et ressemblent à
+ ceci:
+\begin_inset Formula \[
+\begin{CD}A@>>>B@>>>C\\
+@AAA@.@VVV\\
+F@<<<E@<<<D\end{CD}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Pour les obtenir, on insère la commande
+\series bold
+
+\backslash
+CD
+\begin_inset LatexCommand index
+name "Commandes ! C ! \\textbackslash CD"
+
+\end_inset
+
+
+\series default
+ dans une formule.
+ Une boîte bleue apparaît avec deux lignes en pointillé entre lesquelles
+ on peut insérer d'autres commandes.
+ On crée une nouvelle ligne avec
+\family sans
+Ctrl-Entrée
+\family default
+.
+ Les relations horizontales sont insérées dans les lignes impaires et les
+ relations verticales dans les lignes paires.
+\end_layout
+
+\begin_layout Standard
+Pour créer les relations, il y a les commandes suivantes:
+\end_layout
+
+\begin_layout Itemize
+
+\series bold
+@<<<
+\series default
+ crée une flèche gauche,
+\series bold
+@>>>
+\series default
+ une flèche droite, et
+\series bold
+@=
+\series default
+ un long signe égal
+\end_layout
+
+\begin_layout Itemize
+
+\series bold
+@AAA
+\series default
+ crée une flèche vers le haut,
+\series bold
+@VVV
+\series default
+ une flèche vers le bas, et
+\series bold
+@|
+\series default
+ un signe égal vertical
+\end_layout
+
+\begin_layout Itemize
+
+\series bold
+@.
+
+\series default
+ sert de remplissage pour une relation inexistante
+\end_layout
+
+\begin_layout Standard
+Toutes les flèches peuvent être étiquetées de la façon suivante:
+\end_layout
+
+\begin_layout Itemize
+Si le texte est inséré entre les deux premiers < ou >, il est placé au dessus
+ de la flèche.
+ Quand il est placé entre le deuxième et le troisième, il apparaît sou la
+ flèche.
+\end_layout
+
+\begin_layout Itemize
+Quand le texte destiné à une flèche verticale est inséré entre le premier
+ et le second A ou V, il est placé sur le côté gauche de la flèche.
+ Si il est inséré entre le deuxième et le troisième, il apparaît à droite
+ de la flèche.
+ Si le texte contient un A ou un V, ces lettres doivent être placées entre
+ des accolades TeX.
+\end_layout
+
+\begin_layout Standard
+Comme exemple, un diagramme avec toutes les relations possibles:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+\begin{CD}A@>j>>B@>>k>C@=F\\
+@AmAA@.@VV{V}V@|\\
+D@<<j<E@>k>>F@=C\end{CD}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+La commande pour l'obtenir:
+\newline
+
+\series bold
+
+\backslash
+CD
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A@>j>>B@>>k>C@=F Ctrl-Enter
+\newline
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+hphantom{
+\end_layout
+
+\end_inset
+
+
+\backslash
+CD
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+@AmAA@.@VV
+\backslash
+{V
+\series default
+
+\begin_inset Formula $\to$
+\end_inset
+
+
+\series bold
+V@| Ctrl-Enter
+\newline
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+hphantom{
+\end_layout
+
+\end_inset
+
+
+\backslash
+CD
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+D@<<j<E@>k>>F@=C
+\end_layout
+
+\begin_layout Standard
+
+\newpage
+
+\end_layout
+
+\begin_layout Section
+Astuces
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+texorpdfstring{
+\end_layout
+
+\end_inset
+
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+On peut trouver d'autres astuces mathématiques très utiles dans
+\begin_inset LatexCommand cite
+key "Voss"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}{}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\backslash
+texorpdfstring est utilisé pour éviter que la note de bas de page apparaisse
+ dans les signets PDF.
+\end_layout
+
+\begin_layout Standard
+Plus d'infos sur
+\backslash
+texorpdfstring dans la section
+\begin_inset LatexCommand ref
+reference "sub:formules-dans-les-entêtes"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Astuces"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Ions|see{Symboles chimiques}"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Symboles et équations chimiques
+\begin_inset LatexCommand label
+name "sub:Symboles-chimiques"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "E@Équations chimiques"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Symboles ! chimiques"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Un exemple de texte de chimie:
+\end_layout
+
+\begin_layout Quote
+L'ion
+\begin_inset Formula $\mathrm{SO_{4}^{2-}}$
+\end_inset
+
+réagit avec deux ions
+\begin_inset Formula $\mathrm{Na^{+}}$
+\end_inset
+
+ pour donner du sulfate de sodium
+\begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
+\end_inset
+
+.
+ La réaction chimique peut être mise sous la forme:
+\begin_inset Formula \[
+\mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Cette équation chimique peut être créée directement sous la forme d'une
+ formule.
+ Pour éviter que les symboles apparaissent en italiques, sélectionnez tout
+ et mettez-le dans la police droite avec le raccourci
+\family sans
+Alt-c\InsetSpace ~
+r
+\family default
+ .
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Style de polices, voir
+\begin_inset LatexCommand ref
+reference "sub:Styles-de-polices"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Nombres négatifs
+\begin_inset LatexCommand index
+name "Nombres ! négatifs"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Les nombres négatifs ont souvent un aspect horrible dans les formules parce
+ que le signe moins qui est devant le nombre a la même longueur que l'opérateur
+ moins.
+ Quand on écrit un nombre négatif en texte normal, le signe moins apparaît
+ correctement.
+\end_layout
+
+\begin_layout Standard
+Le problème disparaît donc en convertissant le signe moins en texte mathématique.
+\end_layout
+
+\begin_layout Standard
+Un exemple pour illustrer le problème:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features>
+<column alignment="right" valignment="top" leftline="true" width="0">
+<column alignment="left" valignment="top" rightline="true" width="0">
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+texte normal:
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+x = -2
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+formule:
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $x=-2$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+solution:
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $x=\textrm{-}2$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+La virgule comme séparateur décimal
+\begin_inset LatexCommand index
+name "Virgule"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Avec LaTeX la virgule, en accord avec la convention anglaise, est utilisée
+ pour grouper les chiffres dans un nombre.
+ Il y aura donc de l'espace d'ajouté après toutes les virgules dans les
+ formules.
+\end_layout
+
+\begin_layout Standard
+Pour éviter cela, on sélectionne la virgule et on la passe en texte mathématique
+ (raccourci
+\family sans
+Alt-m\InsetSpace ~
+m
+\family default
+).
+\end_layout
+
+\begin_layout Standard
+Pour utiliser toutes les virgules d'un document comme séparateur décimal,
+ on doit charger le fichier
+\series bold
+icomma.sty
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+icomma
+\series default
+ fait partie du paquetage
+\series bold
+was
+\series default
+
+\begin_inset LatexCommand index
+name "Paquetages ! was\\vspace{4mm}"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Paquetages ! icomma"
+
+\end_inset
+
+ dans le préambule LaTeX avec la ligne
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{icomma}
+\end_layout
+
+\begin_layout Subsection
+Les vecteurs physiques
+\begin_inset LatexCommand label
+name "sub:Vecteurs-physiques"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Vecteurs ! physiques"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Des vecteurs prédéfinis sont proposés par le paquetage LaTeX
+\series bold
+ braket
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+braket
+\series default
+ fait partie de toutes les installations LaTeX standard.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Paquetages ! braket"
+
+\end_inset
+
+ que l'on charge en mettant dans le préambule LaTeX la ligne
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{braket}
+\end_layout
+
+\begin_layout Standard
+Les commandes suivantes sont définies:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Bra{
+\backslash
+psi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Bra{\psi}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Ket{
+\backslash
+psi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Ket{\psi}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Braket{
+\backslash
+psi|
+\backslash
+phi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Braket{\psi|\phi}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+La commande
+\series bold
+
+\backslash
+Braket
+\series default
+ assure que toutes les barres verticales ont la même taille que les crochets
+ englobants:
+\begin_inset Formula \[
+\Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+L'effet de la commande
+\series bold
+
+\backslash
+Braket
+\series default
+ peut aussi être obtenu en utilisant la commande
+\series bold
+
+\backslash
+middle
+\series default
+, qui est décrite dans
+\begin_inset LatexCommand ref
+reference "sub:Taille-parenthèses-automatique"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Fractions personnalisées
+\begin_inset LatexCommand label
+name "sub:Fractions-personnalisées"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Fractions ! personnalisées"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Pour définir des commandes personnalisées pour les fractions, on utilise
+ la commande
+\series bold
+
+\backslash
+genfrac
+\series default
+
+\begin_inset LatexCommand index
+name "Commandes ! G ! \\textbackslash genfrac"
+
+\end_inset
+
+ avec la syntaxe suivante:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+genfrac{parenthèse gauche}{parenthèse droite}
+\newline
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+phantom{
+\end_layout
+
+\end_inset
+
+
+\backslash
+genfrac
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+{épaisseur barre de fraction}{style}{numérateur}{dénominateur}
+\end_layout
+
+\begin_layout Standard
+Le style est un nombre allant de 0 à 3.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Nombre
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Style (Taille)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+formule hors ligne
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+1
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+formule en ligne
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+2
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+petit (small)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+3
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+minuscule (tiny)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Quand on ne donne pas de style, la taille est adaptée à celle de l'environnement
+ dans lequel on se trouve, comme avec la commande
+\series bold
+
+\backslash
+frac
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+Quand on ne donne pas d'épaisseur pour la barre de fraction, la valeur prédéfini
+e de 0.4\InsetSpace \thinspace{}
+pt est utilisée.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Par exemple les commandes
+\series bold
+
+\backslash
+dfrac
+\series default
+ et
+\series bold
+
+\backslash
+tbinom
+\series default
+ vues en
+\begin_inset LatexCommand ref
+reference "sub:Fractions"
+
+\end_inset
+
+ sont définies avec les commandes
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+newcommand{
+\backslash
+dfrac}[2]{
+\backslash
+genfrac{}{}{}{0}{#1}{#2}}
+\end_layout
+
+\begin_layout Standard
+et
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+newcommand{
+\backslash
+tbinom}[2]{
+\backslash
+genfrac{(}{)}{0pt}{1}{#1}{#2}}
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Pour définir une fraction où on peut donner l'épaisseur de la barre de fraction
+ en argument, on insère la ligne suivante dans le préambule LaTeX:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+newcommand{
+\backslash
+fracS}[3][]{
+\backslash
+genfrac{}{}{#1}{}{#2}{#3}}
+\end_layout
+
+\begin_layout Standard
+Un test:
+\begin_inset Formula \begin{align*}
+\text{Commande} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
+\text{Résultat} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
+
+\end_inset
+
+Comme on peut le voir, la distance entre le numérateur et le dénominateur
+ à la barre de fraction est à peu près trois fois l'épaisseur de la barre.
+\end_layout
+
+\begin_layout Subsection
+Formules barrées
+\begin_inset LatexCommand label
+name "sub:Formules-barrées"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formules ! barrées"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Pour barrer une formule ou une portion de formule, on doit charger le paquetage
+ LaTeX
+\series bold
+cancel
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+cancel
+\series default
+ fait partie de toutes les distributions LaTeX standard.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Paquetages ! cancel"
+
+\end_inset
+
+ dans le préambule LaTeX avec la ligne
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage[samesize]{cancel}
+\end_layout
+
+\begin_layout Standard
+Il y a quatre façon de barrer une formule:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Résultat
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+hspace
+\series default
+ et
+\series bold
+
+\backslash
+raisebox
+\series default
+sont seulement utilisées pour faire de la place.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+cancel{
+\backslash
+int
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bcancel{
+\backslash
+int
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+xcancel{
+\backslash
+int
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+cancelto{1
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{
+\backslash
+int
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+cancelto
+\series default
+ est particulièrement utile pour visualiser des simplifications de fractions
+ dans les formules:
+\begin_inset Formula \[
+\frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Formules dans les entêtes de section
+\begin_inset LatexCommand label
+name "sub:formules-dans-les-entêtes"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formules ! dans les entêtes de section"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Quand des formules sont utilisées dans des entêtes de section, on doit prendre
+ en compte les points suivants:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Standard
+Quand on utilise le paquetage LaTeX
+\series bold
+hyperref
+\series default
+
+\begin_inset LatexCommand index
+name "Paquetages ! hyperref"
+
+\end_inset
+
+, les signets PDF sont automatiquement créés dans la table des matières
+ pour chaque entête de section.
+ Si l'entête de section contient une formule, elle est affichée de façon
+ incorrecte dans le texte du signet parce que les formules dans les signets
+ ne respectent pas certaines conventions du PDF.
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Les deux problèmes peuvent être résolus en insérant à la fin de l'entête
+ de section un titre court avec le menu
+\family sans
+Insérer\SpecialChar \menuseparator
+Titre\InsetSpace ~
+court
+\family default
+.
+ Les titres courts sont en général utilisés avec des entêtes de section
+ couvrant plusieurs lignes pour garder une table des matière bien ordonnée.
+ Seul le titre court apparaît dans la table des matières et donc dans les
+ signets PDF.
+\end_layout
+
+\begin_layout Standard
+Quand des formules doivent apparaître dans la table des matières mais que
+ l'on utilise aussi
+\series bold
+hyperref
+\series default
+, on peut utiliser la commande suivante en mode TeX:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+texorpdfstring{partie à problème}{alternative}
+\begin_inset LatexCommand index
+name "Commandes ! T ! \\textbackslash texorpdfstring"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Quotes eld
+\end_inset
+
+Partie à problème
+\begin_inset Quotes erd
+\end_inset
+
+ est la partie de l'entête qui ne doit pas apparaître dans les signets PDF.
+ Cela peut être des caractères, des formules, des notes de bas de page,
+ mais aussi des références croisées.
+ L'
+\begin_inset Quotes erd
+\end_inset
+
+alternative
+\begin_inset Quotes erd
+\end_inset
+
+ est utilisée à la place de la
+\begin_inset Quotes eld
+\end_inset
+
+partie à problème
+\begin_inset Quotes erd
+\end_inset
+
+ pour les signets.
+\end_layout
+
+\begin_layout Standard
+Voici deux exemples d'entêtes de section:
+\begin_inset VSpace -3mm
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+boldmath
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsubsection
+Entête de section sans formule dans la table des matières
+\begin_inset Formula $\sqrt{-1}=\mathrm{i}$
+\end_inset
+
+
+\begin_inset OptArg
+status open
+
+\begin_layout Standard
+Entête sans formule dans la table des matières
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsubsection
+Entête de section avec formule dans la table des matières
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+texorpdfstring{
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula $\sqrt{-1}=\mathrm{i}$
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}{}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+unboldmath
+\end_layout
+
+\end_inset
+
+Dans le premier entête, on a utilisé un titre court, dans le second la commande
+
+\series bold
+
+\backslash
+texorpdfstring
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+Pour avoir la même mise en forme que les autres entêtes, toute l'entête
+ a été placée dans un environnement
+\series bold
+boldmath
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+voir
+\begin_inset LatexCommand ref
+reference "sub:Formules-en-gras"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Formules dans du texte multi-colonnes
+\begin_inset LatexCommand index
+name "Formules ! dans du texte multi-colonnes"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Quand elles se trouvent dans un texte multi-colonnes, les formules sont
+ souvent trop larges pour tenir sur une colonne et donc elles doivent pouvoir
+ utiliser toute la largeur de la page.
+ Pour faire cela, on utilise le paquetage LaTeX
+\series bold
+multicol
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+multicol
+\series default
+ fait partie de toutes les installations LaTeX standard.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Paquetages ! multicol"
+
+\end_inset
+
+, qui est chargé avec la ligne suivante dans le préambule LaTeX
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{multicol}
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Standard
+Noter que dans ce cas on ne
+\emph on
+doit pas
+\emph default
+activer l'option
+\family sans
+Document\InsetSpace ~
+sur\InsetSpace ~
+deux\InsetSpace ~
+colonnes
+\family default
+ dans la rubrique
+\family sans
+Format\InsetSpace ~
+du\InsetSpace ~
+texte
+\family default
+du menu
+\family sans
+Document\SpecialChar \menuseparator
+Paramètres
+\family default
+.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Avant le texte multi-colonnes on met la commande
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+begin{multicols}{nombre de colonnes}
+\end_layout
+
+\begin_layout Standard
+en mode TeX.
+ Le nombre de colonnes est un entier entre 2 et 10.
+ Avant la formule, le texte multi-colonnes et interrompu avec la commande
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+end{multicols}
+\end_layout
+
+\begin_layout Standard
+en mode TeX.
+\end_layout
+
+\begin_layout Standard
+À cause de la commande, un peu d'espace est ajouté automatiquement avant
+ la formule.
+ Pour le supprimer, on peut insérer avant la formule un espace vertical
+ de -6\InsetSpace \thinspace{}
+mm.
+ Quand on utilise le style de formules
+\series bold
+Indenté
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+voir
+\begin_inset LatexCommand ref
+reference "sec:Styles-de-formules"
+
+\end_inset
+
+ pour les styles de formules.
+\end_layout
+
+\end_inset
+
+
+\series default
+, il faut mettre un espace de -9\InsetSpace \thinspace{}
+mm à la place.
+\end_layout
+
+\begin_layout Standard
+Comme exemple, un texte multi-colonne avec une formule hors-ligne:
+\end_layout
+
+\begin_layout Standard
+
+\lang german
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+begin{multicols}{2}
+\end_layout
+
+\end_inset
+
+Das Spektrum wird fouriertransformiert.
+ the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
+, Lösungsmittel) zu trennen.
+ Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
+ nun das Aussehen des Ausgangssignals.
+ Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
+ über alle Phasen integrieren muss.
+ Sei nun
+\begin_inset Formula $S$
+\end_inset
+
+ unser normiertes Ausgangssignal and
+\begin_inset Formula $P$
+\end_inset
+
+ the Phasenverteilungsfunktion, so ergibt sich the Beziehung
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+end{multicols}
+\end_layout
+
+\end_inset
+
+
+\begin_inset VSpace -6mm
+\end_inset
+
+
+\begin_inset Formula \begin{equation}
+S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\label{eq:fouriertrafo}\end{equation}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+begin{multicols}{2}
+\end_layout
+
+\end_inset
+
+wobei
+\begin_inset Formula $S_{0}$
+\end_inset
+
+ das Signal ohne Gradient ist and the Normierungsbedingung
+\begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
+\end_inset
+
+ gilt.
+ Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
+ Direkt nach the
+\begin_inset Formula $\nicefrac{\pi}{2}$
+\end_inset
+
+\InsetSpace \thinspace{}
+-rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
+ das Signal zusätzlich abschwächt.
+ Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
+
+\begin_inset Formula $T_{2}$
+\end_inset
+
+-Zeit.
+\end_layout
+
+\begin_layout Standard
+
+\lang german
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+end{multicols}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Formules avec description des variables
+\begin_inset LatexCommand index
+name "Formules ! avec description des variables"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Pour décrire les variable au sein d'une formule, comme dans la formule
+\begin_inset LatexCommand eqref
+reference "eq:within"
+
+\end_inset
+
+, on peut utiliser une matrice\InsetSpace ~
+2
+\series bold
+×
+\series default
+
+\begin_inset Formula $n$
+\end_inset
+
+ avec une colonne alignée à gauche pour les
+\begin_inset Formula $n$
+\end_inset
+
+ variables utilisées
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+pour les matrices, voir
+\begin_inset LatexCommand ref
+reference "sec:Matrices"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+ Pour mettre la description en plus petits caractères, on peut insérer par
+ exemple la commande
+\series bold
+
+\backslash
+footnotesize
+\series default
+ avant la matrice
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+pour les tailles de polices, voir
+\begin_inset LatexCommand ref
+reference "sub:Tailles-polices"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+Quand on utilise le style de formules
+\series bold
+Indenté
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+pour les styles de formules, voir
+\begin_inset LatexCommand ref
+reference "sec:Styles-de-formules"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series default
+, on insère un
+\series bold
+
+\backslash
+hfill
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+hfill
+\series default
+ marche seulement avec des formules dans le style
+\series bold
+Indenté
+\series default
+, voir
+\begin_inset LatexCommand ref
+reference "sub:Espace-variable"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+ avant et après la matrice pour avoir la même séparation entre la matrice
+ et la formule et entre la matrice et la marge.
+\end_layout
+
+\begin_layout Standard
+Quand on utilise le style de formules
+\series bold
+ Centré
+\series default
+, on utilise la méthode décrite dans
+\begin_inset LatexCommand ref
+reference "sub:environnement-Flalign"
+
+\end_inset
+
+ pour indenter les formules.
+ La formule
+\begin_inset LatexCommand eqref
+reference "eq:within"
+
+\end_inset
+
+ consiste en cinq colonnes dont les deux premières contiennent l'équation,
+ la troisième la matrice et la dernière une accolade TeX vide.
+\begin_inset Formula \begin{flalign}
+\hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
+\rho & \textrm{density}\\
+V & \textrm{volume}\\
+g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Lettres grecques minuscules droites
+\begin_inset LatexCommand label
+name "sub:minuscules-grecques-droites"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Lettres grecques ! droites"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+La plupart des polices de caractères mathématiques ne fournissent que des
+ minuscules grecques italiques.
+ Mais pour les symboles des particules élémentaires comme les pions et le
+ neutrinos, on a besoin de lettre grecques droites.
+ Elles sont fournies par le fichier
+\series bold
+upgreek.sty
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+upgreek
+\series default
+ fait partie du paquetage LaTeX
+\series bold
+was
+\series default
+
+\begin_inset LatexCommand index
+name "Paquetages ! was\\vspace{4mm}"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Paquetages ! upgreek"
+
+\end_inset
+
+ qui est chargé avec la ligne suivante dans le préambule LaTeX:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{upgreek}
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+ifupgreek
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Standard
+Ce qui suit ne sera affiché que si le paquetage LaTeX
+\series bold
+upgreek
+\series default
+ est installé
+\end_layout
+
+\end_inset
+
+ On crée ces minuscules droites en commençant la commande pour une minuscule
+ grecque par
+\series bold
+up
+\series default
+.
+ Par exemple, la commande
+\series bold
+
+\backslash
+uptau
+\series default
+ donne ceci:
+\begin_inset Formula $\uptau$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Avec ces commandes, on peut typographier des réactions entre particules
+ élémentaires:
+\begin_inset Formula \[
+\uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Les lettres droites sont plus grasses et plus larges que les italiques.
+ On ne doit donc pas les utiliser pour des unités comme
+\begin_inset Quotes eld
+\end_inset
+
+µm
+\begin_inset Quotes erd
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+else
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Standard
+Ce qui suit sera affiché si la paquetage LaTeX
+\series bold
+upgreek
+\series default
+ n'est pas installé:
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Vous avez besoin du paquetage LaTeX
+\series bold
+upgreek
+\series default
+ pour voir le reste de cette sous section dans la sortie finale.
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+fi
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Caractères texte dans les formules
+\begin_inset LatexCommand label
+name "sub:Caractères-texte"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Texte ! dans les formules"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Dans certains cas, vous pouvez vouloir insérer des caractères en mode texte
+ directement dans des formules.
+ Quand, par exemple, vous utilisez souvent le point centré · dans des formules
+ du genre
+\begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
+\end_inset
+
+, vous devrez insérer tout le temps la commande
+\series bold
+
+\backslash
+cdot
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+voir
+\begin_inset LatexCommand ref
+reference "sub:Opérateurs-binaires"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+, puisque ce caractère est défini dans tous les encodages comme un caractère
+ texte.
+ Mais l'encodage peut être modifié avec cette ligne dans le préambule LaTeX:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+Declare Inputtext{183}{
+\backslash
+ifmmode
+\backslash
+cdot
+\backslash
+else
+\backslash
+textperiodcentered
+\backslash
+f\SpecialChar \textcompwordmark{}
+i}
+\end_layout
+
+\begin_layout Standard
+En plus du point centré, dans ce document on a défini le symbole degré °
+ pour qu'il puisse être inséré directement dans une formule grâce à la ligne
+ suivante dans le préambule LaTeX:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+DeclareInputtext{176}{
+\backslash
+ifmmode^
+\backslash
+circ
+\backslash
+else
+\backslash
+textdegree
+\backslash
+f\SpecialChar \textcompwordmark{}
+i}
+\end_layout
+
+\begin_layout Standard
+
+\newpage
+
+\end_layout
+
+\begin_layout Section
+\start_of_appendix
+Conseils Typographiques
+\begin_inset LatexCommand index
+name "Typographiques, conseils"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+Les symboles d'unités sont
+\emph on
+toujours
+\emph default
+ en caractères droits
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+obtenu avec les styles de polices, voir
+\begin_inset LatexCommand ref
+reference "sub:Styles-de-polices"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+: 30\InsetSpace \thinspace{}
+km/h
+\newline
+Entre la valeur numérique et l'unité on a la plus petite espace,
+ voir
+\begin_inset LatexCommand ref
+reference "sub:Espace-prédéfini"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Itemize
+Les symboles pourcent et les pour mille sont présentés comme les symboles
+ d'unités:
+\newline
+1,2\InsetSpace \thinspace{}
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+textperthousand
+\end_layout
+
+\end_inset
+
+\InsetSpace ~
+d'alcool dans le sang
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Le symbole pour mille est déconseillé par l'AFNOR (NdT).
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+Le symbole degré suit directement la valeur numérique: 15°, sauf quand il
+ est utilisé dans une unité: 15\InsetSpace \thinspace{}
+°C
+\end_layout
+
+\begin_layout Itemize
+Dans les nombres de plus de quatre chiffres, une espace fine est insérée
+ tous les trois chiffres pour les grouper: 18\InsetSpace \thinspace{}
+473\InsetSpace \thinspace{}
+588
+\end_layout
+
+\begin_layout Itemize
+Pour exprimer des dimensions comme par exemple 120×90×40\InsetSpace \thinspace{}
+cm on utilise le
+ signe de la multiplication
+\begin_inset Quotes eld
+\end_inset
+
+×
+\begin_inset Quotes erd
+\end_inset
+
+ .
+ On peut l'obtenir avec la commande LaTeX
+\series bold
+
+\backslash
+texttimes
+\series default
+, mais il peut aussi être accessible directement sur certains claviers
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Par exemple sous Windows on l'obtient avec
+\family sans
+Alt-0215
+\family default
+ (NdT).
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Itemize
+Les fonctions mathématiques dont le nom est composé de plusieurs lettres
+ sont écrites en caractères droits pour éviter toute confusion, voir
+\begin_inset LatexCommand ref
+reference "sub:Fonctions-prédéfinies"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Itemize
+Les indices composés de plusieurs caractères sont écrits en caractères droits:
+
+\begin_inset Formula $E_{\mathrm{kin}}$
+\end_inset
+
+
+\newline
+Les composants de matrices sont en italiques:
+\begin_inset Formula $\hat{H}_{kl}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+L'opérateur 'd' de différentiation/intégration, la constante d'Euler 'e',
+ et la base des nombre imaginaires 'i' devraient être écrits en caractères
+ droits pour éviter de les mélanger avec les autres variables.
+\end_layout
+
+\begin_layout Standard
+
+\newpage
+
+\end_layout
+
+\begin_layout Section
+Synonymes
+\begin_inset LatexCommand index
+name "Synonymes"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Certains caractères peuvent être obtenus en utilisant différentes commandes.
+ Voici une liste de commandes synonymes:
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="12" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Commande
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+est équivalente à
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox est seulement utilisée pour faire de la place
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ast
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+raisebox{-1.2mm}{
+\end_layout
+
+\end_inset
+
+*
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+choose
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+binom
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+geq
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ge
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+lbrace
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+{
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+lbracket
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+[
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+leftarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+gets
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+leq
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+le
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+lor
+\end_layout
+
+\end_inset
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projects / features.git / commitdiff