LaTeX writing tips

Layout and Typesetting

See also: English writing tips

• Maintain the relation 1 paragraph = 1 thought across the document.
• English requires longer space after the dots terminating a sentence (see \@); French does not (see \frenchspacing}.
• Add footnote after the word or sentence they refer to (i.e. after the comma or periodrelated to a sentence after the terminating dot.
• Avoid ligatures crossing morpheme boundary in a composite word, like shelfful ([1])
• Use ` and ' or `` and as quotation marks in English (or << and >> in French)
• Use the correct dash for each use (X-rated, page 13--67, yes---or no?, $-1$)
• Use \dots{} instead of \dots to add a space after the dots:

This is the end\dots Bye!        # Bad
This is the end\dots{} Bye!      # Good

• Use the correct semantic \dotsx command, depending on context:

We have the series $A_1,A_2,\dotsc$,                  % for comma list
the sum $A_1+A_2+\dotsb$,                             % for binary op
the orthogonal product $A_1A_2\dotsm$,                % for multiplication dots
the infinite integral $$\int_{A_1}\int_{A_2}\dotsi$$. % for dots with integrals

• Use roman style for 'd' in the differential:

\newcommand{\ud}{\,\mathrm{d}}
\begin{equation*}
\int_a^b f(x)\ud x
\end{equation*}

• Use \textsubscript{} or \textsuperscript{} for subscripts our superscripts outside math (like CO₂ or 4^th). The preferred option for ordinals in mathematics texts (or even english) seems to use $n$th or $n$-th (like nth or n-th) [2], [3], [4]. Yet another option is $n^{\text{th}}$ (with amsmath package). Finally, there is the package nth that can render ordinal with \nth{4} but it only works with numbers.

The $4$th, or the $4$-th, or the $4^{\text{th}}$ or the $4^{\text{\tiny{th}}}$ or the $4$\textsuperscript{th} or \nth{4}?

• Cut long line by adding a % at the cut to avoid LaTeX adding unwanted space where the cut occurs:

  \State $u \gets (v_i - x)\cdot C_i \bmod \rsamod_i$, $x \gets x + u \cdot% This comment will prevent LaTex adding space
    \prod_{j=1}^{i-1}\rsamod_j$

• When using cleveref, use \Cref{} instead of \cref{} at the beginning of a sentence to enforce capitalization.
• Interword spaces [5] — “TeX assumes a period ends a sentence unless it follows an uppercase letter.” (Lamport p. 14). So, put a \ in a sentence like Smith et al.\ say that .... And, if an uppercase letter ends a sentence, do a \@ before the period: In the class, I gave Bob a C\@..
• The small package xspace (by David Carlisle) defines the \xspace command, for use at the end of macros that produce text. It adds a space unless the macro is followed by certain punctuation characters..

\newcommand\eg{e.g.\@\xspace}
\newcommand\ie{i.e.\@\xspace}
\newcommand\etc{etc.\xspace}

• Units [6] — Use a non-breaking space between quantity and unit: 10~m. Or use package siunitx package (\SI{10}{m})
• Numbers — Use \num{123456} along with package siunitx. Or consider using another package like numprint.
• Use unbreakable space in compound names (like Van~Allen)
• Comma as decimal point — Surround the comma with braces (or consider using the package icomma. Additionally, in number list, separate numbers with semicolons:

$x_i\in[-1{,}5;1{,}5]$

Conventions and Examples

See also latex_templates examples. __MATHJAX_DOLLAR__

Usual conventions

• $\ln x$ is the natural logarithm of $x$; that is, the logarithm of $x$ to the base $e$.
• $\lg x$ is the logarithm of $x$ to the base $2$.
• Convention about positive, greater than...
  • Positive integers are integers greater than 0, i.e. $$x>0$$.
  • Non-positive integers are integers less than or equal to 0, i.e. $$x\le 0$$.
  • Negative integers are integers less than 0, i.e. $$x<0$$.
  • Non-negative integers are integers greater than or equal to 0, i.e. $$x\ge 0$$.

These are the English conventions. The French conventions are different: positif means $$x\ge 0$$, and supérieur means supérieur ou égal, and strictement supérieur excludes equality.

Bitsize

• A $$n$$-bit integer $N$ ... we know the high order $$(1/4+c)(log_2 N)$$ bits of P ... $$\lceil log_2 N \rceil$$-bit integer

Integers

$$\mathbb{N\ Z\ Q\ R}$$ $$\textsf$\textbf{N Z Q R}}$$	$\mathbb N$ \textsf{\textbf N}	Sets in algebra are usually denoted with blackboard typeface. Bold sans-serif is also a possible, but a bit less convenient in $\LaTeX$.
$$\mathbb N$$	$\mathbb N$	The set of natural numbers, including 0, $$\{0,1,2,\dotsc\}$$. Other notations include $$\N^0\ \N_0$$.
$$\mathbb N^*$$	$\mathbb N^*$	The set of positive natural numbers, $$\{1,2,\dotsc\}$$. Other notations include $$\N^+\ \N_1\ \N_{>0}$$.
$$\mathbb Z$$	$\mathbb Z$	The set of integers, $\{\dotsc,-2,-1,0,1,2,\dotsc\}$
$$\mathbb Z_{\ge 0}$$ (or $$\mathbb Z_+$$)	$\mathbb Z_{\ge 0}$ (or $\mathbb Z_+$)	The set of non-negative integers, $$\{0,1,2,\dotsc\}$$
$$\mathbb Z_{> 0}$$ (or $$\mathbb Z^*_+$$)	$\mathbb Z_{> 0}$ (or $\mathbb Z_+^*$)	The set of strictly positive integers, i.e. $$\{1,2,\dotsc\}$$
$$\{1,2,\dotsc,n\}$$ (or $$\N_{n}^*$$ or $$\Z \left({n}\right)$$)	$\{1,2,\dotsc,n\}$	A finite set of integers.
$$\Z_n$$	$\Z_n$	The set of integers modulo n, $$\{0,1,2,\dotsc,n-1\}$$
$$\Z_n^*$$	$\Z_n^*$	The multiplicative group of $$\Z_n$$, $$\{a \in \Z_n | \gcd(a,n) = 1\}$$ This is also known as the set of coprime integers to $$n$$, denoted as $$\Z'_n = \{ k \in \Z_n : a \perp n\}$$
$$n \mathbb Z$$	$n \mathbb Z$	The set of integer multiples $$n \mathbb Z$$

Tuples

• a 2-tuple is an ordered pair (aka. couple in french, not be confused with pair where element order does not matter) (source ).
• a 3-tuple is a triplet (source ).

Graphs (tree...)

• Height of a node = distance to root node; height of the tree = maximum height.
• degree of a node = number of children of a node; node with degree 0 = leaf node; node with no parent = root node.

Matrices

• Vector or matrix transpose: Use ^\top $$\mathbf M^\top$$ (alt. ^\mathsf{T} $$\mathbf M^\mathsf{T}$$, or ^\intercal $$\mathbf M^\intercal$$) [7]
• Vector or matrix conjugate: Use ^* $$\mathbf A^*$$

Sets

• Isomorphism between 2 sets: A \cong B $$A \cong B$$, or A \simeq B$$A \simeq B$$.

Functions

• Example of function definitions:

$$\begin{array}{llll} f : & \Z_N \to \Z_N & \qquad f^{-1}: & \Z_N \to \Z_N\\ & x \mapsto x^e \bmod N & & x \mapsto x^d \bmod N \end{array}$$

$$\begin{array}{llll} f : & \Z_N \to \Z_N & \qquad f^{-1}: & \Z_N \to \Z_N\\ & x \mapsto x^e \bmod N & & x \mapsto x^d \bmod N \end{array}$$

• Inline function definition:

$$f : \{0,1\}^* \to \ZZ_{N}$$, $$x\mapsto b^x\bmod N$$

$$f$$ is defined as $$f : \{0,1\}^* \to \ZZ_{N}$$, $$x\mapsto b^x\bmod N$$

Logic

• \iff and \implies (do not use with other arrows symbols like \Leftrightarrow))

$$A \iff B$$ $$P \implies Q$$

$$A \iff B$$ $$P \implies Q$$