Symbolic expression from a string

main.jl

using MacroTools
using Symbolics

function parse(strexpr)
    expr = Meta.parse(strexpr)
    freevars = Set()
    expr = MacroTools.postwalk(x -> begin
        if isa(x, Symbol) && !isdefined(Base, x)
            push!(freevars, Variable(x))
            Expr(:call, Variable, QuoteNode(x))
        else
            x
        end
    end, expr)
    eval(expr), collect(freevars)
end

s, _ = parse("(x1 + x2)^2")
#> ((x1 + x2)^2, Any[x2, x1])

expand(s)
#> x1^2 + x2^2 + 2x1*x2