Chapter 5 Authoring

\usepackage{mathpage}

This is the first paragraph! This is the second sentence.
This is the third sentence.

\chapter{Authoring}

This is the first sentence.

\section{Sectioning}

This is the first sentence.

\subsection{Subsection}

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\subsubsection{Subsubsection}

This is the first sentence.

\paragraph{Paragraph} This is the first sentence.

The equation $e^{\pi i}+1=0$ holds.

The equation
\[
    e^{\pi i}+1=0
\]
holds.

\[
    \int_{-1}^2e^x dx
\]

\[
    \int\sin(x)dx=-\cos(x)+C
\]

\[
    \begin{bmatrix}
    1 & 2 \\
    3 & 4
    \end{bmatrix}
\]

\[
    \begin{matrix}
    1 & 2 \\
    3 & 4
    \end{matrix}
\]

\[
    \left\{\begin{matrix}
    1 & 2 \\
    3 & 4
    \end{matrix}\right.
\]

\[
    \begin{array}{|rl|}
    \hline
    a & b \\
    aa & bb \\
    \hline
    c & d \\
    cc & dd \\
    \hline
    \end{array}
\]

\begin{itemize}
  \item Sine addition formula
  \item Cosine addition formula
\end{itemize}

• •
  Sine addition formula
• •
  Cosine addition formula

\begin{itemize}
  \item Sine addition formula
  \begin{itemize}
    \item $\sin(x+y)=\sin x\cos y + \cos x\sin y$
    \item $\sin(x-y)=\sin x\cos y - \cos x\sin y$
  \end{itemize}
  \item Cosine addition formula
  \begin{itemize}
    \item $\cos(x+y)=\cos x\cos y - \sin x\sin y$
    \item $\cos(x-y)=\cos x\cos y + \sin x\sin y$
    \begin{itemize}
      \item Note 1
      \item Note 2
    \end{itemize}
  \end{itemize}
\end{itemize}

• •
  Sine addition formula

  • –
    ​\(\sin (x+y)=\sin x\cos y + \cos x\sin y\)
  • –
    ​\(\sin (x-y)=\sin x\cos y - \cos x\sin y\)
• •
  Cosine addition formula

  • –
    ​\(\cos (x+y)=\cos x\cos y - \sin x\sin y\)
  • –
    ​\(\cos (x-y)=\cos x\cos y + \sin x\sin y\)

    • *
      Note 1
    • *
      Note 2

\begin{enumerate}
  \item $\sin(x+y)=\sin x\cos y + \cos x\sin y$
  \item $\cos(x+y)=\cos x\cos y - \sin x\sin y$
\end{enumerate}

• 1.
  ​\(\sin (x+y)=\sin x\cos y + \cos x\sin y\)
• 2.
  ​\(\cos (x+y)=\cos x\cos y - \sin x\sin y\)

\begin{enumerate}
  \item Sine addition formula
  \begin{enumerate}
    \item $\sin(x+y)=\sin x\cos y + \cos x\sin y$
    \item $\sin(x-y)=\sin x\cos y - \cos x\sin y$
  \end{enumerate}
  \item Cosine addition formula
  \begin{enumerate}
    \item $\cos(x+y)=\cos x\cos y - \sin x\sin y$
    \item $\cos(x-y)=\cos x\cos y + \sin x\sin y$
    \begin{enumerate}
      \item Note 1
      \item Note 2
    \end{enumerate}
  \end{enumerate}
\end{enumerate}

• 1.
  Sine addition formula

  • (a)
    ​\(\sin (x+y)=\sin x\cos y + \cos x\sin y\)
  • (b)
    ​\(\sin (x-y)=\sin x\cos y - \cos x\sin y\)
• 2.
  Cosine addition formula

  • (a)
    ​\(\cos (x+y)=\cos x\cos y - \sin x\sin y\)
  • (b)
    ​\(\cos (x-y)=\cos x\cos y + \sin x\sin y\)

    • i.
      Note 1
    • ii.
      Note 2

\begin{description}
  \item[Sine addition formula:] $\sin(x+y)=\sin x\cos y + \cos x\sin y$
  \item[Cosine addition formula:] $\cos(x+y)=\cos x\cos y - \sin x\sin y$
\end{description}

• Sine addition formula:
  ​\(\sin (x+y)=\sin x\cos y + \cos x\sin y\)
• Cosine addition formula:
  ​\(\cos (x+y)=\cos x\cos y - \sin x\sin y\)

\begin{tabular}{|c|c||c|c|}
\hline
OS & Browser & Wifi & Camera \\
\hline\hline
Windows & Chrome & O & O \\
Windows & Edge   & O & O \\
Mac & Chrome     & O & O \\
Mac & Safari     & X & O \\
\hline
\end{tabular}

Refer to Chapter \ref{chap:abc}

Refer to Section \ref{sec:abc}

The equation \eqref{equ:abc} is true

The equation \eqref{equ:bcd} is false

\chapter{Authoring}\label{chap:abc}

\section{Cross Reference 2}\label{sec:abc}

\begin{equation}\label{equ:abc}
    1 + 1 = 2
\end{equation}

\[\tag{S}\label{equ:bcd}
    1 + 1 = 3
\]

Consult the TeXbook \cite{knuth1984texbook}

\begin{thebibliography}{1}

\bibitem{knuth1984texbook}
Donald~Ervin Knuth and Duane Bibby.
\newblock The TeXbook, volume~3.
\newblock Addison-Wesley Reading, 1984.

\end{thebibliography}

\makeindex

\printindex

MathPage\index{MathPage} is a system for online publishing

\begin{center}
    \includegraphics{pics/graph}
\end{center}

\begin{center}
    \includegraphics[scale=1.5]{pics/graph}
\end{center}

\begin{center}
    \includemedia{media/sine}
\end{center}

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    \includemedia{media/Star Wars}
\end{center}

\begin{center}
    \includemedia{media/bitcoin.pdf}
\end{center}

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    \includemedia{media/notebook.html}
\end{center}

\begin{center}
    \includefile{supplements/book-ko.cls}
\end{center}

\begin{center}
    \includewebpage{https://en.wikipedia.org/wiki/LaTeX}
\end{center}

\begin{displaycode}{python}
a = 10
b = 15
print(a / b)
\end{displaycode}

\begin{evaluatecode}{python}
a = 10
b = 15
print(a / b)
\end{evaluatecode}

\begin{evaluatecode}{sage}
@interact
def _(n=input_box(10, label='n', width=10)):
    v = [(random(), random(), random()) for _ in [1..n]]
    g = sum([cube((10*a, 10*b, 10*c), size=random(), color=(a,b,c))
             for a,b,c in v])
    show(g)
\end{evaluatecode}

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\usepackage{name}

\begin{framed}
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\end{framed}

\href{https://en.wikipedia.org/wiki/Law_of_large_numbers}{Law of large numbers}

\url{http://www.sagemath.org}

\mintinline{python}{s = "hello"}

s = "hello"

\begin{minted}{python}
def sum(n):
    s = 0
    for i in range(1, n + 1):
        s = s + i
    return s
\end{minted}

def sum(n):
    s = 0
    for i in range(1, n + 1):
        s = s + i
    return s

\newenvironment{python}{\VerbatimEnvironment\begin{displaycode}{python}}{\end{displaycode}}

\begin{python}
2**10
\end{python}