Symbolic math for ruby.
Installation
Symbolic needs Ruby 1.9.
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.
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
You can accomplish the same thing with subs:
f.subs(x,3) # => 7
Or make a more complicated substitution:
f.subs(x,x**2) # => 2*x**2+1
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 information about the number of different operations used in a symbolic expression:
f = (2*xy+2)*x2**(x*y)
f.operations # => {"+"=>1, ""=>2, "*"=>3, "/"=>0, "**"=>1, "@"=>0}
You can also take derivitives and do taylor expansions:
Symbolic::Math.cos(x**2).diff(x)
# => 2*(sin(x**2))*x
Symbolic::Math.cos(x).taylor(x,0,3)
# => 0.5*x**2+1.0
TODO

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

plotting capabilities

integrals

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