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% Chapter Template
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\chapter{Sage\TeX} % Main chapter title
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\label{Chapter2} % Change X to a consecutive number; for referencing this chapter elsewhere, use \ref{ChapterX}
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\section{This is a test}
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Testing $\frac{1}{178} = \sage{n(1/178)}$.
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\section{plotting}
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is always fun ...
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\sageplot[width=.5\textwidth]{plot(sin(x), (x,-10,10))}
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\section{This is a test}
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Testing $(1-x-x^2)^3 = \sage{((1-x-x^2)^2).expand()}$.
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Using Sage\TeX, one can use Sage to compute things and put them into
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your \LaTeX{} document. For example, there are
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$\sage{number_of_partitions(1269)}$ integer partitions of $1269$.
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You don't need to compute the number yourself, or even cut and paste
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it from somewhere.
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Here's some Sage code:
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\begin{sageblock}
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f(x) = sin(cos(2*x)^2 / (2+x))
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\end{sageblock}
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The first derivative of $f$ is $\sage{diff(f,x)}$.
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The second derivative of $f$ is
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\[
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  \frac{\mathrm{d}^{2}}{\mathrm{d}x^{2}} \sage{f(x)} =
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  \sage{diff(f, x, 2)(x)}.
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\]
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Here's a plot of $f$ from $-1$ to $10$:
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\sageplot[width=.5\textwidth]{plot(f, -1, 10)}
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\section{AMS Math}
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$$P\left(A=2\middle|\frac{A^2}{B}>4\right)$$
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Matrix:
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\begin{equation*}
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A_{m,n} =
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 \begin{pmatrix}
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  a_{1,1} & a_{1,2} & \cdots & a_{1,n} \\
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  a_{2,1} & a_{2,2} & \cdots & a_{2,n} \\
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  \vdots  & \vdots  & \ddots & \vdots  \\
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  a_{m,1} & a_{m,2} & \cdots & a_{m,n}
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 \end{pmatrix}
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\end{equation*}
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More here: \url{https://en.wikibooks.org/wiki/LaTeX/Mathematics}.
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