Introduction to LATEX
Lesson 6: User-defined commands and theorem environments
Dept. of Mathematical Sciences
User-defined commands I
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In addition to builtin LATEX commands, the user may define
her own commands.
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This is done in the preamble using \newcommand whose basic
form is
\newcommand{\com}{def}
where \com is the newly defined command and def its
definition.
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For instance,
\newcommand{\com}{My command}
\begin{document}
\com\com\com
My commandMy commandMy command
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User-defined commands II
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The command definition may contain also math. For
example,
\newcommand{\Z}{\mathbb{Z}}
\begin{document}
$k\in\Z$
k∈Z
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Note that the command above must be used in math mode.
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One may use \ensuremath to ensure that the argument is
processed in math mode. For example,
\newcommand{\Z}{\ensuremath{\mathbb{Z}}}
\begin{document}
Now both $\Z$ and \Z{} work.
Now both Z and Z work.
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User-defined commands III
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Also user-defined commands may receive arguments. To that
end the command must be defined as
\newcommand{\com}[n]{def}
where n is the number of arguments (1-9).
One refers to arguments using #k, where k= 1, 2, . . . , n.
For example, command for norm with one argument:
\newcommand{\norm}[1]{\left\|#1\right\|}
\begin{document}
$\norm{f+g}\leq\norm{f}+\norm{g}$
kf + gk ≤ kf k + kgk
Default values for possible optional arguments can be given
using the form:
\newcommand{\com}[n][default]{defn}
Existing commands may be redefined using \renewcommand
in a similar fashion.
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Counters I
I LATEX
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keeps track of chapter, section, equation, page etc.
numbering using counters.
Key counters are:
part
page
enumi
chapter
equation enumii
section
figure
enumiii
subsection
table
enumiv
subsubsection
Of these, enumX keeps track of four levels of items in
numbered lists (enumerate). Others are self-explanatory.
The current value of a counter may be printed out using the
following commands:
\arabic{counter} 1,2,3,... \alph{counter} a,b,c,...
\roman{counter}
i,ii,iii,... \Alph{counter} A,B,C,...
\Roman{counter}
I,II,III,... \counter
1,2,3,...
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Counters II
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The value of a counter may be set using
\setcounter{counter}{num}
which sets the value of counter to be the integer num.
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The value of a counter may be incremented or decremented
using
\addtocounter{counter}{num}
which increments (decrements) the value of counter by num
if num is positive (negative).
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New counters may be created using
\newcounter{counter}
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Theorem environments I
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Theorems, lemmas, proofs etc. are best typeset using
user-defined theorem environments.
These are defined in the preamble using the amsthm
command \newtheorem{name}{Title}.
For example, how to define and use one’s own theorem
environment: (square brackets are optional)
\usepackage{amsthm}
\newtheorem{thm}{Theorem}
\begin{document}
\begin{thm}[Prime number theorem]
There are infinitely many primes.
\end{thm}
Theorem 1 (Prime number theorem). There are infinitely
many primes.
This creates a thm environment with title "Theorem" and
with automatic numbering. Note the body of theorem in
italics.
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Theorem environments II
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One can control the numbering by passing a counter as an
optional argument. For example,
\newtheorem{thm}{Theorem}[section]
creates a theorem environment, which numbers theorems 1.1,
1.2, 1.3,. . . within section 1.
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The form
\newtheorem{lemma}[thm]{Lemma}
creates a lemma environment which uses the same counter as
thm environment. Then
\begin{thm}...\end{thm}
\begin{lemma}...\end{lemma}
\begin{thm}...\end{thm}
produces: Theorem 1.1, Lemma 1.2, Theorem 1.3
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Theorem environments III
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The command \theoremstyle{style} sets the style of
theorem environments that follow. Here style must be one
of plain, definition or remark.
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For instance,
\theoremstyle{definition}
\newtheorem{defn}{Definition}
creates a defn environment for definitions so that the body is
not in italics (cf. the default plain style above for theorems).
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Analogously
\theoremstyle{remark}
\newtheorem{rem}{Remark}
creates a rem environment whose title ("Remark") is in
italics.
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amsthm package provides proof environment for proofs.
Hence the user needs not define it herself.
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Theorem environments IV
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Similarly to other document structures, one can refer also to
theorems using \label{} and \ref{}.
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For example,
\begin{thm}\label{thm_1}
...
\end{thm}
\begin{proof}
...
\end{proof}
It follows from Theorem \ref{thm_1} that...
It follows from Theorem 1.2 that...
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Unnumbered environments can be defined using
\newtheorem*{}{}
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Summary
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\newcommand{\com}{defn}, \ensuremath{...}
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\newcommand{\com}[n]{defn}, \renewcommand{...}
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\setcounter{counter}{num},
\addtocounter{counter}{num}
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\newtheorem{}{}, \newtheorem*{}{}
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\newtheorem{thm}{Theorem}[section]
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\newtheorem{lemma}[thm]{Lemma}
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\theoremstyle{...}
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\begin{proof}...\end{proof}
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\begin{thm}\label{key}
...
\end{thm}
\ref{key}
11/11