SageMath
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SageMath (formerly Sage) is a program for numerical and symbolic mathematical computation that uses Python as its main language. It is meant to provide an alternative for commercial programs such as Maple, Matlab, and Mathematica.
SageMath provides support for the following:
- Calculus: using Maxima and SymPy.
- Linear Algebra: using the GSL, SciPy and NumPy.
- Statistics: using R (through RPy) and SciPy.
- Graphs: using matplotlib.
- An interactive shell using IPython.
- Access to Python modules such as PIL, SQLAlchemy, etc.
Contents
Installation
- sagemath contains the command-line version;
- sagemath-doc for HTML documentation and inline help from the command line.
- sage-notebook includes the browser-based notebook interface.
Usage
SageMath mainly uses Python as a scripting language with a few modifications to make it better suited for mathematical computations.
SageMath command-line
SageMath can be started from the command-line:
$ sage
For information on the SageMath command-line see this page.
The command-line is based on the IPython shell so you can use all its tricks with SageMath. For an extensive tutorial on IPython see the community maintained IPython Cookbook.
Note, however, that it is not very comfortable for some uses such as plotting. When you try to plot something, for example:
sage: plot(sin,(x,0,10))
SageMath opens the plot in an external application.
Sage Notebook
A better suited interface for advanced usage in SageMath is the Notebook. To start the Notebook server from the command-line, execute:
$ sage -n
The notebook will be accessible in the browser from http://localhost:8080 and will require you to login.
However, if you only run the server for personal use, and not across the internet, the login will be an annoyance. You can instead start the Notebook without requiring login, and have it automatically pop up in a browser, with the following command:
$ sage -c "notebook(automatic_login=True)"
For a more comprehensive tutorial on the Sage Notebook see the Sage documentation. For more information on the notebook()
command see this page.
Jupyter Notebook
SageMath also provides a kernel for the Jupyter notebook. To use it, install ipython2-notebook and mathjax, launch the notebook with the command
$ jupyter notebook
and choose "SageMath" in the drop-down "New..." menu. The SageMath Jupyter notebook supports LaTeX output via the %display latex
command and 3D plots if jmol is installed.
Cantor
Cantor is an application included in the KDE Edu Project. It acts as a front-end for various mathematical applications such as Maxima, SageMath, Octave, Scilab, etc. See the Cantor page on the Sage wiki for more information on how to use it with SageMath.
Cantor can be installed with the cantor package or as part of the kde-applications or kdeedu groups, available in the official repositories.
Optional additions
SageTeX
If you have installed TeX Live on your system, you may be interested in using SageTeX, a package that makes the inclusion of SageMath code in LaTeX files possible. TeX Live is made aware of SageTeX automatically so you can start using it straight away.
As a simple example, here is how you include a Sage 2D plot in your TEX document (assuming you use pdflatex
):
- include the
sagetex
package in the preamble of your document with the usual
\usepackage{sagetex}
- create a
sagesilent
environment in which you insert your code:
\begin{sagesilent} dob(x) = sqrt(x^2 - 1) / (x * arctan(sqrt(x^2 - 1))) dpr(x) = sqrt(x^2 - 1) / (x * log( x + sqrt(x^2 - 1))) p1 = plot(dob,(x, 1, 10), color='blue') p2 = plot(dpr,(x, 1, 10), color='red') ptot = p1 + p2 ptot.axes_labels(['$\\xi$','$\\frac{R_h}{\\max(a,b)}$']) \end{sagesilent}
- create the plot, e.g. inside a
float
environment:
\begin{figure} \begin{center} \sageplot[width=\linewidth]{ptot} \end{center} \end{figure}
- compile your document with the following procedure:
$ pdflatex <doc.tex> $ sage <doc.sage> $ pdflatex <doc.tex>
- you can have a look at your output document.
The full documentation of SageTeX is available on CTAN.
Troubleshooting
TeX Live does not recognize SageTex
If your TeX Live installation does not find the SageTex package, you can try the following procedure (as root or use a local folder):
- Copy the files to the texmf directory:
# cp /opt/sage/local/share/texmf/tex/* /usr/share/texmf/tex/
- Refresh TeX Live:
# texhash /usr/share/texmf/ texhash: Updating /usr/share/texmf/.//ls-R... texhash: Done.