language for symbolic mathematics



Symbolic mathematics language

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About versions

For Julia v0.5, install branch jv0.5only. No development is done on this branch, only fixes for changing dependencies.

For Julia v0.6.2, install the lastest tagged version. Compared to the jv0.5only branch, a few features are disabled due to changes between v0.5 and v0.6.2. Three percent of the tests fail.

Symata is sufficiently complex to make keeping up with changes to Julia an enormous task, requiring much more than simply changing syntax. I won't update Symata (much) until after the Julia API stabilizes with 1.0.

Symata is

  • a language for symbolic computations and mathematics, where, for the most part, "mathematics" means what it typically does for a scientist or engineer.

  • a language based mostly on expressions, on "evaluating" and rewriting them, like Wolfram, Maple, or Maxima. It is neither a language, nor an extension of a language, that is mostly procedural, or designed around data types and functions, or a hierarchy of classes, etc., like C or Python or Java. Nor is it language like Sage; that is, one meant to provide a unifying interface to a number of mathematics languages with various programming models.

  • meant to be useful to people who do not like to program computers, as well as those who do. The former includes people who prefer not to think about classes, methods, objects, dispatch, stack traces, etc.

Symata is largely modeled on the pattern matching and evaluation sequence of Mathematica. Evaluation, pattern matching, flow control, etc. are written in Julia. Much of the mathematics and symbolic manipulation is achieved by wrapping SymPy. There are more than 500 functions implemented, including integration, transformation of special functions, expression manipulation, writing and reading expressions to and from a file etc. These are the best places for examples and help:

NEW: Mathematica syntax.

You can use Symata with Mathematica syntax in addition to the usual Julia-like syntax. To use Mathematica syntax, install the SymataSyntax.jl package.

IJulia Notebooks

A few tutorial notebooks can be viewed here. Lower-quality renderings of the same notebooks are in the example directory. These are all snapshots, not live, so you can view them immediately with your browswer.

In order to run the examples in the notebooks, you need to use the development version of Symata Switch to the development version with Pkg.checkout("Symata"). (Later, you can return to the latest versioned branch with Pkg.free("Symata").)


Symata is a registered module. It can be installed like this

julia> Pkg.update()
julia> Pkg.add("Symata")
julia> using Symata
symata> Help()    # type '=' alone on a line to enter symata mode

Symata can be installed on Linux, OSX, and Windows, and Julia v0.5, and v0.6.

Symata depends on the PyCall package and the python sympy module. When you load Symata with using Symata, sympy is installed automatically via PyCall, which uses Conda. However, to do this, PyCall must be configured to not use you system version of python. If you do not have PyCall installed, do this

julia> ENV["PYTHON"]=""
julia> Pkg.add("PyCall")

If you do have PyCall installed, but it is configured to use your system python, reconfigure it like this.

julia> ENV["PYTHON"]=""
julia> Pkg.build("PyCall")

If you use linux, you may have your distribution's sympy package installed and it may be out of date. In this case, try the procedure above, and/or try removing your distribution's sympy package.


SymPy, or sympy, here refers to the python SymPy distribution (sometimes called sympy), not the Julia package SymPy. Symata does not require the Julia package SymPy.jl, which has a different goal.

Symata requires mpmath package for python. This should be automatically installed when installing sympy via PyCall as described above. This also works on OSX. However, if you use pip, you should just be able to run pip install mpmath.

Running Symata

Three environments for running Symata are supported: the Julia REPL, Jupyter, and a dumb terminal

Symata REPL mode

A Symata mode is added to the Julia REPL. Enter the mode by typing = as the first character. Exit the mode by typing backspace as the first character.

julia> using Symata

symata 1>     # after entering `=`

There is also an executable symata included in top level directory of this distribution. It is a (UNIX sh) shell script that just starts julia and loads the module.

julia -i -e "using Symata" $*

Upon running this script, Symata mode is entered automatically. Toggle between Julia and Symata modes by typing = as the first character on a line. (If loading Symata from the julia prompt via using Symata, you use = and backspace.)

In Symata mode, the input is not interpreted as Julia expressions, but rather Symata expressions. You can do tab completion to see a list of functions and symbols.

Jupyter / IJulia

Versions v1.3.0 through v1.3.2 of IJulia.jl are supported.

In [1]:  using Symata

In [2]:  Expand((a+b)^2)

Out[2]:  a^2 + 2a*b + b^2

In [3]:  Julia()   # return to Julia mode

In Jupyter, the Symata expressions In(n) and Out(n) reevaluate the input and output cells. TAB completion works in Jupyter. To see a list of all possible completions, type *[TAB].

Dumb terminal

If you do using Symata in a dumb terminal, the Symata prompt should appear automatically.

sympy shell

From the julia prompt, type isympy() to enter the sympy shell.

Help, examples, tests

The best source of examples is the test directory. The documentation can be printed from within Symata by entering ? SymName at the symata prompt. Help(Symname) prints the same documentation. For many Symata functions, the SymPy docstring is printed along with the Symata documentation.

Try Help(). Type h"topic" to search for items containing the string "topic". Hit TAB at the command line REPL for a list of all builtin symbols. (i.e. variables and functions) Symbols that are associated with some functionality can be listed with BuiltIns(). Type Example() to see a list of topics with examples. Type Example(topic) to run the examples. (But, far more examples are in the test directory ). The input strings from the examples are pushed to the history so that they can be recalled and edited and re-evaluated.


Run the test suite from the symata prompt with Tests(). This runs tests in the directory sjtest. Pkg.test("Symata") runs the same test suite from Julia.

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