📂Julia

Methods for Symbolic Computation in Julia

Overview

Symbolic operations in Julia can be used through the SymEngine.jl¹ package.

Code

Defining Symbols

Symbols can be defined in the following way.

julia> using SymEngine

julia> x = symbols(:x)
x

julia> x, y = symbols("x y")
(x, y)

julia> @vars x, y
(x, y)

julia> x = symbols(:x)
x

julia> f = 2x + x^2 + cos(x)
2*x + x^2 + cos(x)

Vectors and Matrices

julia> v = [symbols("v_▷eq1◁i$j") for i in 1:2, j in 1:3]
2×3 Matrix{Basic}:
 a_11  a_12  a_13
 a_21  a_22  a_23

julia> A*v
2-element Vector{Basic}:
 v_1*a_11 + v_2*a_12 + v_3*a_13
 v_1*a_21 + v_2*a_22 + v_3*a_23

julia> @vars a, b, c, d, x, y
(a, b, c, d, x, y)

julia> [a b; c d] * [a x; b y]
2×2 Matrix{Basic}:
 a^2 + b^2  a*x + b*y
 a*c + b*d  c*x + d*y

Differentiation

Symbolic differentiation can also be used with the Calculus.jl package.

julia> f = 2x + x^2 + cos(x)
2*x + x^2 + cos(x)

julia> diff(f, x)
2 + 2*x - sin(x)

Environment

• OS: Windows10
• Version: Julia v1.7.1, SymEngine v0.8.7