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# 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.

## Installation

- sagemath contains the command-line version;
- sagemath-doc for HTML documentation and inline help from the command line.

Note: Many Sage packages are available as optional dependencies of the sagemath package or in AUR, therefore they have to be installed additionally as normal Arch packages in order to take advantage of their features. Note that there is no need to install them with `sage -i`, in fact this command will not work if you installed SageMath with pacman.

## 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.

### Jupyter Notebook

SageMath also provides a kernel for the Jupyter notebook. To use it, 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 kde-education groups.

## Optional additions

### SageTeX

If you have TeX Live installed 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.sagetex.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.

## See also

- Official Website
- SageMath Documentation
- Planet Sage
- SageMath Wiki
- Software Used by SageMath

Category:

- Numerical analysis