Symbolic evaluation in Julia language via SymPy.jl interface to the Python CAS library SumPy. Illustrative tutorials at http://mth229.github.io/symbolic.html

julia_symcas.jl

## first verify python-sympy Ubuntu package is installed,
##  and Pkg.add("SymPy") in Julia
using Gadfly # before SymPy to have automatic plotting as below
using SymPy

# declare symbols: one of several ways
#  see https://github.com/jverzani/SymPy.jl
x, a, b, c = @syms x a b c
typeof(x)
f(x) = a*exp(-(x - b)^2/c)
f(x) # prints formatted expression

# symbolic derivative
diff(f(x), x)

# gadfly plotting
f(x) = x^x; c = 1
m = diff(f(x)) |> replace(x, c);
fs = [f(x), f(c) + m*(x-c)] # Array with 2 Sym-elements
plot(fs, .5, 1.5)