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% Sample file: gallery.tex formula template file
% Typeset with LaTeX format
\documentclass{article}
\usepackage{amssymb,latexsym,amsmath}
\begin{document}
Section 1.4. 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
\[
\sum_{i = 1}^{ \left[ \frac{n}{2} \right] }
\binom{ x_{i, i + 1}^{i^{2}} }
{ \left[ \frac{i + 3}{3} \right] }
\frac{ \sqrt{ \mu(i)^{ \frac{3}{2}} (i^{2} - 1) } }
{ \sqrt[3]{\rho(i) - 2} + \sqrt[3]{\rho(i) - 1} }
\]
\[\sum_{i=1}^{\left[\frac{n}{2}\right]}\binom{x_{i,i+1}^{i^{2}}}
{\left[\frac{i+3}{3}\right]}\frac{\sqrt{\mu(i)^{\frac{3}
{2}}(i^{2}-1)}}{\sqrt[3]{\rho(i)-2}+\sqrt[3]{\rho(i)-1}}\]
%\[\sum_{i=1}^{\left[\frac{n}{2}\right]}\binom{x_{i,i+1}^{i^{2}}}
%{\left[\frac{i+3}{3}\right]}\frac{\sqrt{\mu(i)^{\frac{3}
%{2}}}(i^{2}-1)}}{\sqrt[3]{\rho(i)-2}+\sqrt[3]{\rho(i)-1}}\]
Section 1.5 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
\[
y^C \equiv z \vee \bigvee_{ i \in C } \left[ s_{i}^{C} \right]
\pmod{ \Phi }
\]
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
\[
\begin{vmatrix}
a + b + c & uv\\
a + b & c + d
\end{vmatrix}
= 7
\]
\[
\begin{Vmatrix}
a + b + c & uv\\
a + b & c + d
\end{Vmatrix}
= 7
\]
\[
\left\|\begin{array}{cc}
a + b + c & uv\\
a + b & c + d
\end{array}\right\|
= 7
\]
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 9.1.3 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}}
\[
\mathbf{A} =
\begin{pmatrix}
\quot{1}{1} & \exn{2} & \cdots & \exn{n - 1}
& \exn{n}\\[10pt]
\quot{1}{2} & \quot{2}{2} & \cdots & \exn{n - 1}
&\exn{n}\\
\hdotsfor{5}\\
\quot{1}{n} & \quot{2}{n} & \cdots &
\quot{n - 1}{n} & \quot{n}{n}
\end{pmatrix}
+ \mathbf{I}_{n}
\]
\end{document}
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