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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.


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