# SageMath

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 can be installed from the official repositories:

- 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.

The sagemath package has number of optional dependencies for various features that will be disabled if the needed packages are missing.

## 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 a browser window with the Sage Notebook.

### 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.

### Documentation

For local documentation, one can compile it into multiple formats such as HTML or PDF. To build the whole SageMath reference, execute the following command (as root):

# sage --docbuild reference html

This builds the HTML documentation for the whole *reference* tree (may take longer than an hour). An option is to build a smaller part of the documentation tree, but you would need to know what it is you want. Until then, you might consider just browsing the online reference.

For a list of documents see `sage --docbuild --documents`

and for a list of supported formats see `sage --docbuild --formats`

.

## 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.

## Install Sage package

If you installed sagemath from the official repositories, it is not possible to install sage packages using the sage option `sage -i packagename`

.

Instead, you should install the required packages system-wide. For example, if you need `jmol`

(for 3D plots):

$ sudo pacman -S jmol

An alternative would be to have a local installation of sagemath and to manage optional packages manually.

## 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.

### Starting Sage Notebook Server throws an ImportError

The Sage Notebook Server is in an extra package sage-notebook. So, if you get an ImportError when launching

% sage --notebook ┌────────────────────────────────────────────────────────────────────┐ │ Sage Version 6.4.1, Release Date: 2014-11-23 │ │ Type "notebook()" for the browser-based notebook interface. │ │ Type "help()" for help. │ └────────────────────────────────────────────────────────────────────┘ Please wait while the Sage Notebook server starts... Traceback (most recent call last): File "/usr/bin/sage-notebook", line 180, in <module> launcher(unknown) File "/usr/bin/sage-notebook", line 58, in __init__ from sagenb.notebook.notebook_object import notebook ImportError: No module named sagenb.notebook.notebook_object

you most likely do not have the package sage-notebook installed.

### sage -i doesn't work

If you have installed Sage from the official repositories, then you have to install your additional packages system-wide. See Install Sage package

### 3D plot fails in notebook

If you get the following error while trying to plot a 3D object:

/usr/lib/python2.7/site-packages/sage/repl/rich_output/display_manager.py:570: RichReprWarning: Exception in _rich_repr_ while displaying object: Jmol failed to create file '/home/nicolas/.sage/temp/archimede/3188/dir_cCpcph/preview.png', see '/home/nicolas/.sage/temp/archimede/3188/tmp_JVpSqF.txt' for details RichReprWarning, Graphics3d Object

then you probably miss the jmol package. See Install Sage package to install it.