Methods for Symbolic Computation in Julia
Overview
Symbolic operations in Julia can be used through the SymEngine.jl
1 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