symengine/SymEngine.jl

Name: SymEngine.jl

Owner: symengine

Description: Julia wrappers of SymEngine

Created: 2015-06-07 17:41:32.0

Updated: 2018-01-16 11:04:52.0

Pushed: 2017-12-22 15:41:42.0

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Size: 131

Language: Julia

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README

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.

a> 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.

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


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

a> @vars a b
b)

Simple expressions

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

a> ex1 = a + 2(b+2)^2 + 2a + 3(a+1)
+ 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 matricies 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.

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

Matrix-vector multiplication

Now using the matrix we can perform matrix operations:

a> W*[1.0, 2.0, 3.0, 4.0]
ement Array{SymEngine.Basic,1}:
*W_11 + 2.0*W_12 + 3.0*W_13 + 4.0*W_14
*W_21 + 2.0*W_22 + 3.0*W_23 + 4.0*W_24
*W_31 + 2.0*W_32 + 3.0*W_33 + 4.0*W_34

Operations

expand

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

subs

Performs subsitution.

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

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


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

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

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

diff

Peforms differentiation

a> diff(a + 2(b+2)^2 + 2a + 3(a+1), b)`
 + b)

License

SymEngine.jl is licensed under MIT open source license.