%&latex %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %% This is the file testmath.mk, part of the MathKit package %% (version 0.7, January , 1998) for math font %% generation. (Author: Alan Hoenig, ajhjj@cunyvm.cuny.edu) %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \documentclass{article} \renewcommand{\encodingdefault}{OT1} \usepackage{z} \title{A \LaTeX\ math test document} \author{for fonts installed by MathKit} \raggedbottom \font\TTT=cmr7 \newcount\cno \def\TT{\T\setbox0=\hbox{\char\cno}\ifdim\wd0>0pt \box0\lower4pt\hbox{\TTT\the\cno}\else \ifdim\ht0>0pt \box0\lower4pt\hbox{\TTT\the\cno}\fi\fi \global\advance\cno by1 } \def\showfont#1{\font\T=#1 at 10pt\global\cno=0 \tabskip1pt plus2pt minus1pt\halign to\textwidth{&\hss\TT ##\hss\cr \multispan{16}\hfil \tt Font #1\hfil\cr\noalign{\smallskip} &&&&&&&&&&&&&&&\cr &&&&&&&&&&&&&&&\cr &&&&&&&&&&&&&&&\cr &&&&&&&&&&&&&&&\cr &&&&&&&&&&&&&&&\cr &&&&&&&&&&&&&&&\cr &&&&&&&&&&&&&&&\cr &&&&&&&&&&&&&&&\cr &&&&&&&&&&&&&&&\cr &&&&&&&&&&&&&&&\cr &&&&&&&&&&&&&&&\cr &&&&&&&&&&&&&&&\cr &&&&&&&&&&&&&&&\cr &&&&&&&&&&&&&&&\cr &&&&&&&&&&&&&&&\cr }} \newcommand{\testsize}[1]{ #1 \texttt{\string#1}: \(a_{c_e}, b_{d_f}, C_{E_G}, 0_{1_2}, a_{0_a}, 0_{a_0}, \sum_{i=0}^\infty\) \\ } \newcommand{\testdelims}[3]{\sqrt{ #1|#1\|#1\uparrow #1\downarrow#1\updownarrow#1\Uparrow#1\Downarrow #1\Updownarrow#1\lfloor#1\lceil #1(#1\{#1[#1\langle #3 #2\rangle#2]#2\}#2) #2\rceil#2\rfloor#2\Updownarrow#2\Downarrow #2\Uparrow#2\updownarrow#2\downarrow#2\uparrow #2\|#2| }\\} \newcommand{\testglyphs}[1]{ \begin{quote} #1a#1b#1c#1d#1e#1f#1g#1h#1i#1j#1k#1l#1m #1n#1o#1p#1q#1r#1s#1t#1u#1v#1w#1x#1y#1z #1A#1B#1C#1D#1E#1F#1G#1H#1I#1J#1K#1L#1M #1N#1O#1P#1Q#1R#1S#1T#1U#1V#1W#1X#1Y#1Z #10#11#12#13#14#15#16#17#18#19 #1\Gamma#1\Delta#1\Theta#1\Lambda#1\Xi #1\Pi#1\Sigma#1\Upsilon#1\Phi#1\Psi#1\Omega #1\alpha#1\beta#1\gamma#1\delta#1\epsilon #1\varepsilon#1\zeta#1\eta#1\theta#1\vartheta #1\iota#1\kappa#1\lambda#1\mu#1\nu#1\xi#1\omicron #1\pi#1\varpi#1\rho#1\varrho #1\sigma#1\varsigma#1\tau#1\upsilon#1\phi #1\varphi#1\chi#1\psi#1\omega #1\partial#1\ell#1\imath#1\jmath#1\wp \end{quote} } \newcommand{\sidebearings}[1]{ \(|#1|\) } \newcommand{\subscripts}[1]{ \(#1_\circ\) } \newcommand{\supscripts}[1]{ \(#1^\circ\) } \newcommand{\scripts}[1]{ \(#1^\circ_\circ\) } \newcommand{\vecaccents}[1]{ \(\vec#1\) } \newcommand{\tildeaccents}[1]{ \(\tilde#1\) } \ifx\omicron\undefined \let\omicron=o \fi \begin{document} \maketitle \subsection*{Introduction} This document tests the math capabilities of a math package, and is strongly modelled after a similar document by Alan Jeffrey. This test exercises the {\tt } math fonts combined with the {\tt } text fonts. \showfont{r7t} \smallskip \showfont{r7m} \smallskip \showfont{sy10} \smallskip \showfont{ex10} \smallskip \subsection*{Fonts} Math italic: \[ ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz \] Text italic: \[ \mathit{ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz} \] Roman: \[ \mathrm{ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz} \] [b]Bold: [b]\[ [b] \mathbf{ABCDEFGHIJKLMNOPQRSTUVWXYZ [b] abcdefghijklmnopqrstuvwxyz} [b]\] [b]{\mathversion{boldmath} [b]\[ [b] \Gamma\Delta\Theta\Lambda\Xi\Pi\Sigma [b] \Upsilon\Phi\Psi\Omega [b]\]} [tt]Typewriter: [tt]\[ [tt] \mathtt{ABCDEFGHIJKLMNOPQRSTUVWXYZ [tt] abcdefghijklmnopqrstuvwxyz} [tt]\] Greek: \[ \Gamma\Delta\Theta\Lambda\Xi\Pi\Sigma\Upsilon\Phi\Psi\Omega \alpha\beta\gamma\delta\epsilon\varepsilon\zeta\eta\theta\vartheta \iota\kappa\lambda\mu\nu\xi\omicron\pi\varpi\rho\varrho \sigma\varsigma\tau\upsilon\phi\varphi\chi\psi\omega \] Calligraphic: \[A\mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ}Z\] Sans: \[ A\mathsf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}Z \quad a\mathsf{abcdefghijklmnopqrstuvwxyz}z \] [fr]Fraktur: [fr]\[ [fr] A\mathfr{ABCDEFGHIJKLMNOPQRSTUVWXYZ}Z \quad [fr] a\mathfr{abcdefghijklmnopqrstuvwxyz}z [fr]\] [bb]Blackboard Bold: [bb]\[ [bb] A\mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ}Z [bb]\] Do these line up appropriately? \[ \forall \mathcal{B} \Gamma [b]\mathbf{D} \exists [tt]\mathtt{F} G \mathcal{H} \Im [b]\mathbf{J} \mathsf{K} \Lambda M \aleph \emptyset \Pi \mathit{Q} \Re \Sigma [tt]\mathtt{T} \Upsilon \mathcal{V} [b]\mathbf{W} \Xi \mathsf{Y} Z \quad a [b]\mathbf{c} \epsilon [tt]\mathtt{i} \kappa [b]\mathbf{m} \nu o \varpi \mathsf{r} s \tau \mathit{u} v \mathsf{w} z \quad [tt]\mathtt{g} j \mathsf{q} \chi y \quad b \delta [b]\mathbf{f} [tt]\mathtt{h} k \mathsf{l} \phi \] \subsection*{Accents} \[ \hbox{% \'o \`o \^o \"o \~o \=o \.o \u o \v o \H o \t oo \c o \d o \b o \t oo} \quad \hat o \check o \tilde o \acute o \grave o \dot o \ddot o \breve o \bar o \vec o \vec h \hbar \] \subsection*{Glyph dimensions} These glyphs should be optically centered: \testglyphs\sidebearings These subscripts should be correctly placed: \testglyphs\subscripts These superscripts should be correctly placed: \testglyphs\supscripts These subscripts and superscripts should be correctly placed: \testglyphs\scripts These accents should be centered: \testglyphs\vecaccents As should these: \testglyphs\tildeaccents \subsection*{Symbols} These arrows should join up properly: \[ a \hookrightarrow b \hookleftarrow c \longrightarrow d \longleftarrow e \Longrightarrow f \Longleftarrow g \longleftrightarrow h \Longleftrightarrow i \mapsto j \] \[ g^\circ \mapsto g^\bullet\quad x\equiv y\not\equiv z \] These symbols should be of similar weights: \[ \pm + - \mp = / \backslash ( \langle [ \{ \} ] \rangle ) < \leq > \geq \] Are these the same size? \[\textstyle \oint \int \quad \bigodot \bigoplus \bigotimes \sum \prod \bigcup \bigcap \biguplus \bigwedge \bigvee \coprod \] Are these? \[ \oint \int \quad \bigodot \bigoplus \bigotimes \sum \prod \bigcup \bigcap \biguplus \bigwedge \bigvee \coprod \] \subsection*{Sizing} \[ abcde + x^{abcde} + 2^{x^{abcde}} \] The subscripts should be appropriately sized: \begin{quote} %\testsize\tiny %\testsize\scriptsize %\testsize\footnotesize %\testsize\small \testsize\normalsize %\testsize\large %\testsize\Large %\testsize\LARGE %\testsize\huge %\testsize\Huge \end{quote} \subsection*{Delimiters} Each row should be a different size, but within each row the delimiters should be the same size. First with \verb|\big|, etc: \[\begin{array}{c} \testdelims\relax\relax{a} \testdelims\bigl\bigr{a} \testdelims\Bigl\Bigr{a} \testdelims\biggl\biggr{a} \testdelims\Biggl\Biggr{a} \end{array}\] Then with \verb|\left| and \verb|\right|: \[\begin{array}{c} \testdelims\left\right{\begin{array}{c} a \end{array}} \testdelims\left\right{\begin{array}{c} a\\a \end{array}} \testdelims\left\right{\begin{array}{c} a\\a\\a \end{array}} \testdelims\left\right{\begin{array}{c} a\\a\\a\\a \end{array}} \end{array}\] \subsection*{Spacing} This paragraph should appear to be a monotone grey texture. Suppose \(f \in \mathcal{S}_n\) and \(g(x) = (-1)^{|\alpha|}x^\alpha f(x)\). Then \(g \in \mathcal{S}_n\); now (\emph{c}) implies that \(\hat g = D_\alpha \hat f\) and \(P \cdot D_\alpha\hat f = P \cdot \hat g = (P(D)g)\hat{}\), which is a bounded function, since \(P(D)g \in L^1(R^n)\). This proves that \(\hat f \in \mathcal S_n\). If \(f_i \rightarrow f\) in \(\mathcal S_n\), then \(f_i \rightarrow f\) in \(L^1(R^n)\). Therefore \(\hat f_i(t) \rightarrow \hat f(t)\) for all \(t \in R^n\). That \(f \rightarrow \hat f\) is a \emph{continuous} mapping of \(\mathcal S_n\) into \(\mathcal S_n\) follows now from the closed graph theorem. And thus for \(x_1\) through \(x_i\). \emph{Functional Analysis}, W.~Rudin, McGraw--Hill, 1973. [b]\begin{boldface} [b]This paragraph should appear to be a monotone dark texture. Suppose [b]\(f \in \mathcal{S}_n\) and \(g(x) = (-1)^{|\alpha|}x^\alpha [b]f(x)\). Then \(g \in \mathcal{S}_n\); now (\emph{c}) implies [b]that \(\hat g = D_\alpha \hat f\) and \(P \cdot D_\alpha\hat [b]f = P \cdot \hat g = (P(D)g)\hat{}\), which is a bounded function, [b]since \(P(D)g \in L^1(R^n)\). This proves that \(\hat f \in [b]\mathcal S_n\). If \(f_i \rightarrow f\) in \(\mathcal S_n\), [b]then \(f_i \rightarrow f\) in \(L^1(R^n)\). Therefore \(\hat [b]f_i(t) \rightarrow \hat f(t)\) for all \(t \in R^n\). That \(f [b]\rightarrow \hat f\) is a \emph{continuous} mapping of [b]\(\mathcal S_n\) into \(\mathcal S_n\) follows now from the [b]closed graph theorem. And thus for \(x_1\) through \(x_i\). [b]\emph{Functional Analysis}, W.~Rudin, McGraw--Hill, 1973. [b]\end{boldface} {\itshape This paragraph should appear to be a monotone grey texture. Suppose \(f \in \mathcal{S}_n\) and \(g(x) = (-1)^{|\alpha|}x^\alpha f(x)\). Then \(g \in \mathcal{S}_n\); now (\emph{c}) implies that \(\hat g = D_\alpha \hat f\) and \(P \cdot D_\alpha\hat f = P \cdot \hat g = (P(D)g)\hat{}\), which is a bounded function, since \(P(D)g \in L^1(R^n)\). This proves that \(\hat f \in \mathcal S_n\). If \(f_i \rightarrow f\) in \(\mathcal S_n\), then \(f_i \rightarrow f\) in \(L^1(R^n)\). Therefore \(\hat f_i(t) \rightarrow \hat f(t)\) for all \(t \in R^n\). That \(f \rightarrow \hat f\) is a \emph{continuous} mapping of \(\mathcal S_n\) into \(\mathcal S_n\) follows now from the closed graph theorem. \emph{Functional Analysis}, W.~Rudin, McGraw--Hill, 1973.} The text in these boxes should spread out as much as the math does: \[\begin{array}{c} \framebox[.95\width][s]{For example \(x+y = \min\{x,y\} + \max\{x,y\}\) is a formula.} \\ \framebox[.975\width][s]{For example \(x+y = \min\{x,y\} + \max\{x,y\}\) is a formula.} \\ \framebox[\width][s]{For example \(x+y = \min\{x,y\} + \max\{x,y\}\) is a formula.} \\ \framebox[1.025\width][s]{For example \(x+y = \min\{x,y\} + \max\{x,y\}\) is a formula.} \\ \framebox[1.05\width][s]{For example \(x+y = \min\{x,y\} + \max\{x,y\}\) is a formula.} \\ \framebox[1.075\width][s]{For example \(x+y = \min\{x,y\} + \max\{x,y\}\) is a formula.} \\ \framebox[1.1\width][s]{For example \(x+y = \min\{x,y\} + \max\{x,y\}\) is a formula.} \\ \framebox[1.125\width][s]{For example \(x+y = \min\{x,y\} + \max\{x,y\}\) is a formula.} \\ \end{array}\] \end{document}