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Symbolic math for ruby

# brainopia/symbolic

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Symbolic math for ruby.

## Installation¶ ↑

Symbolic needs Ruby 1.9.

gem install symbolic

## Introduction¶ ↑

• 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
-(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 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:

```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.

Symbolic math for ruby

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