README.md in dydx-0.0.9 vs README.md in dydx-0.1.0

@@ -1,52 +1,86 @@
 # Dydx
-It always happens you want to differentiate with ruby. right?
+It always happens you want to differentiate some formulas with ruby. right?.....
 
-Dydx will eliminate this. Like this
+After `inlcude Dydx` , ruby become like other language.
 
-
 ```
-( d/dx(:x ^ 2) ).to_s
+require 'dydx'
+include Dydx
+
+# There are three types of differential interface
+
+( d/dx(x^2) ).to_s
 => "( 2 * x )"
 
-# pretermit '#to_s'
+log(z).d(z).to_s
+=> "( 1 / z )"
 
-d/dx(e ^ :x)
+$y = e ^ x
+(dy/dx).to_s
 => "( e ^ x )"
 
-d/dz(log(:z))
-=> "( 1 / z )"
+```
 
-d/dx(:x^:n)
-=> "( n * ( x ^ ( n - 1 ) ) )"
+You may wonder why undefined `x` , `e` and `z` are handleable?
 
+`method_missing` solve this problem by converting undefine variable into internal class object.
+
+Like this.
+
 ```
+ x + x
+=> #<Dydx::Algebra::Formula:0x007fb0a4039fb0 @f=#<Dydx::Algebra::Set::Num:0x007fb0a48169e0 @n=2>, @operator=:*, @g=:x>
 
-you can do like ``` dy/dx ```, if you use global var.
+e
+=> #<Dydx::Algebra::Set::E:0x007fb0a383e9f0>
 
+log(sin(x))
+=> #<Dydx::Algebra::Set::Log:0x007fe7cd971528 @f=#<Dydx::Algebra::Set::Sin:0x007fe7cd971550 @x=:x>>
 ```
-$y = cos(:x)
+
+And this DSL has strong simplify.
+
+```
+((x * y) + (z * x)).to_s
+=> "( x * ( y + z ) )"
+
+((x ^ y) / (x ^ z)).to_s
+=> "( x ^ ( y - z ) )"
+
+(x + x).to_s
+=> "( 2 * x )"
+```
+
+I show some differential calculus.
+
+```
+# pretermit '#to_s'
+
+d/dz(log(z))
+=> "( 1 / z )"
+
+d/dx(x^n)
+=> "( n * ( x ^ ( n - 1 ) ) )"
+
+$y = cos(x)
 dy/dx
 => "( - sin( x ) )"
 
-$x = :a * ( (:t ^ 2) / 2 )
+$x = a * ( (t ^ 2) / 2 )
 dx/dt
 => "( a * t )"
 
 d/dt(dx/dt)
 =>"a"
 
-```
-
-you can use method chaining.
-
-```
-((:x ^ 2) * :y).d(:x)
+((x ^ 2) * y).d(x)
 => "( ( 2 * x ) * y )"
 
-((:x ^ 2) * :y).d(:x).d(:y)
+((x ^ 2) * y).d(x).d(y)
 => "( 2 * x )"
+
 ```
 
 
 (That's wonderful!!!!! ..............)
 
@@ -68,10 +102,19 @@
 
     include Dydx
 
 ## Contributing
 
-1. Fork it ( https://github.com/[my-github-username]/dydx/fork )
+1. Fork it ( https://github.com/gogotanaka/dydx/fork )
 2. Create your feature branch (`git checkout -b my-new-feature`)
 3. Commit your changes (`git commit -am 'Add some feature'`)
 4. Push to the branch (`git push origin my-new-feature`)
 5. Create a new Pull Request
+
+## Test
+
+run `bundle exec rake spec`
+
+```
+Finished in 0.11282 seconds
+231 examples, 0 failures
+```