This is an example 2 + 2 = 4. If you raise the current year mod 100 (which equals 10) to the power of the current day (20), you get 100000000000000000000. Also, 2010 modulo 42 is 36.
Code block which uses a variable s to store the solutions:
{{{id=1| 1+1 var('a,b,c') eqn = [a+b*c==1, b-a*c==0, a+b==5] s = solve(eqn, a,b,c) /// }}}Solutions of \text{eqn} = \left [bc + a = 1,−ac + b = 0,a + b = 5\right ]:
Now we evaluate the following block:
{{{id=3| E = EllipticCurve("37a") /// }}}You can’t do assignment inside \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 {y}^{2} + y = {x}^{3} − x has discriminant 37.
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.
{{{id=5| try: E = load('E2') except IOError: E = EllipticCurve([1,2,3,4,5]) E.anlist(100000) E.save('E2') /// }}}The 9999th Fourier coefficient of {y}^{2} + xy + 3y = {x}^{3} + 2{x}^{2} + 4x + 5 is − 27.
The following code block doesn’t appear in the typeset file…
{{{id=7| e = 2 e = 3*e + 1 /// }}}but we can refer to whatever we did in that code block: e = 7.
{{{id=9| var('x') f(x) = log(sin(x)/x) /// }}}The Taylor Series of f begins: x\ \mapsto \ − {1\over 467775}\,{x}^{10} − {1\over 37800}\,{x}^{8} − {1\over 2835}\,{x}^{6} − {1\over 180}\,{x}^{4} −{1\over 6}\,{x}^{2}.
Here’s a plot of the elliptic curve E.
You can use variables to hold plot objects and do stuff with them.
{{{id=13| p = plot(f, x, -5, 5) /// }}}Here’s a small plot of f from − 5 to 5, which I’ve centered:
On second thought, use the default size of 3∕4 the \textwidth and don’t use axes:
Remember, you’re using Sage, and can therefore call upon any of the software packages Sage is built out of.
{{{id=15| f = maxima('sin(x)^2*exp(x)') g = f.integrate('x') /// }}}Plot g(x), but don’t typeset it.
{{{id=17| # g is a Maxima thingy, it needs to get converted into a Sage object plot1 = plot(g.sage(),x,-1,2*pi) /// }}}You can specify a file format and options for 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.)
??
If you use regular latex to make a DVI file, you’ll see a box, because DVI files can’t include PNG files. If you use pdflatex that will work. See the documentation for details.
When using \sageplot, you can pass in just about anything that Sage can call .save() on to produce a graphics file:
To fiddle with aspect ratio, first save the plot object:
{{{id=21| p = plot(x, 0, 1) + circle((0,0), 1) p.set_aspect_ratio(1) /// }}}Now plot it and see the circular circle and nice 45 degree angle:
Indentation and so on works fine.
{{{id=23| s = 7 s2 = 2^s P.And here’s the picture:
Reset x in Sage so that it’s not a generator for the polynomial ring: x
Sage now includes some nice support for plotting graphs using TikZ. Here, we mean things with vertices and edges, not graphs of a function of one or two variables.
First define our graph:
{{{id=25| g = graphs.PetersenGraph() g.set_latex_options(tkz_style='Art') /// }}}Now just do \sage{} on it to plot it. You’ll need to use the tkz-berge package for this to work; that package in turn depends on tkz-graph and TikZ. See “LATEX Options for Graphs” in the Sage reference manual for more details.
The above command just outputs a tikzpicture environment, and you can control that environment using anything supported by TikZ—although the output of \sage{g} explicitly hard-codes a lot of things and cannot be flexibly controlled in its current form.
3D plotting right now is problematic because there’s no convenient way to produce vector graphics. We can make PNGs, though, and since the sageplot command defaults to EPS and PDF, you must specify a valid format for 3D plotting. Sage right now (version 4.2.1) 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 “imagemagick” option, which will use the Imagemagick convert utility to make EPS files. See the documentation for details.
Here’s the famous Sage cube graph in 3D.
{{{id=27| G = graphs.CubeGraph(5) /// }}}??
And here’s a regular sort of 3D plot. Since plot3d objects don’t properly support the kind of .save() method that we need, so we have to work around it a bit and do things manually. Note that we can’t use \jobname below. The sage.misc.viewer.BROWSER bit tells Sage to not pop up a viewer program; otherwise, when you run the .sage script, it will try to start a viewer program on the resulting image, which we don’t want.
{{{id=29| sage.misc.viewer.BROWSER='' x, y = var('x y') g = plot3d(sin(pi*(x^2+y^2))/2,(x,-1,1),(y,-1,1)) g.show(filename='sage-plots-for-example.tex/my-3d-plot', viewer='tachyon') /// }}} 
Sometimes you want to “pause” for a bit while writing your document if you have embedded a long calculation or just want to concentrate on the LATEX and ignore any Sage stuff. You can use the \sagetexpause and \sagetexunpause macros to do that.
A calculation: \text{(Sage
Graphics are also skipped: SageTEX is paused; no graphic
With SageTEX, you can not only have Sage do your math for you, it can write parts of your LATEX document for you! For example, I hate writing tabular environments; there’s too many fiddly little bits of punctuation and whatnot\ldots and what if you want to add a column? It’s a pain—or rather, it was a pain. Here’s how to make Pascal’s triangle. It requires the amsmath package because of what Sage does when producing a LATEX representation of a string. (It puts it inside a \text macro.)
{{{id=33| def pascals_triangle(n): # start of the table s = r"\begin{tabular}{cc|" + "r" * (n+1) + "}" s += r" & & $k$: & \\" # second row, with k values: s += r" & " for k in [0..n]: s += "& %d " % k s += r"\\" # the n = 0 row: s += r"\hline" + "\n" + r"$n$: & 0 & 1 & \\" # now the rest of the rows for r in [1..n]: s += " & %d " % r for k in [0..r]: s += "& %d " % binomial(r, k) s += r"\\" # add the last line and return s += r"\end{tabular}" return s # how big should the table be? n = 8 /// }}}Okay, now here’s the table. To change the size, edit n above. If you have several tables, you can use this to get them all the same size, while changing only one thing.
| k: | ||||||||||
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | ||
| n: | 0 | 1 | ||||||||
| 1 | 1 | 1 | ||||||||
| 2 | 1 | 2 | 1 | |||||||
| 3 | 1 | 3 | 3 | 1 | ||||||
| 4 | 1 | 4 | 6 | 4 | 1 | |||||
| 5 | 1 | 5 | 10 | 10 | 5 | 1 | ||||
| 6 | 1 | 6 | 15 | 20 | 15 | 6 | 1 | |||
| 7 | 1 | 7 | 21 | 35 | 35 | 21 | 7 | 1 | ||
| 8 | 1 | 8 | 28 | 56 | 70 | 56 | 28 | 8 | 1 | |