Symbolic math for ruby.
Installation
gem install symbolic
Introduction
This gem can help you

if you want to get a simplified form of a big equation

if you want to speed up similar calculations

if you need an abstraction layer for math
Symbolic doesn't have any external dependencies. It uses only pure ruby (less than 400 lines of code).
Tutorial
First, you need to create a symbolic variable.
x = var
# you can set a name of variable (useful if you print equations)
angle = var :name => 'θ'
# or starting value
pi = var :value => 3.14
# or bind its value to a proc
y = var { x ** 2 }
# you can set a value for already created variable
x.value = 3
Now, you can do any math operations with it.
f = 2*x + 1
puts f # => 2*x+1
To get value of symbolic expression you just call value:
f.value # => 7
If symbolic expression contains variables without value then it returns nil.
z = var
(z+1).value # => nil
All symbolic expression are automatically simplified when created:
0 * x # => 0
2 + x + 1 # => x + 3
(xy) + 2*x # => x + y
(x**2)**3 / x # => x**5
# etc. (more examples can be found in symbolic_spec.rb)
If you need to use a function from Math module with symbolic variable, use Symbolic::Math module.
cos = Symbolic::Math.cos(x)
x.value = 0
cos.value # => 1.0
You can get a list of variables from symbolic expression:
(x+y+1).variables # => [x, y]
So you can get a list of variables without value:
(x+y+1).variables.select {var var.value.nil? }
You can get an information about number of different operations used in a symbolic expression:
f = (2*xy+2)*x2**(x*y)
f.operations # => {"+"=>1, ""=>2, "*"=>3, "/"=>0, "**"=>1, "@"=>0}
TODO

a lot of refactoring (code is pretty messy at this stage)

plotting capabilities

derivatives

integrals

thorough documentation
Author
brainopia (ravwar at gmail.com).
I am ready to help with any questions related to Symbolic. I welcome any contribution.