Symbolic math with julia

[szcf-weiya]

SymPy

http://mth229.github.io/symbolic.html it is required to install sympy

julia> using SymPy
[ Info: Precompiling SymPy [24249f21-da20-56a4-8eb1-6a02cf4ae2e6]
ERROR: InitError: PyError (PyImport_ImportModule

The Python package sympy could not be imported by pyimport. Usually this means
that you did not install sympy in the Python version being used by PyCall.

PyCall is currently configured to use the Python version at:

/home/weiya/anaconda3/envs/py37/bin/python3.7

and you should use whatever mechanism you usually use (apt-get, pip, conda,
etcetera) to install the Python package containing the sympy module.

[szcf-weiya]

julia> @vars x
(x,)

julia> exp(-x^2/2)/sqrt(2pi)
                     2 
                   -x  
                   ────
                    2  
0.398942280401433⋅ℯ    

julia> f(x) = exp(-x^2/2)/sqrt(2pi)
f (generic function with 1 method)

julia> integrate(f(x), x)
                           ⎛√2⋅x⎞
0.199471140200716⋅√2⋅√π⋅erf⎜────⎟
                           ⎝ 2  ⎠

julia> integrate(f(x), (x, -Inf, Inf))
0.398942280401433⋅√2⋅√π

julia> integrate(x*f(x), (x, -Inf, Inf))
0

julia> integrate(x*f(x), x)
                      2 
                    -x  
                    ────
                     2  
-0.398942280401433⋅ℯ    

julia> integrate(x*f(x), (x, -Inf, Inf))
0

julia> integrate(f(x)^2, (x, -Inf, Inf))
0.159154943091895⋅√π

julia> integrate(f(x)^2, x)
0.0795774715459477⋅√π⋅erf(x)

where erf is the https://en.wikipedia.org/wiki/Error_function