Source file basics part 8

Below is the source file (.tex) demonstrating the basics of LaTeX.

• Greek letters
• Operators
• Multiline subscripts and superscripts
• Math accents
• Stretchable braces, bars and arrows
• STIX

\documentclass{sample}
\usepackage{booktabs}
\usepackage{caption}
\begin{document}
\section{Greek letters}
Uppercase and lowercase Greek letters are a common symbology. These letters must be typed in math environments.

\begin{center}
	\begin{tabular}{llc}
	\toprule
	Name & Typeset \\
	\midrule
	alpha & $\alpha$\\
	beta & $\beta$\\
	gamma & $\gamma$\\
	delta & $\delta$\\
	epsilon & $\epsilon$\\
	zeta & $\zeta$\\
	eta & $\eta$\\
	theta & $\theta$\\
	iota & $\iota$\\
	kappa & $\kappa$\\
	lambda & $\lambda$\\
	mu & $\mu$\\
	nu & $\nu$\\
	xi & $\xi$\\
	pi & $\pi$\\
	rho & $\rho$\\
	sigma & $\sigma$\\
	tau & $\tau$\\
	upsilon & $\upsilon$\\
	phi & $\phi$\\
	chi & $\chi$\\
	psi & $\psi$\\
	omega & $\omega$\\
	varepsilon & $\varepsilon$\\
	vartheta & $\vartheta$\\
	varpi & $\varpi$\\
	varrho & $\varrho$\\
	varsigma & $\varsigma$\\
	varphi & $\varphi$\\
	digamma & $\digamma$\\
	varkappa & $\varkappa$\\
	\bottomrule
	\end{tabular}
	\captionof{table}{Lowercase Greek letters (see source for type or command)}
	\label{Ta:lowgreek}
\end{center}

\begin{center}
	\begin{tabular}{llc}
	\toprule
	Name & Typeset & Typeset \\
	\midrule
	alpha & A (just type A)\\
	gamma & $\Gamma$\\
	delta & $\Delta$\\
	theta & $\Theta$\\
	lambda & $\Lambda$\\
	xi & $\Xi$\\
	pi & $\Pi$\\
	sigma & $\Sigma$\\
	upsilon & $\Upsilon$\\
	phi & $\Phi$\\
	psi & $\Psi$\\
	omega & $\Omega$\\
	vargamma & $\varGamma$\\
	vardelta & $\varDelta$\\
	vartheta & $\varTheta$\\
	varlambda & $\varLambda$\\
	varxi & $\varXi$\\
	varpi & $\varPi$\\
	varsigma & $\varSigma$\\
	varupsilon & $\varUpsilon$\\
	varphi & $\varPhi$\\
	varpsi & $\varPsi$\\
	varomega & $\varOmega$\\
	\bottomrule
	\end{tabular}
	\captionof{table}{Uppercase Greek letters (see source for type or command)}
	\label{Ta:uppgreek2}
\end{center}
\newpage
\section{Delimiters}
Delimiters enclose expressions.Like Greek letters, delimiters always go inside math environments.
\begin{center}
	\begin{tabular}{llc}
	\toprule
	Name & Typeset \\
	\midrule
	left parenthesis & $($\\
	right parenthesis & $)$\\
	left bracket & $[$\\
	right bracket & $]$\\
	left brace & $\{$\\
	right brace & $\}$\\
	backslash & $\backslash$\\
	forward slash & $/$\\
	left angle bracket & $\langle$\\
	right angle bracket & $\rangle$\\
	vertical line & $|$\\
	double vertical line (note this one) & $\|$\\
	left floor & $\lfloor$\\
	right floor & $\rfloor$\\
	left ceiling & $\lceil$\\
	right ceiling & $\rceil$\\
	upward & $\uparrow$\\
	double upward & $\Uparrow$\\
	downward & $\downarrow$\\
	double downward & $\Downarrow$\\
	up-and-down & $\updownarrow$\\
	double up-and-down & $\Updownarrow$\\
	upper-left corner & $\ulcorner$\\
	upper-right corner & $\urcorner$\\
	lower-left corner & $\llcorner$\\
	lower-right corner & $\lrcorner$\\
	\bottomrule
	\end{tabular}
	\captionof{table}{Delimiters (see source for type or command)}
	\label{Ta:delimiters}
\end{center}
With the exception of the corner delimiters, it is possible to stretch delimiters with \textbackslash left and \textbackslash right, in the form \textbackslash left \textit{delim1} \textbackslash right \textit{delim2}.

For example:
\[
\left|\frac{a+b}{2}\right|
\]

Note that the slightly modified command \textbackslash left. introduces a blank delimiter (as does the right counterpart) and is needed when stretching sible delimiters.
\[
\left. F(x) \right|_{a}^{b}\text{ note how this stretches the F to match the vertical bar}
\]

\section{Operators}
LaTeX defines e.g. trigonometric functions and mathematical limits as operators. The former does not involve limits while the latter can.
\begin{center}
	\begin{tabular}{llc}
	\toprule
	Typeset\\
	\midrule
	$\arccos$\\
	$\arcsin$\\
	$\arctan$\\
	$\arg$\\
	$\cos$\\
	$\cosh$\\
	$\cot$\\
	$\coth$\\
	$\csc$\\
	$\deg$\\
	$\dim$\\
	$\exp$\\
	$\hom$\\
	$\ker$\\
	$\lg$\\
	$\ln$\\
	$\log$\\
	$\sec$\\
	$\sin$\\
	$\sinh$\\
	$\tan$\\
	$\tanh$\\
	\bottomrule
	\end{tabular}
	\captionof{table}{Operators without limits (see source for type or command)}
	\label{Ta:opsnolimit}
\end{center}

\begin{center}
	\begin{tabular}{llc}
	\toprule
	Typeset\\
	\midrule
	$\det$\\
	$\gcd$\\
	$\inf$\\
	$\lim$\\
	$\liminf$\\
	$\injlim$\\
	$\varliminf$\\
	$\varinjlim$\\
	$\limsup$\\
	$\max$\\
	$\min$\\
	$\Pr$\\
	$\sup$\\
	$\projlim$\\
	$\varlimsup$\\
	$\varprojlim$\\
	\bottomrule
	\end{tabular}
	\captionof{table}{Operators with limits (see source for type or command)}
	\label{Ta:opsnolimit}
\end{center}

The limits to the operators are passed as parameters, for example:
\[
\projlim_{x \to 0}
\]

One can force limits in the subscript position with command \textbackslash nolimits:
\[
\projlim\nolimits_{x \to 0}
\]

\section{Multiline subscripts and superscripts}
It is also possible to apply multiline subscripts and superscripts, with \textbackslash substack. Each line is delimited with double backslashes:
\[
\sum_{\substack{i < n\\i \text{even}}}x_{i}^2
\]

To place the subscripts and superscripts flushed-left, use \textbackslash subarray instead of \textbackslash substack:
\[
\sum_{
\begin{subarray}{1}
i < n\\i \text{even}
\end{subarray}}
x_{i}^2
\]
\newpage
\section{Math accents}
Like text accents, these typically require a letter to accent but must be used within math environments.
\begin{center}
	\begin{tabular}{llc}
	\toprule
	Typeset\\
	\midrule
	$\acute{a}$\\
	$\bar{a}$\\
	$\breve{a}$\\
	$\check{a}$\\
	$\dot{a}$\\
	$\ddot{a}$\\
	$\dddot{a}$\\
	$\ddddot{a}$\\
	$\grave{a}$\\
	$\hat{a}$\\
	$\widehat{a}$\\
	$\mathring{a}$\\
	$\tilde{a}$\\
	$\widetilde{a}$\\
	$\vec{a}$\\
	\bottomrule
	\end{tabular}
	\captionof{table}{Math accents (see source for type or command)}
	\label{Ta:mathaccents}
\end{center}
\newpage
\section{Stretchable horizontal lines}
Three types in LaTeX: braces, bars and arrows.

Braces are typset with \textbackslash overbrace. A superscripts is optional. For example:
\[
\overbrace{a + b + \dots + n}^{m}
\]

Similarly, \textbackslash underbrace and optional subscripts are possible:
\[
\underbrace{a + b + \dots + n}_{m}
\]

Both braces can be nested.

Bars are typset with \textbackslash underline and \textbackslash overline as required, here shown as nested lines:
\[
\overline{
\overline{X} \cup \overline{\overline{X}}
} = \overline{\overline{X}}
\]

Arrows are either over or under and left, leftright or right, and have the same sort of features as braces and bars. Some examples:
\begin{gather*}
\overleftarrow{a}\\
\overrightarrow{ab}\\
\overleftrightarrow{abc}
\end{gather*}

The environment denoted by \texttt{gather} is used to gather single line formulae, in this case without numbering (as denoted by the asterisk).
\end{document}

The source file and (required) document class file are included. A generated PDF can be found here.

STIX - Scientific and Technical Information Exchange

This package can be added to LaTeX as shown next:

\documentclass{sample}
\usepackage{stix}
\usepackage{booktabs}
\usepackage{caption}
\begin{document}
\section{Greek letters with STIX}
Uppercase and lowercase Greek letters are a common symbology. These letters must be typed in math environments.

\begin{center}
	\begin{tabular}{llc}
	\toprule
	Name & Typeset \\
	\midrule
	alpha & $\alpha$\\
	beta & $\beta$\\
	gamma & $\gamma$\\
	delta & $\delta$\\
	epsilon & $\epsilon$\\
	zeta & $\zeta$\\
	eta & $\eta$\\
	theta & $\theta$\\
	iota & $\iota$\\
	kappa & $\kappa$\\
	lambda & $\lambda$\\
	mu & $\mu$\\
	nu & $\nu$\\
	xi & $\xi$\\
	pi & $\pi$\\
	rho & $\rho$\\
	sigma & $\sigma$\\
	tau & $\tau$\\
	upsilon & $\upsilon$\\
	phi & $\phi$\\
	chi & $\chi$\\
	psi & $\psi$\\
	omega & $\omega$\\
	varepsilon & $\varepsilon$\\
	vartheta & $\vartheta$\\
	varpi & $\varpi$\\
	varrho & $\varrho$\\
	varsigma & $\varsigma$\\
	varphi & $\varphi$\\
	digamma & $\digamma$\\
	varkappa & $\varkappa$\\
	\bottomrule
	\end{tabular}
	\captionof{table}{Lowercase Greek letters (see source for type or command)}
	\label{Ta:lowgreek}
\end{center}
\end{document}

STIX comes with all manner of symbols for scientific journals with its own set of fonts. Go here for more on STIX fonts. The fonts come with most TeX installations from 2014 or later, including Tex Live, as shown here