LaTeX writing tips: Difference between revisions

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;Functions
;Functions
* Example of function definitions:
* Example of function definitions:
{| width=100%
|-
|width=50%|
<source lang=latex>
$$\begin{array}{llll}
$$\begin{array}{llll}
f : & \Z_N \to \Z_N & \qquad f^{-1}: & \Z_N \to \Z_N\\
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
& x \mapsto x^e \bmod N & & x \mapsto x^d \bmod N
\end{array}$$
\end{array}$$
</source>
* Inline function definition: $f$ is defined as $f : \{0,1\}^* \to \ZZ_{N}$, $x\mapsto b^x\bmod N$.
|
$$\begin{array}{llll}
f : & \Z_N \to \Z_N & \qquad f^{-1}: & \Z_N \to \Z_N\\
& x \mapsto x^e \bmod N & & x \mapsto x^d \bmod N
\end{array}$$
|}
* Inline function definition:
{| width=100%
|-
|width=50%|
<source lang=latex>
$f : \{0,1\}^* \to \ZZ_{N}$, $x\mapsto b^x\bmod N$
</source>
|align=center|
$f$ is defined as $f : \{0,1\}^* \to \ZZ_{N}$, $x\mapsto b^x\bmod N$
|}


== References ==
== References ==

Revision as of 19:26, 27 October 2014

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 4th). 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.[1].
\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})
  • Use unbreakable space in compound names (like Van~Allen)

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, $\{0,1,2,\dotsc\}$.
$\mathbb N^*$ $\mathbb N^*$ The set of positive natural numbers, $\{1,2,\dotsc\}$.
$\mathbb Z$ $\mathbb Z$ The set of integers, $\{\dotsc,-2,-1,0,1,2,\dotsc\}$ [2]
$\mathbb Z_{\ge 0}$

(or $\mathbb Z_+$)

$\mathbb Z_{\ge 0}$

(or $\mathbb Z_+$)

The set of non-negative integers, $\{0,1,2,\dotsc\}$ [2]
$\mathbb Z_{> 0}$

(or $\mathbb Z^*_+$)

$\mathbb Z_{> 0}$

(or $\mathbb Z_+^*$)

The set of strictly positive integers, i.e. $\{1,2,\dotsc\}$ [2]
$\{1,2,\dotsc,n\}$

(or $\N_{n}^*$ or $\Z \left({n}\right)$)

$\{1,2,\dotsc,n\}$ A finite set of integers. [3][2]
$\Z_n$ $\Z_n$ The set of integers modulo n, $\{0,1,2,\dotsc,n-1\}$ [3]
$\Z_n^*$ $\Z_n^*$ \gcd(a,n) = 1\}$

This is also known as the set of coprime integers to $n$, denoted as $\Z'_n = \{ k \in \Z_n : a \perp n\}$

[3][2]
$n \mathbb Z$ $n \mathbb Z$ The set of integer multiples $n \mathbb Z$ [2]
Tuples
  • a 2-tuple is an ordered pair (aka. couple in french, not be confused with pair where element order does not matter) (source [4]).
  • a 3-tuple is a triplet (source [4]).
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 $f : \{0,1\}^* \to \ZZ_{N}$, $x\mapsto b^x\bmod N$

References

  1. Frank Mittelbach,Michel Goossens: The LaTEX Companion — Second Edition. Addison-Wesley, 2004
  2. 2.0 2.1 2.2 2.3 2.4 2.5 ProofWiki, Symbols:Z — ProofWiki, http://www.proofwiki.org/wiki/Symbols:Z, 2013
  3. 3.0 3.1 3.2 Menezes, A., van Oorschot, P., Vanstone, S.: Handbook of Applied Cryptography, 1997
  4. 4.0 4.1 Wikipedia, https://en.wikipedia.org/wiki/Tuple