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
-(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).variables.select {|var| var.value.nil? }

You can get an information about 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}

TODO

• a lot of refactoring (code is pretty messy at this stage);
• plotting capabilities;
• derivatives;
• integrals;
• thorough documentation.

Author

brainopia (ravwar@gmail.com).

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