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| -rw-r--r-- | Master/texmf-dist/doc/fonts/firamath-otf/README.md | 11 | ||||
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| -rw-r--r-- | Master/texmf-dist/doc/fonts/firamath-otf/firamath-otf-doc.tex | 948 | ||||
| -rw-r--r-- | Master/texmf-dist/tex/latex/firamath-otf/firamath-otf.sty | 79 | ||||
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| -rw-r--r-- | Master/tlpkg/tlpsrc/collection-fontsextra.tlpsrc | 1 | ||||
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diff --git a/Master/texmf-dist/doc/fonts/firamath-otf/Changes b/Master/texmf-dist/doc/fonts/firamath-otf/Changes new file mode 100644 index 00000000000..e2c21702711 --- /dev/null +++ b/Master/texmf-dist/doc/fonts/firamath-otf/Changes @@ -0,0 +1 @@ +0.01 2018-09-17 - first CTAN version diff --git a/Master/texmf-dist/doc/fonts/firamath-otf/README.md b/Master/texmf-dist/doc/fonts/firamath-otf/README.md new file mode 100644 index 00000000000..b9d508aff57 --- /dev/null +++ b/Master/texmf-dist/doc/fonts/firamath-otf/README.md @@ -0,0 +1,11 @@ +# README # +Package firamath-otf supports the free math font for Fira Sans + +% This file is distributed under the terms of the LaTeX Project Public +% License from CTAN archives in directory macros/latex/base/lppl.txt. +% Either version 1.3 or, at your option, any later version. +% +% +% Copyright 2018 Herbert Voss hvoss@tug.org +% + diff --git a/Master/texmf-dist/doc/fonts/firamath-otf/firamath-otf-doc.pdf b/Master/texmf-dist/doc/fonts/firamath-otf/firamath-otf-doc.pdf Binary files differnew file mode 100644 index 00000000000..5d510dd4db6 --- /dev/null +++ b/Master/texmf-dist/doc/fonts/firamath-otf/firamath-otf-doc.pdf diff --git a/Master/texmf-dist/doc/fonts/firamath-otf/firamath-otf-doc.tex b/Master/texmf-dist/doc/fonts/firamath-otf/firamath-otf-doc.tex new file mode 100644 index 00000000000..7c80b1aac0a --- /dev/null +++ b/Master/texmf-dist/doc/fonts/firamath-otf/firamath-otf-doc.tex @@ -0,0 +1,948 @@ +%% $Id: firamath-otf-doc.tex 809 2018-09-17 06:58:43Z herbert $ +\listfiles +\documentclass[english,log-declarations=false]{article} +\usepackage{amsmath,esvect} +\usepackage{FiraSans} +\usepackage{FiraMono} +\usepackage[fakebold]{firamath-otf} +\usepackage{babel} +\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{dtk-extern} + +\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 + + + +\renewcommand\familydefault{\sfdefault} + + + +\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{Usage} + +\begin{verbatim} +\usepackage[<options>]{firamath-otf} +\end{verbatim} + +Optional arguments are + +\begin{description} +\item[\texttt{fakebold}] Use faked bold symbols +\item[\texttt{usefilenames}] Use filenames for the fonts instead of the symbolic font names +\end{description} + + +The package itself loads by default + +\begin{verbatim} +\RequirePackage{ifxetex,ifluatex,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{{\setBold\symup{T}\unsetBold}} +\def\DD{{\setBold\symup{D}\unsetBold}} + + +\subsection{Version normal} + +\begin{align} +\begin{aligned} + \Q{\varrho}{t}+\symup{div}(\varrho\vec{v}) &= 0 \\ + \varrho\Q{\vec{v}}{t}+(\varrho\vec{v}\cdot\nabla)\vec{v} &= \vec{f}_0+\symup{div}\TT=\vec{f}_0 + -\symup{grad}p+\symup{div}\TT' \\ + \varrho T\frac{\diff s}{\diff t} &= \varrho\frac{\diff e}{\diff t} + -\frac{p}{\varrho}\frac{\diff\varrho}{\diff t}=-\symup{div}\vec{q}+\TT':\DD +\end{aligned} +\end{align} + +\begin{align} + \Q{}{t}\iiint\<\varrho\diff^3V+\oiint\varrho(\vec{v}\cdot\vec{v}ec{n})\diff^2A &= 0\\ + \Q{}{t}\iiint\<\varrho\vec{v}\diff^3V+\oiint\varrho\vec{v}(\vec{v}\cdot\vec{n}\,)\diff^2A &= + \iiint\<f_0\diff^3V+\oiint\vec{n}\cdot\TT\diff^2A \\ + \Q{}{t}\iiint\<\left(\half v^2+e\right)\varrho\diff^3V+\oiint\left(\half v^2+e\right) + \varrho\left(\vec{v}\cdot\vec{n}\,\right)\diff^2A & =\\ + \multispan2{\hfill${\displaystyle-\oiint\left(\vec{q}\cdot\vec{v}ec{n}\right)\diff^2A+ + \iiint\<\left(\vec{v}\cdot\vec{f}_0\right)\diff^3V+\oiint\left(\vec{v} + \cdot\vec{n}~\TT\right)\diff^2A}$}.\nonumber +\end{align} + + +\subsection{Version bold} + +The bold characters are created with the optional argument \texttt{fakebold} which loads the +package \texttt{xfakebold} which writes some information into the created PDF to get bold +characters. For more informations see the documentation of \texttt{xfakebold}. + +\setBold +\begin{align} + \Q{}{t}\iiint\<\varrho\diff^3V+\oiint\varrho(\vec{v}\cdot\vec{v}ec{n})\diff^2A &= 0\\ + \Q{}{t}\iiint\<\varrho\vec{v}\diff^3V+\oiint\varrho\vec{v}(\vec{v}\cdot\vec{n}\,)\diff^2A &= + \iiint\<f_0\diff^3V+\oiint\vec{n}\cdot\symup{T}\diff^2A \\ + \Q{}{t}\iiint\<\left(\half v^2+e\right)\varrho\diff^3V+\oiint\left(\half v^2+e\right) + \varrho\left(\vec{v}\cdot\vec{n}\,\right)\diff^2A & =\\ + \multispan2{\hfill${\displaystyle-\oiint\left(\vec{q}\cdot\vec{v}ec{n}\right)\diff^2A+ + \iiint\<\left(\vec{v}\cdot\vec{f}_0\right)\diff^3V+\oiint\left(\vec{v} + \cdot\vec{n}~\symup{T}\right)\diff^2A}$}.\nonumber +\end{align} +\unsetBold + + +\iffalse +\section{The thin weight} + +\setsansfont{FiraSans-Thin.otf}[BoldFont=FiraSans-SemiBold.otf] +\setmathfont{FiraMath-Thin.otf} + +\subsection{Version normal} + +\begin{align} +\begin{aligned} + \Q{\varrho}{t}+\symup{div}(\varrho\vec{v}) &= 0 \\ + \varrho\Q{\vec{v}}{t}+(\varrho\vec{v}\cdot\nabla)\vec{v} &= \vec{f}_0+\symup{div}\TT=\vec{f}_0 + -\symup{grad}p+\symup{div}\TT' \\ + \varrho T\frac{\diff s}{\diff t} &= \varrho\frac{\diff e}{\diff t} + -\frac{p}{\varrho}\frac{\diff\varrho}{\diff t}=-\symup{div}\vec{q}+\TT':\DD +\end{aligned} +\end{align} + +\begin{align} + \Q{}{t}\iiint\<\varrho\diff^3V+\oiint\varrho(\vec{v}\cdot\vec{v}ec{n})\diff^2A &= 0\\ + \Q{}{t}\iiint\<\varrho\vec{v}\diff^3V+\oiint\varrho\vec{v}(\vec{v}\cdot\vec{n}\,)\diff^2A &= + \iiint\<f_0\diff^3V+\oiint\vec{n}\cdot\TT\diff^2A \\ + \Q{}{t}\iiint\<\left(\half v^2+e\right)\varrho\diff^3V+\oiint\left(\half v^2+e\right) + \varrho\left(\vec{v}\cdot\vec{n}\,\right)\diff^2A & =\\ + \multispan2{\hfill${\displaystyle-\oiint\left(\vec{q}\cdot\vec{v}ec{n}\right)\diff^2A+ + \iiint\<\left(\vec{v}\cdot\vec{f}_0\right)\diff^3V+\oiint\left(\vec{v} + \cdot\vec{n}~\TT\right)\diff^2A}$}.\nonumber +\end{align} + +\subsection{Version bold} + + + +\setBold +\begin{align} + \Q{}{t}\iiint\<\varrho\diff^3V+\oiint\varrho(\vec{v}\cdot\vec{v}ec{n})\diff^2A &= 0\\ + \Q{}{t}\iiint\<\varrho\vec{v}\diff^3V+\oiint\varrho\vec{v}(\vec{v}\cdot\vec{n}\,)\diff^2A &= + \iiint\<f_0\diff^3V+\oiint\vec{n}\cdot\symup{T}\diff^2A \\ + \Q{}{t}\iiint\<\left(\half v^2+e\right)\varrho\diff^3V+\oiint\left(\half v^2+e\right) + \varrho\left(\vec{v}\cdot\vec{n}\,\right)\diff^2A & =\\ + \multispan2{\hfill${\displaystyle-\oiint\left(\vec{q}\cdot\vec{v}ec{n}\right)\diff^2A+ + \iiint\<\left(\vec{v}\cdot\vec{f}_0\right)\diff^3V+\oiint\left(\vec{v} + \cdot\vec{n}~\symup{T}\right)\diff^2A}$}.\nonumber +\end{align} +\unsetBold + + + +\section{The light weight} + +\setsansfont{FiraSans-Light.otf}[BoldFont=FiraSans-SemiBold.otf] +\setmathfont{FiraMath-Light.otf} + +\subsection{Version normal} + +\begin{align} +\begin{aligned} + \Q{\varrho}{t}+\symup{div}(\varrho\vec{v}) &= 0 \\ + \varrho\Q{\vec{v}}{t}+(\varrho\vec{v}\cdot\nabla)\vec{v} &= \vec{f}_0+\symup{div}\TT=\vec{f}_0 + -\symup{grad}p+\symup{div}\TT' \\ + \varrho T\frac{\diff s}{\diff t} &= \varrho\frac{\diff e}{\diff t} + -\frac{p}{\varrho}\frac{\diff\varrho}{\diff t}=-\symup{div}\vec{q}+\TT':\DD +\end{aligned} +\end{align} + +\begin{align} + \Q{}{t}\iiint\<\varrho\diff^3V+\oiint\varrho(\vec{v}\cdot\vec{v}ec{n})\diff^2A &= 0\\ + \Q{}{t}\iiint\<\varrho\vec{v}\diff^3V+\oiint\varrho\vec{v}(\vec{v}\cdot\vec{n}\,)\diff^2A &= + \iiint\<f_0\diff^3V+\oiint\vec{n}\cdot\TT\diff^2A \\ + \Q{}{t}\iiint\<\left(\half v^2+e\right)\varrho\diff^3V+\oiint\left(\half v^2+e\right) + \varrho\left(\vec{v}\cdot\vec{n}\,\right)\diff^2A & =\\ + \multispan2{\hfill${\displaystyle-\oiint\left(\vec{q}\cdot\vec{v}ec{n}\right)\diff^2A+ + \iiint\<\left(\vec{v}\cdot\vec{f}_0\right)\diff^3V+\oiint\left(\vec{v} + \cdot\vec{n}~\TT\right)\diff^2A}$}.\nonumber +\end{align} + +\subsection{Bold version with optional argument \texttt{fakebold}} + + +\setBold +\begin{align} + \Q{}{t}\iiint\<\varrho\diff^3V+\oiint\varrho(\vec{v}\cdot\vec{v}ec{n})\diff^2A &= 0\\ + \Q{}{t}\iiint\<\varrho\vec{v}\diff^3V+\oiint\varrho\vec{v}(\vec{v}\cdot\vec{n}\,)\diff^2A &= + \iiint\<f_0\diff^3V+\oiint\vec{n}\cdot\symup{T}\diff^2A \\ + \Q{}{t}\iiint\<\left(\half v^2+e\right)\varrho\diff^3V+\oiint\left(\half v^2+e\right) + \varrho\left(\vec{v}\cdot\vec{n}\,\right)\diff^2A & =\\ + \multispan2{\hfill${\displaystyle-\oiint\left(\vec{q}\cdot\vec{v}ec{n}\right)\diff^2A+ + \iiint\<\left(\vec{v}\cdot\vec{f}_0\right)\diff^3V+\oiint\left(\vec{v} + \cdot\vec{n}~\symup{T}\right)\diff^2A}$}.\nonumber +\end{align} +\unsetBold + + +\fi + + +\section{Examples} + +\subsection{Digits} + +\begin{itemize} + \item Digits: + \[ 0123456789 \] + \item Proportional digits: + \begingroup + \mathversion{pnum} + \[ 0123456789 \] + \endgroup + \item Bold digits (\verb|\symbf|): + \[ \symbf{0123456789} \] + \item Bold proportional digits (\verb|\symbf|): + \begingroup + \mathversion{pnum} + \[ \symbf{0123456789} \] + \endgroup +\end{itemize} + +\subsection{Alphabets} + +\begin{itemize} + \item Latin letters (mathnormal): + \[ \LatinAlphabets \latinAlphabets \] + + \item Latin upright letters (\verb|\symup|): + \[ \symup{\LatinAlphabets} \symup{\latinAlphabets}\] + + \item Latin typewriter letters (\verb|\symtt|): + \[ \symtt{\LatinAlphabets} \symtt{\latinAlphabets} \] + \item Latin bold letters (\verb|\symbf|): + \[ \symbf{\LatinAlphabets} \symbf{\latinAlphabets}\] + \item Latin bold upright letters (\verb|\symbfup|): + \[ \symbfup{\LatinAlphabets} \symbfup{\latinAlphabets} \] + \item Latin blackboard letters (\verb|\symbb|): + \[ \symbb{\LatinAlphabets} \symbb{\latinAlphabets}\] + % \[ \symbb{The\ quick\ brown\ fox\ jumps\ over\ the\ lazy\ dog.} \] + % \[ \symbb{The\ Quick\ Brown\ Fox\ Jumps\ Over\ The\ Lazy\ Dog.} \] + % \[ \symbb{THE\ QUICK\ BROWN\ FOX\ JUMPS\ OVER\ THE\ LAZY\ DOG.} \] + \item Greek letters: + \[ \GreekAlphabets \greekAlphabets \] + \item Greek upright letters (\verb|\symup|): + \[ \symup{\GreekAlphabets} \symup{\greekAlphabets}\] + \item Greek bold letters (\verb|\symbf|): + \[ \symbf{\GreekAlphabets}\symbf{\greekAlphabets} \] + \item Greek bold upright letters (\verb|\symbfup|): + \[ \symbfup{\GreekAlphabets} \symbfup{\greekAlphabets} \] + \item Dotless letters: + \[ \imath + \jmath + \symup{\imath} + \symup{\jmath} \] + % \TopAccentMap{\symbf}{\imath\jmath} + % \TopAccentMap{\symup}{\imath\jmath} + \item Hebrew + \[ \aleph + \beth + \gimel + \daleth \] + \item Ligature (text): + {\firatext\LigatureText} + \item Non-ligature (math): + \[ \LigatureText + \symit{\LigatureText} + \symrm{\LigatureText} \] + \item Miscellaneous: + \[ + \hslash + + \mbox{\mathversion{hbar}$\hslash$} + + \Angstrom + \] + \[ \forall x > x_0, \, \exists \delta, \delta \in \varnothing \] +\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: + \[ + \int_0^\pi \sin x \, \mathrm{d} x + = \int\limits_0^\pi \sin x \, \mathrm{d} x + = \cos 0 - \cos\pi + C + \] + \[ + \int_{-\infty}^{+\infty} \mathrm{d} z + \iint_{-\infty}^{+\infty} \mathrm{d}^2 y + \iiint_{-\infty}^{+\infty} \mathrm{d}^3 x + \iiiint_{-\infty}^{+\infty} \mathrm{d}^4 p + \] + \[ \oint \dd{r} \oiint \dd{\theta} \oiiint \dd{\varphi}\] + \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: + \[ + \bra{x} + \ket{x} + \ip{\alpha}{\beta} + \op{\alpha^2}{\beta^2} + + \bra{\frac{1}{2}} + \ket{\frac{1}{2}} + + \ip{\frac{1}{2}}{\frac{1}{2}} + \op{\frac{1}{2}}{\frac{1}{2}} + + \bra{\frac{a^2}{b^2}} + + \Biggl\vert \frac{\mathrm{e}^{x^2}}{\mathrm{e}^{y^2}} \Biggr\rangle + \] + \[ + \langle \vert \rangle \quad + \bigl\langle \bigl\vert \bigl\rangle \quad + \Bigl\langle \Bigl\vert \Bigl\rangle \quad + \biggl\langle \biggl\vert \biggl\rangle \quad + \Biggl\langle \Biggl\vert \Biggl\rangle \qquad + \lAngle \vert \rAngle \quad + \bigl\lAngle \bigl\vert \bigl\rAngle \quad + \Bigl\lAngle \Bigl\vert \Bigl\rAngle \quad + \biggl\lAngle \biggl\vert \biggl\rAngle \quad + \Biggl\lAngle \Biggl\vert \Biggl\rAngle + \] + \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 + \[ x' x'' x''' x'''' x` x^{x'} x^{x''} x^{x'''} x^{x''''} x^{x`} \] + \[ x \prime x \dprime x \trprime x \qprime \] + \[ x^{\prime} x^{\dprime} x^{\trprime} x^{\qprime} \] % 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_{x\to\infty} \frac{1}{x^2} = 0| +\[ \lim_{x\to\infty} \frac{1}{x^2} = 0 \] + +\verb|\frac{\partial y(x)}{\partial x} = \frac{\mathrm{d}y(x)}{\mathrm{d}x} = y'(x)| +\[ \frac{\partial y(x)}{\partial x} = \frac{\mathrm{d}y(x)}{\mathrm{d}x} = y'(x) \] + + + +\iffalse +\subsection{More Samples} + +\def\ee{\mathrm{e}} +\def\ii{\mathrm{i}} +\def\bm{\symbf} +\newcommand{\innerprod}[2]{\left\langle{#1}\middle\vert{#2}\right\rangle} +\newcommand{\brakket}[3]{\left\langle{#1}\middle\vert{#2}\middle\vert{#3}\right\rangle} +% \newcommand{\ket}[1]{\left\lvert{#1}\right\rangle} +% \newcommand{\bra}[1]{\left\langle{#1}\right\rvert} +% \newcommand{\ip}[2]{\left\langle{#1}\middle\vert{#2}\right\rangle} +% \newcommand{\op}[2]{\left\lvert{#1}\middle\rangle\middle\langle{#2}\right\rvert} +% \newcommand{\dd}{\,\mathrm{d}} +% \newcommand{\norm}[1]{\left\lVert{#1}\right\rVert} + +\[ g^{mn} g_{mn} T^{i}_{jk} \] + +\[ x \to \infty + \infty - \infty \] + +\begin{align*} + \int_{-\infty}^\infty \ee^{-x^2} \dd{x} + &= \qty[\int_{-\infty}^\infty \ee^{-x^2} \dd{x} \, \int_{-\infty}^\infty \ee^{-y^2} \dd{y}]^{1/2} \\ + &= \qty[\int_0^{2\pi} \int_0^\infty \ee^{-r^2} r \dd{r}\dd{\theta}]^{1/2} \\ + &= \qty[\pi \int_0^\infty \ee^{-u} \dd{u}]^{1/2} \\ + &= \sqrt{\pi} +\end{align*} + + +\begin{align*} +\int_{0}^aJ_0\left[\frac{x_n^{(0)}}{a}r\right]J_0\left[\frac{x_m^{(0)}}{a}r\right]r\dd{r}=\frac{a^2}{2}J_1^2[x_n^{(0)}]\delta_m^n.\\ +\int_{0}^{\infty}\frac{\cos x-\ee^{-x}}{x}\dd{x}=0\\ +\end{align*} +\[\oint_{\partial\Sigma}\vec E\cdot \dd{\vec{l}}=-\frac{1}{c}\frac{\dd}{\dd t}\iint_{\Sigma}\vec B \cdot \dd{\vec{S}};\] +\[\partial_{[a}F_{\beta\gamma]}=0;\quad \partial_\alpha F^{\alpha\beta}=\mu_0J^\beta\] +\[\left(\frac{-\hbar^2}{2m}\nabla^2+V\right)\Psi=i\hbar\dot{\Psi}\] +\[\begin{split} +\frac{1}{\mathcal{C}^2}&{}=\frac{\innerprod{g'}{g'}}{\mathcal{C}^2}=\sum_{\bm{k}}\sum_{\bm{k}'}\brakket{g}{c_{\bm{k}',\uparrow}^\dagger c_{\bm{k}',\downarrow} c_{\bm{k},\downarrow}^\dagger c_{\bm{k},\uparrow}}{g}=\sum_{\bm{k}}\brakket{g}{c_{\bm{k},\uparrow}^\dagger c_{\bm{k},\downarrow} c_{\bm{k},\downarrow}^\dagger c_{\bm{k},\uparrow}}{g}\\ +&{}=\sum_{\bm{k}}\brakket{g}{n_{\bm{k},\uparrow}\left(1-n_{\bm{k},\downarrow}\right)}{g}\\ +&{}=\sum_{\norm{\bm{k}}<k_F^\downarrow}\brakket{g}{0}{g}+\sum_{k_F^\downarrow<\norm{\bm{k}}<k_F^\uparrow}\brakket{g}{1}{g}+\sum_{\norm{\bm{k}}>k_F^\uparrow}\brakket{g}{0}{g}\\ +&{}=N_\uparrow-N_\downarrow +\end{split}\] +\[\left[ f,g \right]\equiv \sum_{\alpha =1}^{s}{\left( \frac{\partial f}{\partial {{q}_{\alpha }}}\frac{\partial g}{\partial {{p}_{\alpha }}}-\frac{\partial g}{\partial {{q}_{\alpha }}}\frac{\partial f}{\partial {{p}_{\alpha }}} \right)}=\sum\limits_{\alpha =1}^{s}{\begin{vmatrix} + \partial_{{q}_{\alpha }} f & \partial_{{p}_{\alpha }} f \\ + \partial_{{q}_{\alpha }} g & \partial_{{p}_{\alpha }} g \\ + \end{vmatrix} }=\sum\limits_{\alpha =1}^{s}{\frac{\partial \left( f,g \right)}{\partial \left( {{q}_{\alpha }},{{p}_{\alpha }} \right)}}\] +\[\begin{split} +& \frac{{{\text{d}}^{2}}f}{\text{d}{{t}^{2}}}=\frac{\text{d}}{\text{d}t}\left[ f,H \right]=\left[ \left[ f,H \right],H \right]=\hat{H}\hat{H}f={{{\hat{H}}}^{2}}f \\ +& \vdots \\ +& \frac{{{\text{d}}^{n}}f}{\text{d}{{t}^{n}}}=\underbrace{\left[ \left[ \left[ f,H \right],\cdots \right],H \right]}_{n}={{{\hat{H}}}^{n}}f \\ +\end{split}\] +\[\tilde{U}(r,z)=E_0\dfrac{\omega_0}{\omega(z)}\exp\left[-r^2\left(\dfrac{1}{\omega^2(z)}+\dfrac{\ii k}{2R(z)}\right)-\ii k z+\ii \zeta(z)\right]\] +\[\omega(z)=\omega_0\sqrt{1+\left(\dfrac{\lambda z}{\pi {\omega_0}^2}\right)^2};\quad R(z)=z\left[1+\left(\dfrac{\pi {\omega_0}^2}{\lambda z}\right)^2\right]\] +\[\left( \begin{matrix} +{mg}/{l}\;+k-m\omega _{1}^{2} & -k \\ +-k & {mg}/{l}\;+k-m\omega _{1}^{2} \\ +\end{matrix} \right)\left( \begin{matrix} +{{a}_{11}} \\ +{{a}_{21}} \\ +\end{matrix} \right)=0\] +\[V=\underbrace{{{V}_{0}}}_{=0}+\underbrace{\sum\limits_{\alpha =1}^{s}{{{\left( \frac{\partial V}{\partial {{q}_{\alpha }}} \right)}_{0}}{{q}_{\alpha }}}}_{=0}+\underbrace{\frac{1}{2}\sum\limits_{\alpha ,\beta =1}^{s}{{{\left( \frac{{{\partial }^{2}}V}{\partial {{q}_{\alpha }}\partial {{q}_{\beta }}} \right)}_{0}}{{q}_{\alpha }}{{q}_{\beta }}}}_{>0}+\cdots \] +\[T=\frac{1}{2}\sum\limits_{i=1}^{n}{{{m}_{i}}{{{\dot{\bm r}}}_{i}}\cdot {{{\dot{\bm r}}}_{i}}}=\frac{1}{2}\sum\limits_{\alpha ,\beta =1}^{s}{\left[ \sum\limits_{i=1}^{n}{{{m}_{i}}{{\left( \frac{\partial {{\bm r}_{i}}}{\partial {{q}_{\alpha }}} \right)}_{0}}\cdot {{\left( \frac{\partial {{\bm r}_{i}}}{\partial {{q}_{\beta }}} \right)}_{0}}} \right]{{{\dot{q}}}_{\alpha }}{{{\dot{q}}}_{\beta }}}+\cdots \] +\[\left( \begin{matrix} +{{u}_{0}} \\ +{{u}_{1}} \\ +\vdots \\ +{{u}_{N-1}} \\ +\end{matrix} \right)=\sum\limits_{k>0}{\left[ \left( \begin{matrix} + 1 \\ + \cos ka \\ + \vdots \\ + \cos k\left( N-1 \right)a \\ + \end{matrix} \right)\underbrace{{{C}_{k+}}\cos \left( {{\omega }_{k}}t+{{\varphi }_{k+}} \right)}_{\frac{2}{\sqrt{N}}{{q}_{k+}}}+\left( \begin{matrix} + 0 \\ + \sin ka \\ + \vdots \\ + \sin k\left( N-1 \right)a \\ + \end{matrix} \right)\underbrace{{{C}_{k-}}\cos \left( {{\omega }_{k}}t+{{\varphi }_{k-}} \right)}_{\frac{2}{\sqrt{N}}{{q}_{k-}}} \right]}\] +\[G(\vec{r},{\vec{r}}',\tau )=\int _{-\infty }^{\infty }\tilde{G}(\vec{r},{\vec{r}}',\omega )e^{-i \tau \omega }d\omega=\int_{-\infty }^{\infty } \frac{e^{-i \tau \omega } e^{i k |\vec{r}-{\vec{r}}'| }}{(2 \pi ) |\vec{r}-{\vec{r}}'| } \, d\omega=\frac{\delta \left(\tau -\frac{R}{c}\right)}{|\vec{r}-{\vec{r}}'| }\] +\[ +\begin{split} +\mathcal{F}^{-1}(\ket{j}) +&{}=\frac{1}{\sqrt{2^n}}\sum_{k=0}^{2^n-1}\exp\left(-2\uppi \ii \frac{jk}{2^n}\right)\ket{k}.\\ +&{}=\frac{1}{\sqrt{2^n}}\sum_{k_{n-1}=0}^1\cdots\sum_{k_{0}=0}^1\exp\left(-2\uppi \ii j\sum_{l=0}^{n-1}\frac{2^l k_l}{2^n}\right)\ket{k_{n-1}\cdots k_0}\\ +&{}=\frac{1}{\sqrt{2^n}}\sum_{k_{n-1}=0}^1\cdots\sum_{k_{0}=0}^1\bigotimes_{l=1}^n\left[\exp\left(-2\uppi \ii j\frac{k_{n-l}}{2^l}\right)\ket{k_{n-l}}\right]\\ +&{}=\frac{1}{\sqrt{2^n}}\bigotimes_{l=1}^n\left[\sum_{k_{n-l}=0}^1\exp\left(-2\uppi \ii j\frac{k_{n-l}}{2^l}\right)\ket{k_{n-l}}\right]\\ +&{}=\frac{1}{\sqrt{2^n}}\bigotimes_{l=1}^n\left[\ket{0}_{n-l}+\ee^{-2\uppi \ii j /2^l}\ket{1}_{n-l}\right]\\ +&{}=\frac{1}{\sqrt{2^n}}\bigotimes_{l=1}^n\left[\ket{0}_{n-l}+\ee^{-2\uppi \ii ({0.j_{l-1}\ldots j_0})}\ket{1}_{n-l}\right]. +\end{split} +\] + +\newcommand{\lb}{\left(} +\newcommand{\rb}{\right)} +\newcommand{\ec}{\text{,}} +\newcommand{\ed}{\text{.}} +\newcommand{\bt}{\lb t\rb} +\newcommand{\deltaup}{\updelta} +\newcommand{\piup}{\uppi} +\newcommand{\ndd}{\,\mathrm{d}} +\subsubsection*{Problem 1} +For convenience, first we set $t_i=0$, and in the end, we replace $t_f$ by $t_f-t_i$ and right answer is obtained. +The classical path is \[x_c\lb t\rb=A \cos\omega t+B\sin \omega t\ec\]where $A$ and $B$ can be determined by plugging $\lb0,x_i\rb$ and $\lb t_f, x_f\rb$ into the equation. The result is +\[x_c\lb t\rb=x_i \cos\omega t+\frac{x_f-x_i\cos\omega t_f}{\sin\omega t_f}\sin \omega t\ed\] +We write $x\lb t\rb=x_c\lb t\rb+\deltaup x\bt$. Due to the fact that $\deltaup x$ should vanish at $t=0$ and $t=t_f$, $\deltaup x$ can be expanded as sine series: \[\deltaup x\bt=\sum_{n=1}^\infty a_n\sin\frac{n\piup t}{t_f}\ed\] +Also, the functional integral can be rewritten as \[\int\mathcal{D}\left[x\bt\right]=c\int\prod_{n=1}^\infty \dd a_n\ed\] +So, we have +\[L=\frac{m}{2}\lb\dot{x}_c+\deltaup\dot{x}\rb^2-\frac{m\omega^2}{2}\lb x_c+\deltaup x\rb^2\ec\] +\[\dot{x}\bt=-\omega x_i \sin\omega t +\omega \frac{x_f-x_i\cos\omega t_f}{\sin\omega t_f}\cos\omega t+\sum_{n=1}^\infty\frac{a_n n \piup}{t_f}\cos\frac{n \piup t}{t_f}\ec\] +\[S=\int_0^{t_f} L\ndd t\ed\] +Because $x_c$ is the classical path, $\deltaup S_\text{classical}=0$, so there can't be any the linear term in the expression of $S$, and we also have in mind that the sine and cosine series are orthogonal. So, we can write S as following: +\[\begin{split}S&{}=\frac{m}{2}\int_0^{t_f}\left[\lb-\omega x_i\sin\omega t+\omega \frac{x_f-x_i\cos\omega t_f}{\sin\omega t_f}\cos\omega t\rb^2+\sum_{n=1}^\infty\lb\frac{a_n n \piup}{t_f}\rb^2\cos^2\frac{n \piup t}{t_f}\right]\ndd t\\% +&\quad{}-\frac{m\omega^2}{2}\int_0^{t_f}\left[\lb x_i\cos\omega t+ \frac{x_f-x_i\cos\omega t_f}{\sin\omega t_f}\sin\omega t\rb^2+\sum_{n=1}^\infty {a_n}^2\sin^2\frac{n \piup t}{t_f}\right]\ndd t\\% +&{}=\sum_{n=1}^\infty\int_0^{t_f}\left[\frac{m}{2}\lb\frac{a_n n \piup}{t_f}\rb^2\cos^2\frac{n \piup t}{t_f}-\frac{m\omega^2}{2}{a_n}^2\sin^2\frac{n \piup t}{t_f}\right]\ndd t\\% +&\quad{}+\frac{m\omega^2}{2}\int_0^{t_f}\left[ {x_i}^2-\lb\frac{x_f-x_i\cos\omega t_f}{\sin\omega t_f}\rb^2\right]\lb\sin^2\omega t-\cos^2\omega t\rb\ndd t\\% +&\quad{}-\frac{m\omega^2}{2}\int_0^{t_f}4 {x_i}\lb\frac{x_f-x_i\cos\omega t_f}{\sin\omega t_f}\rb\lb\sin\omega t\cos\omega t\rb\ndd t\ed\end{split}\] +Using +\[\int_0^{t_f}\lb\sin^2\omega t-\cos^2\omega t\rb\ndd t=-\frac{\sin2\omega t_f}{2\omega}\ec\] +\[\int_0^{t_f}\sin\omega t\cdot\cos\omega t\ndd t=\frac{\sin^2\omega t_f}{2\omega}\ec\] +\[\int_0^{t_f}\sin^2\frac{n\piup t}{t_f} \ndd t=\int_0^{t_f}\cos^2\frac{n\piup t}{t_f} \ndd t=\frac{a_n n \piup}{t_f}\ec\] +we get +\[S=\sum_{n=1}^\infty\left[\frac{m}{2}\lb\frac{a_n n \piup}{t_f}\rb^2-\frac{m\omega^2}{2}{a_n}^2\right]\frac{t_f}{2}+\frac{m\omega}{2\sin\omega t_f}\left[\lb {x_i}^2+{x_f}^2\rb\cos\omega t_f-2 x_i x_f\right]\ed\] +\[\begin{split}U={}&\exp\left\{\frac{\ii}{\hbar}\frac{m\omega}{2\sin\omega t_f}\left[\lb {x_i}^2+{x_f}^2\rb\cos\omega t_f-2 x_i x_f\right]\right\}\\% +&{}\times c\prod_{n=1}^{\infty}\int_{-\infty}^\infty\exp{\frac{\ii}{\hbar}\left[\frac{m}{2}\lb\frac{n \piup}{t_f}\rb^2-\frac{m\omega^2}{2}\right]\frac{t_f {a_n}^2}{2}}\ndd a_n\ed\end{split}\] +Using the Fresnel integral formula: +\[\int_{-\infty}^\infty\exp\lb \ii t\rb\ndd t=\sqrt{\piup \ii}\ec\] +\[\int_{-\infty}^\infty\exp{\frac{\ii}{\hbar}\left[\frac{m}{2}\lb\frac{n \piup}{t_f}\rb^2-\frac{m\omega^2}{2}\right]\frac{t_f {a_n}^2}{2}}\ndd a_n\sim\frac{\sqrt{t_f}}{n}\ec\] +\[U\lb x_f,t_f;x_i,t_i\rb=c'\lb t_f-t_i\rb\exp\left\{\frac{\ii m\omega}{2\hbar\sin\left[\omega \lb t_f-t_i\rb\right]}\left[\lb {x_i}^2+{x_f}^2\rb\cos\left[\omega\lb t_f-t_i\rb\right]-2 x_i x_f\right]\right\}\ed\] +Because \[\int\dd x U\lb x_f,t_f;x,t\rb U\lb x,t;x_i,t_i\rb=U\lb x_f,t_f;x_i,t_i\rb\ec\] +By using the Fresnel integral again: +\[c'\lb t_f-t\rb c'\lb t-t_i\rb\sqrt{\frac{2 \piup \ii \hbar}{m \omega}\lb\frac{\cos\left[\omega\lb t_f-t\rb\right]}{\sin\left[\omega\lb t_f-t\rb\right]}+\frac{\cos\left[\omega\lb t-t_i\rb\right]}{\sin\left[\omega\lb t-t_i\rb\right]}\rb}=c'\lb t_f-t_i\rb\ec\] +\[c'\lb t_f-t_i\rb=\sqrt{\frac{m\omega}{2\piup \ii \hbar\sin\left[\omega\lb t_f-t_i\rb\right]}}\ed\] +Thus +\[\begin{split}U\lb x_f,t_f;x_i,t_i\rb=&\sqrt{\frac{m\omega}{2\piup \ii \hbar\sin\left[\omega\lb t_f-t_i\rb\right]}}\\&{}\times\exp\left\{\frac{\ii m\omega}{2\hbar\sin\left[\omega \lb t_f-t_i\rb\right]}\left[\lb {x_i}^2+{x_f}^2\rb\cos\left[\omega\lb t_f-t_i\rb\right]-2 x_i x_f\right]\right\}\ed\end{split}\] + + +\fi + + + +\end{document} diff --git a/Master/texmf-dist/tex/latex/firamath-otf/firamath-otf.sty b/Master/texmf-dist/tex/latex/firamath-otf/firamath-otf.sty new file mode 100644 index 00000000000..e066ad4a89d --- /dev/null +++ b/Master/texmf-dist/tex/latex/firamath-otf/firamath-otf.sty @@ -0,0 +1,79 @@ +%% $Id: firamath-otf.sty 808 2018-09-17 06:52:53Z herbert $ +%% +%% This file is distributed under the terms of the LaTeX Project Public +%% License from CTAN archives in directory macros/latex/base/lppl.txt. +%% Either version 1.3 or, at your option, any later version. +%% +% +% Copyright 2018 Herbert Voss hvoss@tug.org +% +\ProvidesPackage{firamath-otf}[% + 2018/09/17 v. 0.01 (Herbert Voss) Supports fira math fonts for all luatex/xetex .] + +\RequirePackage{ifxetex,ifluatex,xkeyval,textcomp} +\RequirePackage{unicode-math} + +\newif\iffiramath@fakebold \firamath@fakeboldfalse +\newif\iffiramath@lining \firamath@liningtrue +\newif\iffiramath@tabular \firamath@tabulartrue +\newif\iffiramath@usefilenames \firamath@usefilenamesfalse + +\DeclareOptionX{fakebold}[true]{\@nameuse{firamath@fakebold#1}} +\DeclareOptionX{weight}[Regular]{\def\fira@weight{#1}} +\DeclareOptionX{lining}[true]{\@nameuse{firamath@lining#1}} +\DeclareOptionX{nf}[true]{\@nameuse{firamath@lining#1}} +\DeclareOptionX{lf}[true]{\@nameuse{firamath@lining#1}} +\DeclareOptionX{oldstyle}[true]{\@nameuse{if#1}\firamath@liningfalse\else\firamath@liningtrue\fi} +\DeclareOptionX{osf}[true]{\@nameuse{if#1}\firamath@liningfalse\else\firamath@liningtrue\fi} + +\DeclareOptionX{usefilenames}[true]{\@nameuse{firamath@usefilenames#1}} +\DeclareOptionX{nomath}[true]{\@nameuse{firamath@nomath#1}} + +\DeclareOptionX{tabular}[true]{\@nameuse{firamath@tabular#1}} +\DeclareOptionX{t}[true]{\@nameuse{firamath@tabular#1}} +\DeclareOptionX{proportional}[true]{\@nameuse{if#1}\firamath@tabularfalse\else\firamath@tabulartrue\fi} +\DeclareOptionX{p}[true]{\@nameuse{if#1}\firamath@tabularfalse\else\firamath@tabulartrue\fi} + +\newcommand*\firamath@scale{1} +\DeclareOptionX{Scale}{\renewcommand*{\firamath@scale}{#1}} + +\def\firamath@defaultfeatures{} +\DeclareOptionX{defaultfeatures}{\def\firamath@defaultfeatures{#1}} + +\ProcessOptionsX\relax + +\iffiramath@fakebold\RequirePackage{xfakebold}\fi +\iffiramath@lining + \def\firamath@figurestyle{Lining} +\else + \def\firamath@figurestyle{OldStyle} +\fi + +\iffiramath@tabular + \def\firamath@figurealign{Monospaced} +\else + \def\firamath@figurealign{Proportional} +\fi + +\ifxetex\XeTeXtracingfonts=1\fi +\defaultfontfeatures{\firamath@defaultfeatures} + +\iffiramath@usefilenames + \setmathfont{FiraMath-\fira@weight.otf}[ + Scale=\firamath@scale, + Numbers={\firamath@figurestyle,\firamath@figurealign}, +% BoldFont=FiraMath-Medium.otf + ] + \setmathfont[version=pnum,Numbers=Proportional,Scale=\firamath@scale]{FiraMath-Regular.otf} + +\else + \setmathfont{Fira Math Regular}[ + Scale=\firamath@scale, + Numbers={\firamath@figurestyle,\firamath@figurealign}, +% BoldFont=Fira Math Medium + ] + \setmathfont[version=pnum,Numbers=Proportional,Scale=\firamath@scale]{Fira Math Regular} +\fi + + +\endinput
\ No newline at end of file diff --git a/Master/tlpkg/bin/tlpkg-ctan-check b/Master/tlpkg/bin/tlpkg-ctan-check index 1ef47f3c8a2..f6ebf2136ba 100755 --- a/Master/tlpkg/bin/tlpkg-ctan-check +++ b/Master/tlpkg/bin/tlpkg-ctan-check @@ -270,7 +270,8 @@ my @TLP_working = qw( ffslides fge fgruler fibeamer fifinddo-info fifo-stack fig4latex figbas figbib figflow figsize filecontents filecontentsdef filedate filehook fileinfo filemod - findhyph fink finstrut fira firamath first-latex-doc fitbox fithesis + findhyph fink finstrut fira firamath firamath-otf + first-latex-doc fitbox fithesis fix2col fixcmex fixfoot fixjfm fixlatvian fixltxhyph fixme fixmetodonotes fixpdfmag fjodor diff --git a/Master/tlpkg/libexec/ctan2tds b/Master/tlpkg/libexec/ctan2tds index fa0dc5f81f9..ce6f2978fc3 100755 --- a/Master/tlpkg/libexec/ctan2tds +++ b/Master/tlpkg/libexec/ctan2tds @@ -452,6 +452,7 @@ chomp ($Build = `cd $Master/../Build/source && pwd`); 'fetchbibpes', "die 'skipping, per author (dps) request'", 'feynmf', "&MAKEfeynmf", 'findhyph', "&MAKEflatten", + 'firamath-otf',"&MAKEflatten", 'firststeps', "die 'skipping, noinfo license, 1999 book examples'", 'fitr', "die 'skipping, per author (dpstory) request'", 'fixocgx', "die 'skipping, replaced by ocgx2'", diff --git a/Master/tlpkg/tlpsrc/collection-fontsextra.tlpsrc b/Master/tlpkg/tlpsrc/collection-fontsextra.tlpsrc index 391b32436ad..7f733e3537d 100644 --- a/Master/tlpkg/tlpsrc/collection-fontsextra.tlpsrc +++ b/Master/tlpkg/tlpsrc/collection-fontsextra.tlpsrc @@ -121,6 +121,7 @@ depend feyn depend fge depend fira depend firamath +depend firamath-otf depend foekfont depend fonetika depend fontawesome diff --git a/Master/tlpkg/tlpsrc/firamath-otf.tlpsrc b/Master/tlpkg/tlpsrc/firamath-otf.tlpsrc new file mode 100644 index 00000000000..e69de29bb2d --- /dev/null +++ b/Master/tlpkg/tlpsrc/firamath-otf.tlpsrc |