SageTeX

\documentclass{article}
\usepackage{sagetex}
\begin{document}
\section*{SageTeX}

\emph{In this preview:} press \textbf{Run} to run the code with Sagebrush's Sage, in this browser, in page
order; until then each \texttt{\textbackslash sage\{...\}} shows as a placeholder. The results are kept beside
this file (\texttt{sagebrush latex run} on a computer makes the same file); after an edit, press Run again.

\begin{sagesilent}
f(x) = x^3 - 2*x + 1
g = f.diff(x)
\end{sagesilent}

The derivative of $f(x) = x^3 - 2x + 1$ is $f'(x) = \sage{g(x)}$, and
$\int_0^1 f(x)\,dx = \sage{integral(f(x), x, 0, 1)}$.

The 10th prime is $\sage{nth_prime(10)}$, and $2^{100} = \sage{2^100}$.

\begin{sagesilent}
f(x) = sin(x)
\end{sagesilent}

Code runs in page order, so a name can be defined again: from here on $f(x) = \sage{f(x)}$.

\sageplot[width=0.5\textwidth]{plot(f(x), (x, 0, 2*pi))}
\end{document}