Cours LATEX EDITE de Paris

First steps with LATEX

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Page 1 / 62 Pierre Senellart Licence de droits d’usage Outline

LATEX: a typesetting system General Description LATEX Compilation Resources

LATEX Documents

Writing Text with LATEX

Application

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Page 2 / 62 Pierre Senellart Licence de droits d’usage Outline

LATEX: a typesetting system General Description LATEX Compilation Resources

LATEX Documents

Writing Text with LATEX

Application

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Page 3 / 62 Pierre Senellart Licence de droits d’usage General principles

Pronounce “latek”: the last letter is a chi (휒) Typesetting system Not WYSIWYG (what you see is what you get) like classical word processing (Microsoft Word, OpenOffice Writer, etc.) ALATEX document: a text file (or several), usually with the . extension, structured with tags (sometimes called macros or commands) with arguments (e.g., \section{Section title} ) Special case: environments \begin{center} This text is centered \end{center}

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Page 4 / 62 Pierre Senellart Licence de droits d’usage Advantages / a WYSIWYG system

(More or less) semantic structuring of a document into chapters, sections, theorems, etc. Possible to describe (relatively) easily complex mathematical equations Better algorithms for justification, hyphenation, etc., since they do not need to run in real time Better typographic quality (e.g., kerning, ligatures) cf. http://nitens.org/taraborelli/latex Advantage of dealing with text files: arbitrary text editor, version control, regular expressions, production from scripts, etc. De facto standard in academia in mathematics, computer science, theoretical physics, etc.

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Page 5 / 62 Pierre Senellart Licence de droits d’usage History

End of the 1970s Donald E. Knuth creates the typesetting systemTEX to write his book The Art of Computer Programming Beginning of the 1980s Leslie Lamport writes the macro systemLATEX on top of TEX 1985 Release ofLATEX 2.09 1994 Release of the current version of LATEX,LATEX 2휀 In progress Development of version3 ofL ATEX

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Page 6 / 62 Pierre Senellart Licence de droits d’usage First LATEX document

\documentclass{minimal} \usepackage{cmap} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage{lmodern} \usepackage[francais]{babel} Bonjour à tous ! \begin{document} +∞ Bonjour à \emph{tous}! 1 π2 = n2 n 6 % Et une équation X=1 \[ \sum_{n=1}^{+\infty} \frac 1{n^2}=\frac{\pi^2}{6} \] \end{document}

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Page 7 / 62 Pierre Senellart Licence de droits d’usage Equivalent in Plain TEX

\documentclass{minimal} \usepackage{cmap} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} Bonjour \‘a {\it tous\/}~! \usepackage{lmodern} \usepackage[francais]{babel} % Et une équation \begin{document} $$ Bonjour à \emph{tous}! \sum_{n=1}^{+\infty} {1\over n^2}={\pi^2\over 6} % Et une équation $$ \[ \sum_{n=1}^{+\infty} \end \frac 1{n^2}=\frac{\pi^2}{6} \] \end{document}

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Page 8 / 62 Pierre Senellart Licence de droits d’usage Outline

LATEX: a typesetting system General Description LATEX Compilation Resources

LATEX Documents

Writing Text with LATEX

Application

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Page 9 / 62 Pierre Senellart Licence de droits d’usage Output formats

DVI (device-independent file format) historical output format of TEX. Readable with YAP (Windows), (Gnome), (KDE), Skim (Mac OS X), etc. PS (PostScript) page description language, understood by many printers. Readable with GhostView (Windows), Evince (Gnome), Okular (KDE), Skim (Max OS X), etc. PDF (Portable Document Format) page description language. Numerous readers, in particular Adobe Reader. The most convenient to distribute documents. HTMLAL ATEX document can also be turned into a Web page or Web site, but the process is imperfect. ODT It is possible to obtain an OpenDocument output, readable with Openoffice (e.g., to convert then into a Word document), but this does not work very well. 20/01/2011

Page 10 / 62 Pierre Senellart Licence de droits d’usage Compilation of a LATEX document

pdflatex PDF

dvipdfm ps2pdf

dvips LATEX DVI PostScript

mk4ht oolatex ODT

hevea, latex2html, tth, mk4ht htlatex HTML

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Page 11 / 62 Pierre Senellart Licence de droits d’usage Recommended compilation methods

pdflatex to prefer; simple, fast, produces an output format directly readable by all. latex + dvips + ps2pdf if used packages require a PostScript output (e.g., pstricks) hevea or latex2html or tth or mk4ht htlatex for an HTML output. None of them is ideal. Sometimes produce formulas as images, sometimes as MathML, sometimes as enriched text. mk4ht oolatex for an ODT output, convertible then in Word format with OpenOffice. Manual corrections to plan.

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Page 12 / 62 Pierre Senellart Licence de droits d’usage Outline

LATEX: a typesetting system General Description LATEX Compilation Resources

LATEX Documents

Writing Text with LATEX

Application

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Page 13 / 62 Pierre Senellart Licence de droits d’usage LATEX Distributions

ALATEX distribution is a bundle of programs (pdflatex, dvips, etc.), fonts, LATEX packages, etc., with everything required to compile. Depending on the distributions, some slight differences of behavior are to be expected.

Most often used distributions: TeX Live under Unix/Linux MikTeX under Windows; see also proTeXt, that adds some supplementary tools (TeXnicCenter, GhostView) MacTeX under Mac OS X

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Page 14 / 62 Pierre Senellart Licence de droits d’usage How to edit a LATEX document?

With any text editor With a text editor that has syntax highlighting: emacs, vim, gedit, kate, etc. With an integrated environment for editing, compilation, complementary tasks: TeXnicCenter, TeXworks, AucTeX (emacs), etc. With a graphical interface that “hides” LATEX commands: LyX, Scientific Word (commercial)

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Page 15 / 62 Pierre Senellart Licence de droits d’usage Common issues

Overfull hboxesT EX does not manage to find a decomposition of the text into lines that fits in the margins. Identify on a case by case basis if the problem is really apparent, and if so solve it by hand. Underfull vboxesT EX does not manage to put enough content on a page, which may look underfull. Identify on a case by case basis if the problem is really apparent, and if so solve it by hand. Not understandable error message Error messages are (sometimes) not really understandable. No other solutions than to look attentively at the code in question, to try and reproduce the problem on a minimal example, etc. Deleting generated files (e.g., .aux) sometimes helps.

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Page 16 / 62 Pierre Senellart Licence de droits d’usage When there is a compilation error

TEX display the error message: ! Undefined control sequence. l.5 the \foo is The problem is (often) at the end of the first highlighted line; sometimes the problem is a consequence of another problem, difficult to identify. Press to resume, ignoring the incriminated portion, (seldom useful) or x to stop the compilation. TEX sometimes simply displays “*” and waits for an input. Most of the time, it means that an environment has not been closed. Press CTRL+C, then x, to stop the compilation.

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Page 17 / 62 Pierre Senellart Licence de droits d’usage Where to find help?

In the documentation of each package, accessible with “texdoc nom_du_package” if the package is properly installed, can be found on the CTAN package archive otherwise: http://www.ctan.org/ In the TeX FAQ UK, very comprehensive: http://www.tex.ac.uk/cgi-bin/texfaq2html On the newsgroups comp.text.tex or fr.comp.text.tex The Comprehensive LATEX Symbol List, accessible with “texdoc symbols-a4” Find a LATEX symbol by drawing it: http://detexify.kirelabs.org/classify.html

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Page 18 / 62 Pierre Senellart Licence de droits d’usage Books to go further

LATEX par la pratique, Ch. Rolland, O’Reilly France (in French, sold out, very good introduction) The LATEX Companion, F. Mittelbach et al., Addison-Wesley (reference book listing a large number of LATEX packages and describing their use) The TEXbook, D. E. Knuth, Addison-Wesley (very technical on the functioning of the TEX engine, but very interesting)

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Page 19 / 62 Pierre Senellart Licence de droits d’usage Outline

LATEX: a typesetting system

LATEX Documents Structure Classes and Packages LATEX commands

Writing Text with LATEX

Application

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Page 20 / 62 Pierre Senellart Licence de droits d’usage Outline

LATEX: a typesetting system

LATEX Documents Structure Classes and Packages LATEX commands

Writing Text with LATEX

Application

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Page 21 / 62 Pierre Senellart Licence de droits d’usage General structure: 1/2

A class declaration \documentclass{minimal}

Reference to packages, possibly with other declarations \usepackage{cmap} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage{lmodern} \usepackage[francais]{babel}

The beginning of the document \begin{document}

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Page 22 / 62 Pierre Senellart Licence de droits d’usage General structure: 2/2

The body of the document Bonjour à \emph{tous}!

% Et une équation \[ \sum_{n=1}^{+\infty} \frac 1{n^2}=\frac{\pi^2}{6} \]

The end of the document \end{document}

Everything after a % is a comment and is ignored.

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Page 23 / 62 Pierre Senellart Licence de droits d’usage One document, several files

For a large document, useful to split it into several files (e.g., one per chapter, or even one per section) The file content is included with \input{file_name} No need to specify the .tex extension

\begin{document} \input{abstract}

\input{introduction} \input{algorithm} \input{experiments} \input{conclusion} \end{document}

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Page 24 / 62 Pierre Senellart Licence de droits d’usage Outline

LATEX: a typesetting system

LATEX Documents Structure Classes and Packages LATEX commands

Writing Text with LATEX

Application

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Page 25 / 62 Pierre Senellart Licence de droits d’usage Common classes

Standard LATEX classes: article, report, book articles, reports with several chapters, books minimal few features, only useful for very short documents

And others: scrartcl, scrreprt, scrbook (KOMA-Script) a configurable and modern alternative to standard classes memoir an all-in-one alternative to standard classes, regrouping the features of many packages beamer, prosper, foiltex classes for making presentation slides scrlttr2 (KOMA-Script) a class for letters

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Page 26 / 62 Pierre Senellart Licence de droits d’usage Other classes But also: Several classes to make posters Classes provided by the organizers of a conference or the publisher of a scientific journal Custom classes, adapted to your needs, built from the other classes Classes specific to Télécom ParisTech (developed by C. Ware): The Libres Savoirs classes to write up course notes, slides for courses or for scientific talks: http://perso. telecom-paristech.fr/~ware/soft/tptlibressavoirs/ A class (being developed, but usable right now) for your dissertation: http://perso.telecom-paristech.fr/~ware/soft/tpthese/

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Page 27 / 62 Pierre Senellart Licence de droits d’usage Character sets

Unicode: character repertoire, mapping each character, from whatever written language, to a given integer. A → 65 휀 → 949 é → 233 ℵ → 1488 Character encoding: way to concretely represent, with a sequence of 0’s and 1’s, a Unicode character. For instance, for the character “é”: latin1 11101001 (only for some characters) utf8 11000011 10101001 utf16 11101001 00000000 utf-8 has the advantage of representing all Unicode characters, in a manner compatible with the legacy encoding ASCII.

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Page 28 / 62 Pierre Senellart Licence de droits d’usage (Practically) essential packages (1/2)

\usepackage{cmap} annotates PDF files with information allowing better search and copy of text. Imperative to load in first position.

\usepackage[encoding]{inputenc} so that LATEX understands the character encoding of the file (commonly, encoding is utf8, latin1, cp1252, or applemac)

\usepackage[T1]{fontenc} so that LATEX uses the 8 bit internal encoding of fonts, instead of the old OT1 7 bit font encoding, and properly realizes the hyphenation of accented words (sometimes useless if non-standard fonts are used)

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Page 29 / 62 Pierre Senellart Licence de droits d’usage (Practically) essential packages (2/2)

\usepackage{lmodern} so that LATEX uses the Latin Modern typefaces instead of Computer Modern, whose accents are less nicely drawn. Compare: à à.

\usepackage[francais]{babel} so that LATEX properly typesets the French language (many other languages are available); not needed for English, which is the default. It is possible to specify several languages for a multilingual document. Do not use \usepackage[french]{babel} , not maintained anymore.

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Page 30 / 62 Pierre Senellart Licence de droits d’usage Very useful packages (1/2)

amsmath (American Mathematical Society) numerous features to facilitate the production of mathematical texts (equations broken up on several lines, matrices, etc.) amsthm definition of environments for theorems, definitions, proofs, etc. geometry specify the margins and size of a page paralist improved list environments

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Page 31 / 62 Pierre Senellart Licence de droits d’usage Very useful packages (2/2)

array, multirow, booktabs complex tables microtype activates microtypographic extensions that help improving text justification url command \url{http://www.google.com/} hyperref makes links ( \url ) and references ( \ref ) clickable in PDF. To put last in the list of loaded packages.

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Page 32 / 62 Pierre Senellart Licence de droits d’usage Outline

LATEX: a typesetting system

LATEX Documents Structure Classes and Packages LATEX commands

Writing Text with LATEX

Application

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Page 33 / 62 Pierre Senellart Licence de droits d’usage Commands

ALATEX command may have zero, one, or several arguments and is generally used in the following manner (but there are exceptions!): \command[optional argument]{argument 1}{argument 2} A command without argument is written \command{} ; the {} can be omitted if what follows is not a letter, e.g., \LaTeX! Some commands have a local effect, others affect the following of the document until the end of a scope (end of an environment, or } character).

An environment can be used as follows: \begin{environment}[optional argument]{argument 1}{argument 2} Content. \end{environment}

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Page 34 / 62 Pierre Senellart Licence de droits d’usage Title, author, etc.

Most document classes (article, scrartcl, memoir, beamer, etc.) allow defining meta-informations on the document, with the following commands put in the header of the document: \title{Title of the document} \author{Jean Dupont\and Jacques Durand} \date{\today}

These commands do not produce any output, but one can ask LATEX to create a title for the document with \maketitle .

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Page 35 / 62 Pierre Senellart Licence de droits d’usage Example of title

\documentclass{scrartcl} \usepackage{cmap} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage{lmodern} Titre du \usepackage[francais]{babel} document \title{Titre du document} \author{Jean Dupont\and Jacques Durand} Jean Dupont \date{\today} Jacques Durand

\begin{document} \maketitle 14 février 2010 \end{document}

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Page 36 / 62 Pierre Senellart Licence de droits d’usage Outline

LATEX: a typesetting system

LATEX Documents

Writing Text with LATEX Raw text Styling Text Structuring

Application

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Page 37 / 62 Pierre Senellart Licence de droits d’usage Outline

LATEX: a typesetting system

LATEX Documents

Writing Text with LATEX Raw text Styling Text Structuring

Application

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Page 38 / 62 Pierre Senellart Licence de droits d’usage Normal text

Text written normally, accented characters included Spaces delimiting words, two space characters are equivalent to one, a newline character is equivalent to a space Paragraphs are separated with \par or, more simply, by two successive newline characters

This is ordinary text, including accents: This is ordinary text, including éàôïçœ, it is typeset accents: éàôïçœ, it is typeset as as proper by \LaTeX. proper by LATEX. This text has two This text has two paragraphs! paragraphs!

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Page 39 / 62 Pierre Senellart Licence de droits d’usage Punctuation

Punctuation characters must by typed normally in LATEX, preferably without a space before and with a space after. LATEX (with the help of babel for other languages than English) takes care of typography rules. \usepackage[american,ngerman, francais]{babel}

... Bonjour ! Ça va ? Hi! What’s up? Bonjour! Ça va?\par \selectlanguage{american} Hallo! Wie geht’s? Hi! What’s up?\par \selectlanguage{ngerman} Hallo! Wie geht’s?

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Page 40 / 62 Pierre Senellart Licence de droits d’usage Microtype and babel

Microtype can take care of adding spaces following typography rules, instead of what babel traditionally does. Useful if you have problems with “active characters” (e.g., colons causing a bug in a TikZ code).

Activated with: \usepackage[babel=true,kerning=true]{microtype}

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Page 41 / 62 Pierre Senellart Licence de droits d’usage Typographic reminders

French English followed by a double space . followed by a space (sometimes) , followed by a space followed by a space followed by a space and preceded ; followed by a space with a thin unbreakable space followed by a space and preceded : followed by a space with a thin unbreakable space followed by a space and preceded ? followed by a space with a thin unbreakable space followed by a space and preceded ! followed by a space with a thin unbreakable space

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Page 42 / 62 Pierre Senellart Licence de droits d’usage Dashes and quotation marks

LATEX French American English - - petite-fille, 1979 -1981 grand-daughter – -- Je l’ai cru – car il était Perron–Frobenius convaincant – et je l’ai 1979–1981 suivi. Perron–Frobenius — --- — Bonjour I believed him—since he — Ça va ? was convincing—and I fol- lowed him.

“” ‘‘ ’’ He said, “Hi”, I reckon.

‘’ ‘ ’ l’apostrophe “He said, ‘Hi’, didn’t he?” «» \og \fg Il a dit : « Bonjour ».

In British typography, usage of ‘ ’ and “ ” is reversed.

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Page 43 / 62 Pierre Senellart Licence de droits d’usage Special characters

Some characters have a special meaning in LATEX and must be input differently:

_ \_ { \{ } \} $ \$ & \& # \# % \% \ \textbackslash C \texteuro (textcomp package) ~ (unbreakable space) ... \ldots (ellipsis)

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Page 44 / 62 Pierre Senellart Licence de droits d’usage Outline

LATEX: a typesetting system

LATEX Documents

Writing Text with LATEX Raw text Styling Text Structuring

Application

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Page 45 / 62 Pierre Senellart Licence de droits d’usage Font family (typeface)

The choice of a typeface impacts mathematical equations, it is therefore more complicated than in a traditional word processor. Packages allows using another typeface than the default (Computer Modern or Latin Modern with \usepackage{lmodern} ). cf. http://ctan.tug.org/tex-archive/info/Free_Math_Font_Survey/ survey.html

With XeLATEX, a new engine, it is possible to use arbitrary typefaces if they are installed on the computer, but the rendering of mathematics is not homogeneous any more.

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Page 46 / 62 Pierre Senellart Licence de droits d’usage Font size

The following command impact everything that follows: \tiny example \scriptsize example \footnotesize example \small example \normalsize example \large example \Large example \LARGE example \huge example \Huge example

st Also note 1\textsuperscript{st} : 1 . 20/01/2011

Page 47 / 62 Pierre Senellart Licence de droits d’usage Font style (1/2)

The first command impacts the text that follows, the second one the text in argument. \normalfont \textnormal Default style \rmfamily \textrm Serif \sffamily \textsf Sans serif \ttfamily \texttt Typewriter \mdseries \textmd Non bold \bfseries \textbf Bold \upshape \textup Normal variant \itshape \textit Italic \slshape \textsl Slanted \scshape \textsc SMALLCAPS

Example: \rmfamily\textit{Hi, \bfseries Ho} Ha : Hi, Ho Ha

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Page 48 / 62 Pierre Senellart Licence de droits d’usage Font style (2/2)

Do not use \it , \bf , etc.: these commands do not al- low text both in italic and in bold, for instance.

\em et \emph have an effect similar to \itshape and \textit but:

\textit{An \emph{emphasized} An emphasized portion can be portion can be found inside an italic found inside an italic text. text.}

When using \em or \itshape , it is required to end with an italic correction \/ : {\em V}V VV {\em V\/}V V V. Not needed with \emph or \textit .

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Page 49 / 62 Pierre Senellart Licence de droits d’usage Alignment

Environment Command Example flushleft \raggedright This text is left-aligned, it is not justified. flushright \raggedleft This text is right-aligned, not left-aligned. center \centering This text is centered. justify \justifying This text is justified, it is not left-aligned. justify and \justifying require the package ragged2e. The same package provides FlushLeft , \RaggedRight , Center , etc., giving better results than standard LATEX commands. \indent and \noindent specify if the following paragraph is indented.

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Page 50 / 62 Pierre Senellart Licence de droits d’usage Spacing

Horizontal spacing: \hspace{5cm} ou \hspace*{5cm} (the former is ignored at the beginning of a paragraph).

Vertical spacing: \vspace{5cm} ou \vspace*{5cm} (the former is ignored at the beginning of a page). There is also \smallskip , \medskip , \bigskip .

Springs: a\hfill b\par a b a\hfill b\hfill\hfillc a b c

Same with \vfill ! 20/01/2011

Page 51 / 62 Pierre Senellart Licence de droits d’usage Common length units

pt point in inch 1 in = 72,27 pt cm centimeter 2,54 cm = 1 in mm millimeter 10 mm = 1 cm em em natural font height ex ex height of the x letter

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Page 52 / 62 Pierre Senellart Licence de droits d’usage Other useful commands So says Smith:

\begin{quote} So says Smith: \LaTeX, it’s great! LAT X, it’s great! \end{quote} E Some code: Some code: \begin{verbatim} if (i%3==0) then { ++x; } if (i%3==0) then{ ++x;} \end{verbatim} Or inline: i%3.

Or inline: \verb+i%3+.

The character delimiting \verb can be chosen more or less arbitrarily.

\newpage for a page break, \\ or \newline for a line break (without changing paragraphs).

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Page 53 / 62 Pierre Senellart Licence de droits d’usage Outline

LATEX: a typesetting system

LATEX Documents

Writing Text with LATEX Raw text Styling Text Structuring

Application

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Page 54 / 62 Pierre Senellart Licence de droits d’usage Sections

Sections allow structuring a document and giving titles to parts of a document. Existing kinds of sections depend of the document class:

\part \chapter \section \subsection \paragraph \subparagraph

\section{Introduction} is thus put at the beginning of an introduction. In standard classes, if one writes \section*{Introduction} , an unnumbered section is added.

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Page 55 / 62 Pierre Senellart Licence de droits d’usage Table of contents

The \tableofcontents command builds a table of contents.

LATEX: a typesetting system General Description LATEX Compilation Resources LATEX Documents Structure \tableofcontents Classes and Packages LATEX commands Writing Text with LATEX Raw text Styling Text Structuring Application 20/01/2011

Page 56 / 62 Pierre Senellart Licence de droits d’usage References

After defining a chapter, section, etc., the following command creates a label referring to this part of the document: \label{arbitrary_label}

This label can then be used to refer to this part by its number or page number: This notion was defined in Chapter~\ref{arbitrary_label}, starting page~\pageref{arbitrary_label}.

LATEX needs two runs over a document to retrieve these references, it should thus be run twice consecutively!

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Page 57 / 62 Pierre Senellart Licence de droits d’usage Lists, numbered and unnumbered

My favorite cities are: My favorite cities are: \begin{enumerate} 1. Paris; \item Paris; \item Rome; 2. Rome; \item Hong Kong. 3. Hong Kong. \end{enumerate} \bigskip I need to buy: I need to buy: \begin{itemize} milk; \item milk; carrots; \item carrots; \item meat. meat. \end{itemize} See also the environments compactenum , inparaenum , etc., of the paralist package. 20/01/2011

Page 58 / 62 Pierre Senellart Licence de droits d’usage Description lists

\begin{description} \item[HTML] HyperText HTML HyperText Markup Markup Language Language \item[SVG] Scalable SVG Scalable Vector Graphics Vector Graphics XML eXtensible Markup \item[XML] eXtensible Markup Language Language \end{description}

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Page 59 / 62 Pierre Senellart Licence de droits d’usage Footnotes

a I know\footnote{Well, I know . I think I do.}. aWell, I think I do.

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Page 60 / 62 Pierre Senellart Licence de droits d’usage Outline

LATEX: a typesetting system

LATEX Documents

Writing Text with LATEX

Application

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Page 61 / 62 Pierre Senellart Licence de droits d’usage Application

Reproduce the example available on the course Web page (with the document class scrartcl).

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Page 62 / 62 Pierre Senellart Licence de droits d’usage Licence de droits d’usage

Contexte public } avec modifications

Par le téléchargement ou la consultation de ce document, l’utilisateur accepte la licence d’utilisation qui y est attachée, telle que détaillée dans les dispositions suivantes, et s’engage à la respecter intégralement.

La licence confère à l’utilisateur un droit d’usage sur le document consulté ou téléchargé, totalement ou en partie, dans les conditions définies ci-après et à l’exclusion expresse de toute utilisation commerciale. Le droit d’usage défini par la licence autorise un usage à destination de tout public qui comprend : – le droit de reproduire tout ou partie du document sur support informatique ou papier, – le droit de diffuser tout ou partie du document au public sur support papier ou informatique, y compris par la mise à la disposition du public sur un réseau numérique, – le droit de modifier la forme ou la présentation du document, – le droit d’intégrer tout ou partie du document dans un document composite et de le diffuser dans ce nouveau document, à condition que : – L’auteur soit informé.

Les mentions relatives à la source du document et/ou à son auteur doivent être conservées dans leur intégralité.

Le droit d’usage défini par la licence est personnel et non exclusif. Tout autre usage que ceux prévus par la licence est soumis à autorisation préalable et expresse de l’auteur : [email protected]

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Page 63 / 62 Pierre Senellart Licence de droits d’usage