Quick Start
Derived from the project README on GitHub.
Scalar Variables
Definitions
Multiple equivalent methods of variable declaration are supported.
julia> using SymEngine
julia> a=symbols(:a); b=symbols(:b)
b
julia> a,b = symbols("a b")
(a, b)
julia> @vars a b
(a, b)Simple Expressions
Note that by default, values are grouped but no expansion takes place.
julia> using SymEngine
julia> @vars a b
(a, b)
julia> ex1 = a + 2(b+2)^2 + 2a + 3(a+1)
3*a + 3*(1 + a) + 2*(2 + b)^2Vectors and Matrices
Definitions
Vectors
Vectors can be defined through list comprehension and string interpolation.
julia> using SymEngine
julia> [symbols("α_$i") for i in 1:3]
3-element Array{Basic,1}:
α_1
α_2
α_3Matrices
In an analogous manner, matrices are declared with a combination of string interpolation and matrix comprehension.
julia> using SymEngine
julia> W = [symbols("W_$i$j") for i in 1:3, j in 1:4]
3×4 Array{Basic,2}:
W_11 W_12 W_13 W_14
W_21 W_22 W_23 W_24
W_31 W_32 W_33 W_34Matrix Vector Operations
Consider the canonical example of matrix vector multiplication.
julia> using SymEngine
julia> W = [symbols("W_$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
julia> W*[1.0, 2.0, 3.0, 4.0]
3-element Array{Basic,1}:
1.0*W_11 + 2.0*W_12 + 3.0*W_13 + 4.0*W_14
1.0*W_21 + 2.0*W_22 + 3.0*W_23 + 4.0*W_24
1.0*W_31 + 2.0*W_32 + 3.0*W_33 + 4.0*W_34Operations
We will demonstrate the most common operations as follows.
Expansion
julia> using SymEngine
julia> @vars a b
(a, b)
julia> expand(a + 2(b+2)^2 + 2a + 3(a+1))
11 + 6*a + 8*b + 2*b^2Substitution
julia> using SymEngine
julia> @vars a b
(a, b)
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)
5Differentiation
julia> using SymEngine
julia> @vars a b
(a, b)
julia> diff(a + 2(b+2)^2 + 2a + 3(a+1), b)
4*(2 + b)