The Components of Mathics3

At one time, there was a single Python PyPI installable package that made up this open-source version of the Wolfram language. It included for example a Django-based front end.

However in order to facilitate using the parts of it in other projects or the parts you need, the original package and GitHub repositories have been broken up into separately installable packages, and separate GitHub repositories. These repositories are now under the Mathics3 GitHub organization. (The old organization and GitHub repositories are around, but you will find no development there.)

Splitting up into packages reduces the dependencies needed for many of the individual components: when you only need part of Mathics3 you don’t need the code or dependencies for parts you don’t want. For example, if you might not need the Django-based front end; perhaps you do everything from a command line interface. If that is the case, then you don’t need to install Django or MySQL which Django uses in our implementation to save worksheet data.

On the other hand, if you are only interested in the Django interface and will never use the command-line interface, then you don’t need the mathicsscript package and the Python terminal packages that pull in.

Natural-Language Processing (NLP) is a separate Mathics3 module; it requires OS package support and word lists that you might not have installed, and might not want to devote disk space for. Various Python interpreters cannot build the Python NLTK package.

However, if you do want everything, we have a separate package called Mathics-omnibus which pulls in all of the Mathics-related packages. As part of the GitHub project is a docker setup.

Using this, you can use the full Mathics3 suite via dockerhub without having to build Mathics3 or have necessary OS libraries (including Python itself) outside of the docker containers.

The pieces described next go into the individual Python packages that make up the Mathics3 suite.

Mathics3 Core

The Mathics3 Kernel contains a parser, an evaluator, and some formatting routines.

Over time, formatting routines may be packaged separately.

There is also a very rudimentary command-line shell called mathics.

The Mathics3 Kernel is required for any work with Mathics3.

If you are developing a non-interactive application written in Mathics3, you may no more than this.

Although we provide documentation on-line, inside the docker image , and extractable from the that, should you want to build your PDF, you’ll need to have various TeX packages installed.

Front ends Mathics3-Django and mathicsscript use the Mathics3 Kernel.

Mathics3 Character Tables and Tokenizer

This is the tokenizer or scanner portion for the Wolfram Language.

As such, it also contains a full set of translations between Wolfram Language named characters, their Unicode/ASCII equivalents, and code-points.

The scanner is used by Mathics3 Core, but it can also be used for tokenizing and formatting Wolfram Language code. In fact, mathics-pygments described in the next section use this.

You can install this portion from PyPI. The GitHub project is here.

Mathics3 Syntax Highlighting

There is a syntax highlighter called mathics-pygments which uses Pygments. It is based on rsmenon’s pygments-mathematics.

The main difference between the two is that the character tables are used here. Possibly over time more parts of the scanner will be used as well.

Mathicsscript uses this package.

mathicsscript

The Mathics3 core comes with a very rudimentary command-line shell, if you want fancier shell features such as:

  • Prompt toolkit and GNU Readline terminal interaction. This includes

    • saving command history between sessions.

    • variable completion, even for symbol names like \[Sigma]

    • limited ESC keyboard input; for example esc p esc is π

  • Syntax highlighting using mathics-pygments

  • Automatic detection of light or dark terminal background color.

  • Entering and displaying Unicode symbols such as used for Pi or Rule arrows

There is a separately-installable PyPI package called mathicsscript.

Django-based GUI

If you prefer, as many do, browser-based interaction with nicely formatted graphics and MathML-formatted output, right now there is a Django-based PyPI package Mathics-Django.

Some of its features:

  • Extensive online documentation and interactive documentation via Ajax

  • Integrated graphics and MathML mathematics output via MathJax

  • Notebook-like sessions

To use this, you will need Django 6.0 or later installed, and a browser with JavaScript enabled.

Note: in the future, we intend to also provide a Jupyter-like interface.

Mathics3 Python Modules

Some features are optional and not automatically loaded when Mathics3 starts. Instead, these can be loaded from within Mathics3 using the Needs function.

Determining when Something should be a Mathics3 Module

Here are some reasons you would put something inside a Mathics3 Module instead of inside the Mathics3 Kernel:

  • If what you are doing requires a dependency on an OS library. NLP functions are like this. Putting NLP functions in a Mathics3 Module, reduces the dependencies of Mathics3 Kernel and therefore makes it easier to install Mathics3 Kernel and allow it to be available across more environments than if it had a lot of OS dependencies required.

  • If the feature is implemented using a package that can be thought of as one of alternative possibilities. For example, matplotlib rendering of graphs. There are other alternative methods of rendering graphs. However, Mathics3 Core has to provide some basic set of graph rendering; it currently uses SVG and basic Asymptote.

  • Functions that are not listed in the Wolfram Language. For example Formats/Functions like ToPython[] and ToSymPy[] are not Wolfram Builtin Functions, but instead, a natural kind of extension. So that should be in a Mathics3 Module. The Mathics3 debugger also doesn’t follow Wolfram Language behavior, so that is also a Mathics3 Module.

If the thing you want to add is listed as a Wolfram Language Builtin Function, then it goes in Mathics3 Kernel.

Below we list some of Mathics3 module packages. A full list can be found by looking in the Mathics3 organization.

“Hello, World” as a Mathics3 Python Module

This is a minimal Mathics3 Python Module for example or teaching purposes.

In contrast to the Mathics3 Modules, this one is not general useful except for showing how to write a Mathics3 Python Module.

Mathics3 Module ICU

This Mathics3 Module adds ICU functions via PyICU.

To use pyicu needs to be installed.

Natural Language Mathics3 Module

This Mathics3 Python Module adds Natural-Language Processing (NLP) functions via nltk.

To use this, nltk and spacy need to be installed.

Network Graph Mathics3 Python Module

This Mathics3 Python module adds Graph Theory or Networks Builtin Functions.

To use this you will need to have networkx and matplotlib installed.

Matplotlib Python Module Backend Renderer

Currently, this is a work in progress and works only in a very limited way. It provides graphics rendering using matplotlib.

Asymptote Python Module Backend Renderer

Currently, this is a work in progress and works only in a very limited way. It provides graphics rendering using the asymptote vector graphics language.

Mathics3 Debugger https://github.com/Mathics3/Mathics3-Module-trepan

Currently this is a work in progress and works only in very limited way.

It provides the ability debugging Mathics3 code and the Mathics3 implementation