Documentation for SymPy.jl a Julia interface to Python's SymPy library for symbolic mathematics.

    To install the package, run

    (v1.4) pkg> add SymPy

    This package relies on PyCall to provide a link between Julia and Python. Installation should install PyCall, the sympy module for python, and if needed, a python executable.

    Quick example

    This package provides a convenient way to access the functionality of the sympy library for Python from Julia, utilizing the PyCall package to provide the interface. A symbolic type, a wrapper around a PyCall.PyObject, is provided and, as much as reasonable, generic Julia methods are created for this type. Many sympy specific features are available through a qualified function call, e.g. sympy.funcname(...) or a Python method call, e.g., obj.methname(...).

    This example from calculus provides an illustation of each.

    julia> using SymPy

    Here we create some symbolic variables, one with an assumption:

    julia> @vars x
    julia> @vars a real=true

    The basic math functions have methods for symbolic expressions:

    julia> sin(x)
    julia> log(x)

    The output is a symbolic expression.

    A selection of SymPy functions are defined as Julia functions. Here are three common calculus operations:

    julia> limit(sin(a*x)/x, x =>  0)
    julia> diff(x^x, (x,3))
     x ⎛            3   3⋅(log(x) + 1)   1 ⎞
    x ⋅⎜(log(x) + 1)  + ────────────── - ──⎟
       ⎜                      x           2⎟
       ⎝                                 x ⎠
    julia> integrate(exp(-a*x) * sin(x), x)
         a⋅sin(x)          cos(x)
    - ────────────── - ──────────────
       2  a⋅x    a⋅x    2  a⋅x    a⋅x
      a ⋅ℯ    + ℯ      a ⋅ℯ    + ℯ   

    Both limit and integrate are defined within the package, whereas diff, a generic Julia function, has a method defined for the first argument being symbolic.

    The diff function finds derivatives, SymPy's Derivative function defines unevaluated derivatives, which are evaluated through their doit method. Derivative is not a Julia function, so we must qualify it:

    julia> out = sympy.Derivative(x^x, x)
    d ⎛ x⎞
    ──⎝x ⎠
    julia> out.doit()
    x ⋅(log(x) + 1)