Symbolic math for ruby
Switch branches/tags
Nothing to show
Clone or download
Fetching latest commit…
Cannot retrieve the latest commit at this time.
Failed to load latest commit information.


Symbolic math for ruby.


Symbolic needs Ruby 1.9.

gem install symbolic


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.


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
-(x-y) + 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) {|var| var.value.nil? }

You can get information about the number of different operations used in a symbolic expression:

f = (2*x-y+2)*x-2**(x*y)
f.operations # => {"+"=>1, "-"=>2, "*"=>3, "/"=>0, "**"=>1, "-@"=>0}

You can also take derivitives and do taylor expansions:

# => -2*(sin(x**2))*x
# => -0.5*x**2+1.0


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

  • plotting capabilities

  • integrals

  • thorough documentation


brainopia (ravwar at

I am ready to help with any questions related to Symbolic. I welcome any contribution.