GitHub - symengine/SymEngine.jl: Julia wrappers of SymEngine (original) (raw)

SymEngine.jl

Julia Wrappers for SymEngine, a fast symbolic manipulation library, written in C++.

Installation

You can install SymEngine.jl by giving the following command.

julia> Pkg.add("SymEngine")

Quick Start

Working with scalar variables

Defining variables

One can define variables in a few ways. The following three examples are equivalent.

Defining two symbolic variables with the names a and b, and assigning them to julia variables with the same name.

julia> a=symbols(:a); b=symbols(:b) b

julia> a,b = symbols("a b") (a, b)

julia> @vars a b (a, b)

Simple expressions

We are going to define an expression using the variables from earlier:

julia> ex1 = a + 2(b+2)^2 + 2a + 3(a+1) 3a + 3(1 + a) + 2*(2 + b)^2

One can see that values are grouped, but no expansion is done.

Working with vector and matrix variables

Defining vectors of variables

A vector of variables can be defined using list comprehension and string interpolation.

julia> [symbols("α_$i") for i in 1:3] 3-element Array{SymEngine.Basic,1}: α_1 α_2 α_3

Defining matrices of variables

Some times one might want to define a matrix of variables. One can use a matrix comprehension, and string interpolation to create a matrix of variables.

julia> W = [symbols("W_$i$j") for i in 1:3, j in 1:4] 3×4 Array{Basic,2}: W_11 W_12 W_13 W_14 W_21 W_22 W_23 W_24 W_31 W_32 W_33 W_34

Matrix-vector multiplication

Now using the matrix we can perform matrix operations:

julia> W*[1.0, 2.0, 3.0, 4.0] 3-element Array{Basic,1}: 1.0W_11 + 2.0W_12 + 3.0W_13 + 4.0W_14 1.0W_21 + 2.0W_22 + 3.0W_23 + 4.0W_24 1.0W_31 + 2.0W_32 + 3.0W_33 + 4.0W_34

Operations

expand

julia> expand(a + 2(b+2)^2 + 2a + 3(a+1)) 11 + 6a + 8b + 2*b^2

subs

Performs substitution.

julia> subs(a^2+(b-2)^2, b=>a) a^2 + (-2 + a)^2

julia> subs(a^2+(b-2)^2, b=>2) a^2

julia> subs(a^2+(b-2)^2, a=>2) 4 + (-2 + b)^2

julia> subs(a^2+(b-2)^2, a^2=>2) 2 + (-2 + b)^2

julia> subs(a^2+(b-2)^2, a=>2, b=>3) 5

diff

Peforms differentiation

julia> diff(a + 2(b+2)^2 + 2a + 3(a+1), b) 4*(2 + b)

License

SymEngine.jl is licensed under MIT open source license.