%% $Id: firamath-otf-doc.tex 756 2023-09-08 05:54:11Z herbert $ \listfiles \documentclass[english,log-declarations=false]{article} \usepackage{mathtools,esvect} \usepackage{FiraSans} \setmonofont{FiraMono}[ Numbers = {Monospaced}, Scale=MatchUppercase,FakeStretch=0.93] \usepackage[fakebold,mathrm=sym]{firamath-otf} \usepackage{babel} \everymath{}\everydisplay{}% FIX for current babel \usepackage{biblatex} \addbibresource[location=remote]{https://www.ctan.org/tex-archive/biblio/ctan-bibdata/ctan.bib} \usepackage{booktabs} \usepackage{xltabular} \usepackage{listings} \usepackage{xspace} \usepackage{ctexhook} \usepackage{physics} \usepackage{xcolor,url} \usepackage{varioref,multido} \newcommand\Macro[1]{\texttt{\textbackslash#1}} \usepackage{expl3} \usepackage{hvextern} \newenvironment{demoquote} {\begingroup \setlength{\topsep}{0pt} \setlength{\partopsep}{0pt} \list{}{\rightmargin\leftmargin}% \item\relax} {\endlist\endgroup} \def\testfeature#1#2#3{{\fontspec[RawFeature={+#2}]{#1}#3\relax}} \makeatletter \def\e@alloc#1#2#3#4#5#6{% \global\advance#3\@ne \e@ch@ck{#3}{#4}{#5}#1% \allocationnumber#3\relax \global#2#6\allocationnumber } \def\@pr@videpackage[#1]{% \expandafter\xdef\csname ver@\@currname.\@currext\endcsname{#1}} \def\@providesfile#1[#2]{% \expandafter\xdef\csname ver@#1\endcsname{#2}% \endgroup} \def\@latex@info#1{} \def\@font@info#1{} \def\ClassInfo#1#2{} \def\PackageInfo#1#2{} \ExplSyntaxOn \cs_new:Npn \__fonttest_close_msg:nn #1#2 { \msg_redirect_name:nnn {#1} {#2} { none } } \__fonttest_close_msg:nn { LaTeX / xparse } { not-single-char } % \__fonttest_close_msg:nn { fontspec } { defining-font } % \__fonttest_close_msg:nn { fontspec } { no-scripts } \__fonttest_close_msg:nn { unicode-math } { patch-macro } \ctex_at_end_package:nn { geometry } { \def\Gm@showparams#1{} } \unimathsetup { math-style = ISO, bold-style = ISO, mathrm = sym } \str_new:N \l_fonttest_font_str \str_set:Nn \l_fonttest_font_str { fira } % Can be either fira/xits/lm \cs_set:Npn \WIEGHT { Regular } \cs_set:Npn \SSTY { } %%%%%%%%%%%%%%%%%%%% \str_if_eq:VnTF \l_fonttest_font_str { fira } { \cs_new:Npn \__fonttest_set_fira_math:n #1 { \setmathfont { FiraMath-\WIEGHT.otf } [ BoldFont = *, #1 ] } \cs_if_exist:NTF \SSTY { \__fonttest_set_fira_math:n { } \__fonttest_set_fira_math:n { version = pnum, Numbers = Proportional } \__fonttest_set_fira_math:n { version = upintegral, StylisticSet = 1 } \__fonttest_set_fira_math:n { version = hbar, StylisticSet = 2 } \__fonttest_set_fira_math:n { version = complement, StylisticSet = 3 } } { \__fonttest_set_fira_math:n { } \__fonttest_set_fira_math:n { version = pnum } \__fonttest_set_fira_math:n { version = upintegral } \__fonttest_set_fira_math:n { version = hbar } \__fonttest_set_fira_math:n { version = complement } } \newfontface\firatext{FiraMath-\WIEGHT.otf}[BoldFont = *] } { \str_if_eq:VnTF \l_fonttest_font_str { xits } { \setmathfont { XITS~ Math } \setmathfont { XITS~ Math } [ BoldFont = *, version = pnum ] \setmathfont { XITS~ Math } [ BoldFont = *, StylisticSet = 8, version = upintegral ] \setmathfont { XITS~ Math } [ BoldFont = *, StylisticSet = 10, version = hbar ] \setmathfont { XITS~ Math } [ BoldFont = *, version = complement ] \newfontface \firatext { XITS~ Math } [ BoldFont = * ] } { \str_if_eq:VnT \l_fonttest_font_str { lm } { \setmathfont { Latin~ Modern~ Math } \setmathfont { Latin~ Modern~ Math } [ BoldFont = *, version = pnum ] \setmathfont { Latin~ Modern~ Math } [ BoldFont = *, version = upintegral ] \setmathfont { Latin~ Modern~ Math } [ BoldFont = *, version = hbar ] \setmathfont { Latin~ Modern~ Math } [ BoldFont = *, version = complement ] \newfontface \firatext { Latin~ Modern~ Math } [ BoldFont = * ] } } } \cs_set:Npn \LatinAlphabets { ABCDEFGHIJKLMNOPQRSTUVWXYZ } \cs_set:Npn \latinAlphabets { abcdefghijklmnopqrstuvwxyz } % ΑΒΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΩ % αβγδεζηθικλμνξοπρστυφχψω \cs_set:Npn \GreekAlphabets { \Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta \varTheta \Iota \Kappa \Lambda \Mu \Nu \Xi \Omicron \Pi \Rho \Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega } \cs_set:Npn \greekAlphabets { \alpha \beta \gamma \delta \epsilon \varepsilon \zeta \eta \theta \vartheta \iota \kappa \varkappa \lambda \mu \nu \xi \omicron \pi \rho \varrho \sigma \varsigma \tau \upsilon \phi \varphi \chi \psi \omega } % More characters. \AtBeginDocument{ \__um_sym:nnn { "0323 } { \underdot } { \mathbotaccent } \__um_sym:nnn { "0324 } { \twounderdot } { \mathbotaccent } \__um_sym:nnn { "20D3 } { \shortvertoverlay } { \mathaccent } \__um_sym:nnn { "20D6 } { \cev } { \mathaccent } \__um_sym:nnn { "20E1 } { \leftrightarrowaccent } { \mathaccent } \__um_sym:nnn { "20EC } { \underrightharpoon } { \mathbotaccent } \__um_sym:nnn { "20ED } { \underleftharpoon } { \mathbotaccent } \__um_sym:nnn { "20EE } { \underleftarrow } { \mathbotaccent } \__um_sym:nnn { "20EF } { \underrightarrow } { \mathbotaccent } } \tl_const:Nn \c__fonttest_accents_tl { % accent \acute \grave \check \hat \bar \breve % dot \mathring \dot \ddot \dddot \ddddot % arrow \cev \vec \leftrightarrowaccent \leftharpoonaccent \rightharpoonaccent % other \tilde \asteraccent \vertoverlay \shortvertoverlay \annuity % long accent \widehat \widetilde \widebridgeabove % under \underdot \twounderdot \threeunderdot \underleftharpoon \underrightharpoon \underleftarrow \underrightarrow } \cs_set:Npn \MatrixII { a & b & c & d \\ x & y & z & w } \cs_set:Npn \MatrixIII { a & b & c & d \\ k & l & m & n \\ x & y & z & w } \cs_set:Npn \MatrixIV { a & b & c & d \\ k & l & m & n \\ p & q & s & t \\ x & y & z & w } \NewDocumentCommand \TopAccentMap { m m } { \fonttest_top_accent_map:Nx #1 {#2} } \cs_new:Npn \fonttest_top_accent_map:Nn #1#2 { \tl_map_inline:nn {#2} { \[ \__fonttest_top_accent:n { #1 {##1} } \] } } \cs_generate_variant:Nn \fonttest_top_accent_map:Nn { Nx } \cs_new:Npn \__fonttest_top_accent:n #1 { \tl_map_inline:Nn \c__fonttest_accents_tl { ##1 {#1} \, } } \cs_set:Npn \OverUnderline #1 { #1{} \quad #1{b} \quad #1{ab} \quad #1{abc} \quad #1{abcd} \quad #1{abcde} \quad #1{a+b+c} } \cs_set:Npn \ListText { x\sb{1}, \, x\sb{2}, \, \ldots, \, x\sb{n} } \cs_set:Npn \LigatureText { ff \quad fi \quad fl \quad ffi \quad ffl } \NewDocumentCommand \PrintRadical { m m m } { \fonttest_print_root:nnn {#1} {#2} {#3} } \cs_new_protected:Npn \fonttest_print_root:nnn #1#2#3 { \tl_set:Nn \l__fonttest_root_tl {#2} \int_step_inline:nn {#3} { \tl_set:Nx \l__fonttest_root_tl { \exp_not:n {#1} { \exp_not:V \l__fonttest_root_tl } } } \tl_use:N \l__fonttest_root_tl } \tl_new:N \l__fonttest_root_tl \NewDocumentCommand \PrintDelimiters { m m } { \fonttest_print_delimiters:nnnnn {#1} {#2} { 9 } { 1.8 } { 40 } } \cs_new_protected:Npn \fonttest_print_delimiters:nnnnn #1#2#3#4#5 { \cs_set:Npn \__fonttest_left_delimiter:n ##1 { \left #1 \vbox_to_ht:nn { ##1 pt } { } } \cs_set:Npn \__fonttest_right_delimiter:n ##1 { \vbox_to_ht:nn { ##1 pt } { } \right #2 } \tl_set:Nx \l__fonttest_delimiter_tl { \fp_step_function:nnnN {#5} { - #4 } {#3} \__fonttest_left_delimiter:n #1 } \tl_set:Nx \l__fonttest_delimiter_tl { \l__fonttest_delimiter_tl #2 \fp_step_function:nnnN {#3} {#4} {#5} \__fonttest_right_delimiter:n } \tl_use:N \l__fonttest_delimiter_tl } \tl_new:N \l__fonttest_delimiter_tl \ExplSyntaxOff \def\Lcs#1{\texttt{\textbackslash #1}} \renewcommand\familydefault{\sfdefault} \DeclareMathOperator{\Div}{\symup{div}} \DeclareMathOperator{\Grad}{\symup{grad}} \title{OpenType math font Fira} \author{Herbert Voß} \usepackage{parskip} \parindent=0pt \begin{document} \maketitle \tableofcontents \begin{abstract} The math font FIRA is derived from the Fira Sans and Fira Go sans serif. There are several math versions available (\url{https://github.com/Stone-Zeng/FiraMath/}) but only the regular version has from todays update all symbols. \end{abstract} \section{Dependencies} The package needs an installed OpenType font \texttt{firamath.otf}. This can also be done by installing the package \texttt{firamath} from CTAN.~\cite{ctan-firamath} \section{Usage} \begin{verbatim} \usepackage[]{firamath-otf} \end{verbatim} Optional arguments are \begin{description} %\item[\texttt{mathrm=sym}] Use characters from firamath for \Lcs{mathrm} \item[\texttt{fakebold}] Use faked bold symbols \item[\texttt{usefilenames}] Use filenames for the fonts instead of the symbolic font names \end{description} All other unknown options, e.g. \verb|mathrm=sym| will be passed to the main package \texttt{unicode-math}. The package itself loads by default \begin{verbatim} \RequirePackage{iftex,xkeyval,textcomp} \RequirePackage{unicode-math} \end{verbatim} \section{The default regular weight} \def\Q#1#2{\frac{\uppartial #1}{\uppartial #2}} \def\half{\frac{1}{2}} \def\vvec#1{\vv{#1}} \newcommand\uppartial{\symup{\partial}} \newcommand*\diff{\mathop{}\!\symup{d}} \newcommand*\<{\negthickspace} \newcommand*\TT{\symbf{\symup{T}}} \def\DD{\symbf{\symup{D}}} \subsection{Version normal} \begin{align} \begin{aligned} \Q{\varrho}{t}+\Div(\varrho\vec{v}) &= 0 \\ \varrho\Q{\vec{v}}{t}+(\varrho\vec{v}\cdot\nabla)\vec{v} &= \vec{f}_0+\Div\TT=\vec{f}_0 -\Grad p+\Div\TT' \\ \varrho T\frac{\diff s}{\diff t} &= \varrho\frac{\diff e}{\diff t} -\frac{p}{\varrho}\frac{\diff\varrho}{\diff t}=-\Div\vec{q}+\TT':\DD \end{aligned} \end{align} \begin{align} \Q{}{t}\iiint\<\varrho\diff^3V+\oiint\varrho(\vec{v}\cdot\vec{v}\vec{n}) \diff^2 A &= 0\\ \Q{}{t}\iiint\<\varrho\vec{v}\diff^3V+\oiint\varrho\vec{v}(\vec{v}\cdot\vec{n}\,)\diff^2A &= \iiint\ x_0, \, \exists \delta, \delta \in \varnothing $ \end{itemize} \subsection{Equations test} \begin{itemize} \item Basic:\\ $ 1 + 2 - 3 \times 4 \div 5 \pm 6 \mp 7 \dotplus 8 = -a \oplus b \otimes c $ \item Binary relations $ x + - \oplus \otimes \ominus \odot \oslash \cdot \cdotp \times \div y $ \item Set theory $ A \cap B \cup C \sqcap D \sqcup R \cupleftarrow k \cupdot l \uplus m $\\ $ A \subset B \supset C \subseteq D \supseteq E \Subset F \Supset G + A \sqsubset B \sqsupset C \sqsubseteq D \sqsupseteq E $\\ $ \complement_U A \cup \complement_C C \subset \mbox{\mathversion{complement}$\complement_U A \cup \complement_C C$} \in R \smallin Q \ni Z \smallni N $ \item Superscript and subscript:\\ $ 2^2 + 2^{2^2} + 2^{2^{2^2}} + {2^2}^2 + x_a + x_{a_i} + x_{a_{i_1}} $ \item Arrows:\\ $ x \leftarrow y \rightarrow z \leftrightarrow w \nleftarrow y \nrightarrow z \nleftrightarrow w \Leftarrow a = \Rightarrow b \Leftrightarrow c \nLeftarrow a = \nRightarrow b \nLeftrightarrow c $\\ $ x \uparrow y \downarrow z \updownarrow w \Uparrow a \Downarrow b \Updownarrow c $\\ $ p \nwarrow p \nearrow p \searrow p \swarrow p \Nwarrow p \Nearrow p \Searrow p \Swarrow p $\\ $ x \leftharpoonup x \leftharpoondown x \upharpoonright x \upharpoonleft x \rightharpoonup x \rightharpoondown x \downharpoonright x \downharpoonleft x $\\ $ A \longleftarrow B \longrightarrow C \longleftrightarrow D \Longleftarrow E = \Longrightarrow F \Longleftrightarrow G $\\ $ X \mapsfrom Y \mapsto Z \mapsup W \mapsdown P \Mapsfrom S \Mapsto R $\\ $ M \longmapsfrom N \longmapsto O \Longmapsfrom K \Longmapsto L $\\ $ f \rightleftarrows f \updownarrows f \leftrightarrows f \downuparrows g \rightrightarrows g \upuparrows g \leftleftarrows g \downdownarrows h \rightthreearrows h \leftthreearrows p \leftrightharpoons p \rightleftharpoons p \updownharpoonsleftright p \downupharpoonsleftright p $ \item Math accents:\\ \TopAccentMap{\symnormal}{x} % \begin{itemize} % \item Latin capital letters:\\ % \TopAccentMap{\symnormal}{\LatinAlphabets} % \item Latin small letters:\\ % \TopAccentMap{\symnormal}{\latinAlphabets} % \item Latin capital upright letters:\\ % \TopAccentMap{\symup}{\LatinAlphabets} % \item Latin small upright letters:\\ % \TopAccentMap{\symup}{\latinAlphabets} % \item Latin capital bold letters:\\ % \TopAccentMap{\symbf}{\LatinAlphabets} % \item Latin small bold letters:\\ % \TopAccentMap{\symbf}{\latinAlphabets} % \item Latin capital bold upright letters:\\ % \TopAccentMap{\symbfup}{\LatinAlphabets} % \item Latin small bold upright letters:\\ % \TopAccentMap{\symbfup}{\latinAlphabets} % \item Greek capital letters:\\ % \TopAccentMap{\symnormal}{\GreekAlphabets} % \item Greek small letters:\\ % \TopAccentMap{\symnormal}{\greekAlphabets} % \item Greek capital upright letters:\\ % \TopAccentMap{\symup}{\GreekAlphabets} % \item Greek small upright letters:\\ % \TopAccentMap{\symup}{\greekAlphabets} % \item Greek capital bold letters:\\ % \TopAccentMap{\symbf}{\GreekAlphabets} % \item Greek small bold letters:\\ % \TopAccentMap{\symbf}{\greekAlphabets} % \item Greek capital bold upright letters:\\ % \TopAccentMap{\symbfup}{\GreekAlphabets} % \item Greek small bold upright letters:\\ % \TopAccentMap{\symbfup}{\greekAlphabets} % \end{itemize} \item Integral: \[ \int_0^\pi \sin x \, \mathrm{d} x = \int\limits_0^\pi \sin x \, \mathrm{d} x = \cos 0 - \cos\pi=2 \] \[ \int_{-\infty}^{+\infty} \mathrm{d} z \iint_{-\infty}^{+\infty} \mathrm{d}^2 y \iiint_{-\infty}^{+\infty} \mathrm{d}^3 x \iiiint_{-\infty}^{+\infty} \mathrm{d}^4 p \] \[ \oint \dd{r} \oiint \dd{\theta} \oiiint \dd{\varphi}\] \begingroup \mathversion{upintegral} \[ \int_0^\pi \sin x \, \mathrm{d} x = \int\limits_0^\pi \sin x \, \mathrm{d} x = \cos 0 - \cos\pi + C \] \[ \int_{-\infty}^{+\infty} \mathrm{d} z \iint_{-\infty}^{+\infty} \mathrm{d}^2 y \iiint_{-\infty}^{+\infty} \mathrm{d}^3 x \iiiint_{-\infty}^{+\infty} \mathrm{d}^4 p \] \[ \oint \dd{r} \oiint \dd{\theta} \oiiint \dd{\varphi} \] \endgroup \item Huge operators: \[ \int\limits_0^\infty \int_0^\infty \sum_{i=1}^\infty \prod_{j=i}^\infty \coprod_{k=i}^\infty \] \[ \sum_{i=1}^\infty \frac{1}{x^i} = \frac{1}{1-x} \quad \prod_{i=1}^\infty \frac{1}{x^i} = x^{-n(n+1)/2} \quad \coprod_{i=i}^\infty \frac{1}{x^i} = ? \] \item Huge operators (inline): \[ \int\limits_0^\infty \int_0^\infty \iint \dd{x} \iiint \dd{y} \iiiint \dd{p} \oint \dd{r} \oiint \dd{\theta} \oiiint \dd{\varphi} \sum_{i=1}^\infty \prod_{j=i}^\infty \coprod_{i=i}^\infty \] \item Huge operators (inline): \begingroup \mathversion{upintegral} \[ \int\limits_0^\infty \int_0^\infty \iint \dd{x} \iiint \dd{y} \iiiint \dd{p} \oint \dd{r} \oiint \dd{\theta} \oiiint \dd{\varphi} \sum_{i=1}^\infty \prod_{j=i}^\infty \coprod_{i=i}^\infty \] \endgroup \item Fraction: \[ \frac{1}{2} + \frac{1}{\frac{2}{3}+4} + \frac{\frac{1}{2}+3}{4} \] \item Fraction (inline): \[ \frac{1}{2} + \frac{1g}{2} + \frac{1}{\frac{2}{3}+4} + \frac{\frac{1}{2}+3}{4} \] \item Radical: \[ \sqrt{2} + \sqrt{2^2} + \sqrt{1+\sqrt{2}} + \sqrt{1+\sqrt{1+\sqrt{3}}} + \sqrt{\sqrt{\sqrt{\sqrt{2}}}} + \sqrt{\frac{1}{2}} \] \[ \cuberoot{2} + \cuberoot{2^2} + \cuberoot{1+\cuberoot{2}} + \cuberoot{1+\cuberoot{1+\cuberoot{3}}} + \cuberoot{\cuberoot{\cuberoot{\cuberoot{2}}}} + \cuberoot{\frac{1}{2}} \] \[ \fourthroot{2} + \fourthroot{2^2} + \fourthroot{1+\fourthroot{2}} + \fourthroot{1+\fourthroot{1+\fourthroot{3}}} + \fourthroot{\fourthroot{\fourthroot{\fourthroot{2}}}} + \fourthroot{\frac{1}{2}} \] \[ \sqrt[x]{y} + \sqrt[x]{\sqrt[x]{y}} + \sqrt[x]{\sqrt[x]{\sqrt[x]{y}}} + \sqrt[x]{\frac{1}{2}} + \sqrt { \begin{matrix} x \\ y \\ z \\ w \end{matrix} } + \cuberoot { \begin{matrix} x \\ y \\ z \\ w \end{matrix} } + \fourthroot{ \begin{matrix} x \\ y \\ z \\ w \end{matrix} } + \sqrt[x] { \begin{matrix} x \\ y \\ z \\ w \end{matrix} } + \sqrt { \begin{matrix} x \\ y \\ z \\ w \\ p \end{matrix} } + \cuberoot { \begin{matrix} x \\ y \\ z \\ w \\ p \end{matrix} } + \fourthroot{ \begin{matrix} x \\ y \\ z \\ w \\ p \end{matrix} } + \sqrt[x] { \begin{matrix} x \\ y \\ z \\ w \\ p \end{matrix} } \] \[ \PrintRadical{\sqrt}{x}{25} \] \[ \PrintRadical{\cuberoot}{x}{25} \] \[ \PrintRadical{\fourthroot}{x}{25} \] \[ \PrintRadical{\sqrt[x]}{x}{4} \] \item Brackets: \[ (a) (A) (O) (Y) (y) (f) (Q) (T) (Y) (j) (q) \] % \[ \PrintDelimiters{(}{)} \] % \[ \PrintDelimiters{\lgroup}{\rgroup} \] % \[ \PrintDelimiters{[}{]} \] % \[ \PrintDelimiters{\{}{\}} \] % \[ \PrintDelimiters{\vert}{\vert} \] % \[ \PrintDelimiters{\Vert}{\Vert} \] % \[ \PrintDelimiters{\Vvert}{\Vvert} \] % \[ \PrintDelimiters{\langle}{\rangle} \] % \[ \PrintDelimiters{\lAngle}{\rAngle} \] % \[ \PrintDelimiters{\lceil}{\rceil} \] % \[ \PrintDelimiters{\lfloor}{\rfloor} \] \[ \Biggl( \biggl( \Bigl( \bigl( (x) \bigr) \Bigr) \biggr) \Biggr) \quad \Biggl\lgroup \biggl\lgroup \Bigl\lgroup \bigl\lgroup \lgroup x \rgroup \bigr\rgroup \Bigr\rgroup \biggr\rgroup \Biggr\rgroup \quad \Biggl[ \biggl[ \Bigl[ \bigl[ [x] \bigr] \Bigr] \biggr] \Biggr] \quad \Biggl\{ \biggl\{ \Bigl\{ \bigl\{ \{x\} \bigr\} \Bigr\} \biggr\} \Biggr\} \] \[ \left( x \right) + \left( x^2 \right) + \left( \frac{1}{2} \right) + \left( \frac{2^2}{3} \right) + \left( \frac{\frac{1}{2}}{\frac{3}{4}} \right) \] \[ ( \vert ) [ \Vert ] \{ \Vvert \} \quad \bigl( \bigm\vert \bigr) \bigl[ \bigm\Vert \bigr] \bigl\{ \bigm\Vvert \bigr\} \quad \Bigl( \Bigm\vert \Bigr) \Bigl[ \Bigm\Vert \Bigr] \Bigl\{ \Bigm\Vvert \Bigr\} \quad \biggl( \biggm\vert \biggr) \biggl[ \biggm\Vert \biggr] \biggl\{ \biggm\Vvert \biggr\} \quad \Biggl( \Biggm\vert \Biggr) \Biggl[ \Biggm\Vert \Biggr] \Biggl\{ \Biggm\Vvert \Biggr\} \quad \left( \vbox to 40pt {} \middle\vert \right) \left[ \vbox to 40pt {} \middle\Vert \right] \left\{ \vbox to 40pt {} \middle\Vvert \right\} \quad \left( \vbox to 50pt {} \middle\vert \right) \left[ \vbox to 50pt {} \middle\Vert \right] \left\{ \vbox to 50pt {} \middle\Vvert \right\} \] \item More brackets:\\ \[ \lceil ceiling \rceil \quad \lfloor floor \rfloor \quad \lgroup group \rgroup \] \item Bra-kets:\\ \renewcommand\ket[1]{\left\lvert{#1}\right\rangle} \renewcommand\bra[1]{\left\langle{#1}\right\rvert} \renewcommand\ip[2]{\left\langle{#1}\middle\vert{#2}\right\rangle} \renewcommand\op[2]{\left\lvert{#1}\middle\rangle\middle\langle{#2}\right\rvert} \[ \bra{x} + \ket{x} + \ip{\alpha}{\beta} + \op{\alpha^2}{\beta^2} + \bra{\frac{1}{2}} + \ket{\frac{1}{2}} + \ip{\frac{1}{2}}{\frac{1}{2}} + \op{\frac{1}{2}}{\frac{1}{2}} + \bra{\frac{a^2}{b^2}} + \Biggl\vert \frac{\mathrm{e}^{x^2}}{\mathrm{e}^{y^2}} \Biggr\rangle \] \[ \langle \vert \rangle \quad \bigl\langle \bigl\vert \bigl\rangle \quad \Bigl\langle \Bigl\vert \Bigl\rangle \quad \biggl\langle \biggl\vert \biggl\rangle \quad \Biggl\langle \Biggl\vert \Biggl\rangle \qquad \lAngle \vert \rAngle \quad \bigl\lAngle \bigl\vert \bigl\rAngle \quad \Bigl\lAngle \Bigl\vert \Bigl\rAngle \quad \biggl\lAngle \biggl\vert \biggl\rAngle \quad \Biggl\lAngle \Biggl\vert \Biggl\rAngle \] \item Matrices:\\ \[ \mqty(a & b \\ c & d) + \mqty*(a & b \\ c & d) \] \[ \begin{pmatrix} \MatrixII \end{pmatrix} \quad \begin{bmatrix} \MatrixII \end{bmatrix} \quad \begin{Bmatrix} \MatrixII \end{Bmatrix} \quad \begin{vmatrix} \MatrixII \end{vmatrix} \quad \begin{Vmatrix} \MatrixII \end{Vmatrix} \] \[ \begin{pmatrix} \MatrixIII \end{pmatrix} \quad \begin{bmatrix} \MatrixIII \end{bmatrix} \quad \begin{Bmatrix} \MatrixIII \end{Bmatrix} \quad \begin{vmatrix} \MatrixIII \end{vmatrix} \quad \begin{Vmatrix} \MatrixIII \end{Vmatrix} \] \[ \begin{pmatrix} \MatrixIV \end{pmatrix} \quad \begin{bmatrix} \MatrixIV \end{bmatrix} \quad \begin{Bmatrix} \MatrixIV \end{Bmatrix} \quad \begin{vmatrix} \MatrixIV \end{vmatrix} \quad \begin{Vmatrix} \MatrixIV \end{Vmatrix} \] \item Nablas:\\ \[ \nabla x + \grad{f} + \divergence{\symbf{u}} + \curl{\symbf{v}} \] \[ \nabla \quad \symbf{\nabla} \quad \symit{\nabla} \quad \symbfit{\nabla}; \quad \tilde{\nabla} \quad \tilde{\symbf{\nabla}} \quad \tilde{\symit{\nabla}} \quad \tilde{\symbfit{\nabla}} \] \item Over-/underline and over-/underbraces \[ \OverUnderline{\overline} \quad \overline {\ListText} \] \[ \OverUnderline{\overparen} \quad \overparen {\ListText}^n \] \[ \OverUnderline{\overbracket} \quad \overbracket {\ListText}^n \] \[ \OverUnderline{\overbrace} \quad \overbrace {\ListText}^n \] \[ \OverUnderline{\underline} \quad \underline {\ListText} \] \[ \OverUnderline{\underparen} \quad \underparen {\ListText}_n \] \[ \OverUnderline{\underbracket} \quad \underbracket {\ListText}_n \] \[ \OverUnderline{\underbrace} \quad \underbrace {\ListText}_n \] \item Primes \[ x' x'' x''' x'''' x^{x'} x^{x''} x^{x'''} x^{x''''} x^{x`} \] \[ x \prime x \dprime x \trprime x \qprime \] \[ x^{\prime} x^{\dprime} x^{\trprime} x^{\qprime} \] % the same as ', '' or ''' => ssty % \begin{center} % \firatext x\symbol{"2032} x\symbol{"2033} x\symbol{"2034} x' x'' x''' % \end{center} \end{itemize} \verb|\lim\limits_{x\to\infty} \frac{1}{x^2} = 0| $ \lim\limits_{x\to\infty} \dfrac{1}{x^2} = 0 $ \verb|\frac{\partial y(x)}{\partial x} = \frac{\symup{d}y(x)}{\symup{d}x} = y'(x)| \[ \frac{\partial y(x)}{\partial x} = \frac{\symup{d}y(x)}{\symup{d}x} = y'(x) \] \printbibliography \end{document}