diff options
Diffstat (limited to 'Master/texmf-doc/doc/english/firststeps/gallery.tex')
| -rw-r--r-- | Master/texmf-doc/doc/english/firststeps/gallery.tex | 254 |
1 files changed, 254 insertions, 0 deletions
diff --git a/Master/texmf-doc/doc/english/firststeps/gallery.tex b/Master/texmf-doc/doc/english/firststeps/gallery.tex new file mode 100644 index 00000000000..2dee9d3ff09 --- /dev/null +++ b/Master/texmf-doc/doc/english/firststeps/gallery.tex @@ -0,0 +1,254 @@ +% Sample file: gallery.tex formula template file +% Typeset with LaTeX format + +\documentclass{article} + +\usepackage{amssymb,latexsym,amsmath} + +\begin{document} + +Section 3.1 Formula gallery + +Formula 1 +\[ + x \mapsto \{\, c \in C \mid c \leq x \,\} +\] + +Formula 2 +\[ + \left| \bigcup (\, I_{j} \mid j \in J \,) \right| + < \mathfrak{m} +\] + +Formula 3 +\[ + A = \{\, x \in X \mid x \in X_{i}, + \mbox{ for some } i \in I \,\} +\] + +Formula 4 +\[ + \langle a_{1}, a_{2} \rangle \leq \langle a'_{1}, a'_{2}\rangle + \qquad \mbox{if{f}} \qquad a_{1} < a'_{1} \quad \mbox{or} + \quad a_{1} = a'_{1} \mbox{ and } a_{2} \leq a'_{2} +\] + +Formula 5 +\[ + \Gamma_{u'} = \{\, \gamma \mid \gamma < 2\chi, + \ B_{\alpha} \nsubseteq u', \ B_{\gamma} \subseteq u' \,\} +\] + +Formula 6 +\[ + A = B^{2} \times \mathbb{Z} +\] + +Formula 7 +\[ + \left( \bigvee (\, s_{i} \mid i \in I \,) \right)^{c} = + \bigwedge (\, s_{i}^{c} \mid i \in I \,) +\] + +Formula 8 +\[ + y \vee \bigvee (\, [B_{\gamma}] \mid \gamma + \in \Gamma \,) \equiv z \vee \bigvee (\, [B_{\gamma}] + \mid \gamma \in \Gamma \,) \pmod{ \Phi^{x} } +\] + +Formula 9 +\[ + f(\mathbf{x}) = \bigvee\nolimits_{\!\mathfrak{m}} + \left(\, + \bigwedge\nolimits_{\mathfrak{m}} + (\, x_{j} \mid j \in I_{i} \,) \mid i < \aleph_{\alpha} + \,\right) +\] + +Formula 10 +\[ + \left. \widehat{F}(x) \right|_{a}^{b} = + \widehat{F}(b) - \widehat{F}(a) +\] + +Formula 11 +\[ + u \underset{\alpha}{+} v \overset{1}{\thicksim} w + \overset{2}{\thicksim} z +\] + +Formula 12 +\[ + f(x) \overset{ \text{def} }{=} x^{2} - 1 +\] + +Formula 13 +\[ + \overbrace{a + b + \cdots + z}^{n} +\] + +Formula 14 +\[ + \begin{vmatrix} + a + b + c & uv\\ + a + b & c + d + \end{vmatrix} + = 7 +\] + +\[ + \begin{Vmatrix} + a + b + c & uv\\ + a + b & c + d + \end{Vmatrix} + = 7 +\] + +Formula 15 +\[ + \sum_{j \in \mathbf{N}} b_{ij} \hat{y}_{j} = + \sum_{j \in \mathbf{N}} b^{(\lambda)}_{ij} \hat{y}_{j} + + (b_{ii} - \lambda_{i}) \hat{y}_{i} \hat{y} +\] + +Formula 16 +\[ + \left( \prod^n_{\, j = 1} \hat x_{j} \right) H_{c} = + \frac{1}{2} \hat k_{ij} \det \hat{ \mathbf{K} }(i|i) +\] + +\[ + \biggl( \prod^n_{\, j = 1} \hat x_{j} \biggr) H_{c} = + \frac{1}{2} \hat{k}_{ij} \det \widehat{ \mathbf{K} }(i|i) +\] + +Formula 17 +\[ + \det \mathbf{K} (t = 1, t_{1}, \ldots, t_{n}) = + \sum_{I \in \mathbf{n} }(-1)^{|I|} + \prod_{i \in I} t_{i} + \prod_{j \in I} (D_{j} + \lambda_{j} t_{j}) + \det \mathbf{A}^{(\lambda)} (\,\overline{I} | \overline{I}\,) = 0 +\] + +Formula 18 +\[ + \lim_{(v, v') \to (0, 0)} + \frac{H(z + v) - H(z + v') - BH(z)(v - v')} + {\| v - v' \|} = 0 +\] + +Formula 19 +\[ + \int_{\mathcal{D}} | \overline{\partial u} |^{2} + \Phi_{0}(z) e^{\alpha |z|^2} \geq + c_{4} \alpha \int_{\mathcal{D}} |u|^{2} \Phi_{0} + e^{\alpha |z|^{2}} + c_{5} \delta^{-2} \int_{A} + |u|^{2} \Phi_{0} e^{\alpha |z|^{2}} +\] + +Formula 20 +\[ + \mathbf{A} = + \begin{pmatrix} + \dfrac{\varphi \cdot X_{n, 1}} + {\varphi_{1} \times \varepsilon_{1}} + & (x + \varepsilon_{2})^{2} & \cdots + & (x + \varepsilon_{n - 1})^{n - 1} + & (x + \varepsilon_{n})^{n}\\[10pt] + \dfrac{\varphi \cdot X_{n, 1}} + {\varphi_{2} \times \varepsilon_{1}} + & \dfrac{\varphi \cdot X_{n, 2}} + {\varphi_{2} \times \varepsilon_{2}} + & \cdots & (x + \varepsilon_{n - 1})^{n - 1} + & (x + \varepsilon_{n})^{n}\\ + \hdotsfor{5}\\ + \dfrac{\varphi \cdot X_{n, 1}} + {\varphi_{n} \times \varepsilon_{1}} + & \dfrac{\varphi \cdot X_{n, 2}} + {\varphi_{n} \times \varepsilon_{2}} + & \cdots & \dfrac{\varphi \cdot X_{n, n - 1}} + {\varphi_{n} \times \varepsilon_{n - 1}} + & \dfrac{\varphi\cdot X_{n, n}} + {\varphi_{n} \times \varepsilon_{n}} + \end{pmatrix} + + \mathbf{I}_{n} +\] + + +Section 3.2. User-defined commands + +Formula 20 with user-defined commands: + +\newcommand{\quot}[2]{% +\dfrac{\varphi \cdot X_{n, #1}}% +{\varphi_{#2} \times \varepsilon_{#1}}} +\newcommand{\exn}[1]{(x+\varepsilon_{#1})^{#1}} + +\[ + \mathbf{A} = + \begin{pmatrix} + \quot{1}{1} & \exn{2} & \cdots & \exn{n - 1}&\exn{n}\\[10pt] + \quot{1}{2} & \quot{2}{2} & \cdots & \exn{n - 1} &\exn{n}\\ + \hdotsfor{5}\\ + \quot{1}{n} & \quot{2}{n} & \cdots & + \quot{n - 1}{n} & \quot{n}{n} + \end{pmatrix} + + \mathbf{I}_{n} +\] + +Section 3.3. Building a formula step-by-step + +Step 1 +$\left[ \frac{n}{2} \right]$ + +Step 2 +\[ + \sum_{i = 1}^{ \left[ \frac{n}{2} \right] } +\] + +Step 3 +\[ + x_{i, i + 1}^{i^{2}} \qquad \left[ \frac{i + 3}{3} \right] +\] + +Step 4 +\[ + \binom{ x_{i,i + 1}^{i^{2}} }{ \left[ \frac{i + 3}{3} \right] } +\] + +Step 5 +$\sqrt{ \mu(i)^{ \frac{3}{2} } (i^{2} - 1) }$ + +$\sqrt{ \mu(i)^{ \frac{3}{2} } (i^{2} - 1) }$ + +Step 6 +$\sqrt[3]{ \rho(i) - 2 }$ $\sqrt[3]{ \rho(i) - 1 }$ + +Step 7 +\[ + \frac{ \sqrt{ \mu(i)^{ \frac{3}{2}} (i^{2} -1) } } + { \sqrt[3]{\rho(i) - 2} + \sqrt[3]{\rho(i) - 1} } +\] + +Step 8 +\[ + \sum_{i = 1}^{ \left[ \frac{n}{2} \right] } + \binom{ x_{i, i + 1}^{i^{2}} } + { \left[ \frac{i + 3}{3} \right] } + \frac{ \sqrt{ \mu(i)^{ \frac{3}{2}} (i^{2} - 1) } } + { \sqrt[3]{\rho(i) - 2} + \sqrt[3]{\rho(i) - 1} } +\] + +\[\sum_{i=1}^{\left[\frac{n}{2}\right]}\binom{x_{i,i+1}^{i^{2}}} +{\left[\frac{i+3}{3}\right]}\frac{\sqrt{\mu(i)^{\frac{3} +{2}}(i^{2}-1)}}{\sqrt[3]{\rho(i)-2}+\sqrt[3]{\rho(i)-1}}\] + +%\[\sum_{i=1}^{\left[\frac{n}{2}\right]}\binom{x_{i,i+1}^{i^{2}}} +%{\left[\frac{i+3}{3}\right]}\frac{\sqrt{\mu(i)^{\frac{3} +%{2}}}(i^{2}-1)}}{\sqrt[3]{\rho(i)-2}+\sqrt[3]{\rho(i)-1}}\] + + +\end{document} + |