% General example LaTeX file for including Sage calculations and plots % Build with: (pdf)latex example.tex; sage example.sage; pdflatex % example.tex Please read README and the documentation of the SageTeX % package for more information! \documentclass{article} \title{Examples of embedding Sage in \LaTeX{} with \textsf{Sage\TeX}} \author{Dan Drake and others} \usepackage{sagetex} % % If you want sagetex to use Imagemagick's convert utility to make eps % files from png files when generating a dvi file, add the % "imagemagick" option above: % % \usepackage[imagemagick]{sagetex} \setlength{\sagetexindent}{10ex} \begin{document} \maketitle \section{Inline Sage, code blocks} This is an example $2+2=\sage{2+2}$. If you raise the current year mod $100$ (which equals $\sage{mod(\the\year, 100)}$) to the power of the current day ($\the\day$), you get $\sage{Integer(mod(\the\year, 100))^\the\day}$. Also, $\the\year$ modulo $42$ is $\sage{\the\year \percent 42}$. Code block which uses a variable \texttt{s} to store the solutions: \begin{sageblock} var('a,b,c') eqn = [a+b*c==1, b-a*c==0, a+b==5] s = solve(eqn, a,b,c) \end{sageblock} Solutions of $\mbox{eqn}=\sage{eqn}$: $\sage{s[0]}$ $\sage{s[1]}$ Now we evaluate the following block: \begin{sageblock} E = EllipticCurve("37a") \end{sageblock} You can't do assignment inside \verb|\sage| macros, since Sage doesn't know how to typeset the output of such a thing. So you have to use a code block. The elliptic curve $E$ given by $\sage{E}$ has discriminant $\sage{E.discriminant()}$. You can do anything in a code block that you can do in Sage and/or Python. Here we save an elliptic curve into a file. \begin{sageblock} try: E = load('E2') except IOError: E = EllipticCurve([1,2,3,4,5]) E.anlist(100000) E.save('E2') \end{sageblock} The 9999th Fourier coefficient of $\sage{E}$ is $\sage{E.anlist(100000)[9999]}$. The following code block doesn't appear in the typeset file\dots \begin{sagesilent} e = 2 e = 3*e + 1 \end{sagesilent} but we can refer to whatever we did in that code block: $e=\sage{e}$. \begin{sageblock} var('x') f = log(sin(x)/x) \end{sageblock} The Taylor Series of $f$ is: $\sage{ f.taylor(x, 0, 10) }$. \section{Plotting} Here's a plot of the elliptic curve $E$. \sageplot{E.plot(-3,3)} \begin{sagesilent} var('x') f=-x^3+3*x^2+7*x-4 \end{sagesilent} You can use variables to hold plot objects and do stuff with them. \begin{sageblock} p = plot(f, x, -5, 5) \end{sageblock} Here's a small plot of $f$ from $-5$ to $5$, which I've centered: \begin{center} \sageplot[scale=.2]{p} \end{center} On second thought, use the default size of $3/4$ the \verb|\textwidth| and don't use axes: \sageplot{p, axes=False} Remember, you're using Sage, and can therefore call upon any of the software packages Sage is built out of. \begin{sageblock} f = maxima('sin(x)^2*exp(x)') g = f.integrate('x') \end{sageblock} Plot $g(x)$, but don't typeset it. \begin{sagesilent} # g is a Maxima thingy, it needs to get converted into a Sage object plot1 = plot(g.sage(),x,-1,2*pi) \end{sagesilent} You can specify a file format and options for \verb|includegraphics|. The default is for EPS and PDF files, which are the best choice in almost all situations. (Although see the section on 3D plotting.) \sageplot[angle=45, width=.5\textwidth][png]{plot1} If you use regular \verb|latex| to make a DVI file, you'll see a box, because DVI files can't include PNG files. If you use \verb|pdflatex| that will work. See the documentation for details. When using \verb|\sageplot|, you can pass in just about anything that Sage can call \verb|.save()| on to produce a graphics file: \begin{center} \sageplot{plot1 + plot(f.sage(),x,-1,2*pi,rgbcolor=hue(0.4)), figsize=[1,2]} \end{center} \sageplot{graphs.FlowerSnark().plot()} \begin{sageblock} G4 = DiGraph({1:[2,2,3,5], 2:[3,4], 3:[4], 4:[5,7], 5:[6]},\ multiedges=True) G4plot = G4.plot(layout='circular') \end{sageblock} \sageplot{G4plot, axes=False} Indentation and so on works fine. \begin{sageblock} s = 7 s2 = 2^s P. = GF(2)[] M = matrix(parent(x),s2) for i in range(s2): p = (1+x)^i pc = p.coeffs() a = pc.count(1) for j in range(a): idx = pc.index(1) M[i,idx+j] = pc.pop(idx) matrixprogram = matrix_plot(M,cmap='Greys') \end{sageblock} And here's the picture: \sageplot{matrixprogram} \subsection{3D plotting} 3D plotting right now is problematic because there's no convenient way to produce vector graphics. We can make PNGs, though, and since the \verb|sageplot| command defaults to EPS and PDF, \emph{you must specify a valid format for 3D plotting}. Sage right now (version 3.2.2) can't produce EPS or PDF files from plot3d objects, so if you don't specify a valid format, things will go badly. You can specify the \texttt{imagemagick}'' option, which will use the Imagemagick \texttt{convert} utility to make EPS files. See the documentation for details. Here's the famous Sage cube graph: \begin{sageblock} G = graphs.CubeGraph(5) \end{sageblock} % need empty [] so sageplot knows you want png format, and aren't % passing an option to includegraphics \sageplot[][png]{G.plot3d(engine='tachyon')} \end{document}