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diff --git a/fonts/eulerpx/doc/sample.tex b/fonts/eulerpx/doc/sample.tex new file mode 100644 index 0000000000..5505c02a57 --- /dev/null +++ b/fonts/eulerpx/doc/sample.tex @@ -0,0 +1,176 @@ + +\newcommand*\mat[1]{\bm{#1}} +%\newcommand*\mat[1]{\textsf{#1}} + +%The following snippets mostly originated with the \TeX Book and were adapted for \LaTeX{} from Karl~Berry's torture test for plain \TeX{} math fonts. + +$x + y - z$, \quad $x + y * z$, \quad $z * y / z$, \quad +$(x+y)(x-y) = x^2 - y^2$, + +$x \times y \cdot z = [x\, y\, z]$, \quad $x\circ y \bullet z$, \quad +$x\cup y \cap z$, \quad $x\sqcup y \sqcap z$, \quad + +$x \vee y \wedge z$, \quad $x\pm y\mp z$, \quad +$x=y/z$, \quad $x \coloneq y$, \quad $x\le y \ne z$, \quad $x \sim y \simeq z$ +$x \equiv y \nequiv z$, \quad $x\subset y \subseteq z$ + +$\sin2\theta=2\sin\theta\cos\theta$, \quad +$\hbox{O}(n\log n\log n)$, \quad +$\Pr(X>x)=\exp(-x/\mu)$, + +$\bigl(x\in A(n)\bigm|x\in B(n)\bigr)$, \quad +$\bigcup_n X_n\bigm\|\bigcap_n Y_n$ + +% page 178 + +In text matrices $\binom{1\,1}{0\,1}$ and $\bigl(\genfrac{}{}{0pt}{}{a}{1}\genfrac{}{}{0pt}{}{b}{m}\genfrac{}{}{0pt}{}{c}{n}\bigr)$ + +% page 142 + +\[a_0+\frac1{\displaystyle a_1 + +{\strut \frac1{\displaystyle a_2 + +{\strut \frac1{\displaystyle a_3 + +{\strut \frac1{\displaystyle a_4}}}}}}}\] + +% page 143 + +\[\binom{p}{2}x^2y^{p-2} - \frac1{1 - x}\frac{1}{1 - x^2} += +\frac{a+1}{b}\bigg/\frac{c+1}{d}.\] + +%% page 145 + +\[\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+x}}}}}\] + +%% page 147 + +\[\left(\frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2}\right) +\bigl|\varphi(x+iy)\bigr|^2=0\] + +%% page 149 + +% \[\pi(n)=\sum_{m=2}^n\left\lfloor\biggl(\sum_{k=1}^{m-1}\bigl +% \lfloor(m/k)\big/\lceil m/k\rceil\bigr\rfloor\biggr)^{-1}\right\rfloor.\] + +\[\pi(n)=\sum_{m=2}^n\left\lfloor\Biggl(\sum_{k=1}^{m-1}\bigl +\lfloor(m/k)\big/\lceil m/k\rceil\bigr\rfloor\Biggr)^{-1}\right\rfloor.\] + +% page 168 + +\[\int_0^\infty \frac{t - i b}{t^2 + b^2}e^{iat}\,dt=e^{ab}E_1(ab), \quad +a,b > 0.\] + +% page 176 + +\[\mat{A} \coloneq \begin{pmatrix}x-\lambda&1&0\\ +0&x-\lambda&1\\ +0&0&x-\lambda\end{pmatrix}.\] + +\[\left\lgroup\begin{matrix}a&b&c\\ d&e&f\\\end{matrix}\right\rgroup +\left\lgroup\begin{matrix}u&x\cr v&y\cr w&z\end{matrix}\right\rgroup\] + +% page 177 + +\[\mat{A} = \begin{pmatrix}a_{11}&a_{12}&\ldots&a_{1n}\\ +a_{21}&a_{22}&\ldots&a_{2n}\\ +\vdots&\vdots&\ddots&\vdots\\ +a_{m1}&a_{m2}&\ldots&a_{mn}\end{pmatrix}\] + +\[\mat{M}=\bordermatrix{&C&I&C'\cr +C&1&0&0\cr I&b&1-b&0\cr C'&0&a&1-a}\] + +%% page 186 + +\[\sum_{n=0}^\infty a_nz^n\qquad\hbox{converges if}\qquad +|z|<\Bigl(\limsup_{n\to\infty}\root n\of{|a_n|}\,\Bigr)^{-1}.\] + +\[\frac{f(x+\Delta x)-f(x)}{\Delta x}\to f'(x) +\qquad \hbox{as $\Delta x\to0$.}\] + +\[\|u_i\|=1,\qquad u_i\cdot u_j=0\quad\hbox{if $i\ne j$.}\] + +%% page 191 + +\[\it\hbox{The confluent image of}\quad +\begin{Bmatrix}\hbox{an arc}\hfill\\\hbox{a circle}\hfill\\ +\hbox{a fan}\hfill\\\end{Bmatrix} +\quad\hbox{is}\quad +\begin{Bmatrix}\hbox{an arc}\hfill\\ +\hbox{an arc or a circle}\hfill\\ +\hbox{a fan or an arc}\hfill\end{Bmatrix}.\] + +%% page 191 + +\begin{align*} +T(n)\le T(2^{\lceil\lg n\rceil}) +&\le c(3^{\lceil\lg n\rceil}-2^{\lceil\lg n\rceil})\\ +&<3c\cdot3^{\lg n}\\ +&=3c\,n^{\lg3}. +\end{align*} + +%\begin{align*} +%\left\{% +%\begin{gathered}\alpha&=f(z)\\ \beta&=f(z^2)\\ \gamma&=f(z^3) +%\end{gathered} +%\right\} +%\qquad +%\left\{% +%\begin{gathered} +%x&=\alpha^2-\beta\\ y&=2\gamma +%\end{gathered} +%\right\}% +%\end{align*} + +%\[\left\{ +%\begin{align} +%\alpha&=f(z)\cr \beta&=f(z^2)\cr \gamma&=f(z^3)\\ +%%\end{align} +%\right\} +%\qquad +%\left\{ +%%\begin{align} +%x&=\alpha^2-\beta\cr y&=2\gamma\\ +%\end{align} +%\right\}.\] +%%% page 192 + +\begin{align*} +\begin{aligned} +(x+y)(x-y)&=x^2-xy+yx-y^2\\ +&=x^2-y^2\\ +(x+y)^2&=x^2+2xy+y^2. +\end{aligned} +\end{align*} + +%% page 192 + +\begin{align*} +\begin{aligned} +\biggl(\int_{-\infty}^\infty e^{-x^2}\,dx\biggr)^2 +&=\int_{-\infty}^\infty\int_{-\infty}^\infty e^{-(x^2+y^2)}\,dx\,dy\\ +&=\int_0^{2\pi}\int_0^\infty e^{-r^2}\,dr\,d\theta\\ +&=\int_0^{2\pi}\biggl(e^{-\frac{r^2}{2}} +\biggl|_{r=0}^{r=\infty}\,\biggr)\,d\theta\\ +&=\pi. +\end{aligned} +\end{align*} + +%% page 197 + +\[\prod_{k\ge0}\frac{1}{(1-q^kz)}= +\sum_{n\ge0}z^n\bigg/\!\!\prod_{1\le k\le n}(1-q^k).\] + +\[\sum_{\substack{\scriptstyle 0< i\le m\\\scriptstyle0<j\le n}}p(i,j) \,\ne +% +% \[\sum_{i=1}^p \sum_{j=1}^q \sum_{k=1}^r a_{ij} b_{jk} c_{ki}\] +% +\sum_{i=1}^p \sum_{j=1}^q \sum_{k=1}^r a_{ij} b_{jk} c_{ki} \,\ne +% +\sum_{\substack{\scriptstyle 1\le i\le p \\ \scriptstyle 1\le j\le q\\ +\scriptstyle 1\le k\le r}} a_{ij} b_{jk} c_{ki}\] + +\[\max_{1\le n\le m}\log_2P_n \quad \hbox{and} \quad +\lim_{x\to0}\frac{\sin x}{x}=1\] + +\[p_1(n)=\lim_{m\to\infty}\sum_{\nu=0}^\infty\bigl(1-\cos^{2m}(\nu!^n\pi/n)\bigr)\] + |