README.md in dydx-0.1.2 vs README.md in dydx-0.1.3

@@ -1,91 +1,132 @@
-# Dydx
-It always happens you want to differentiate some formulas with ruby. right?.....
+# Dydx is new math DSL in Ruby
 
+### Since you report a bug, I will fix it within 24 hours.
+
+The most important thing in this DSL is
+
+we can handle math in the same sense sense of the math on paper.
+
+ex. limit, trigonometric functions and logarithmic.
+
+
 After `inlcude Dydx` , ruby become like other language.
 
-```
+## Outline
+```ruby:
 require 'dydx'
 include Dydx
 
-# There are three types of differential interface
+# Define the function. syntax is not good enough...
+f(x) <= x ^ 2
 
-( d/dx(x^2) ).to_s
-=> "( 2 * x )"
+f(3)
+=> 9
 
-log(z).d(z).to_s
-=> "( 1 / z )"
+f(x).to_s
+=> "( x ^ 2 )"
 
-$y = e ^ x
-(dy/dx).to_s
-=> "( e ^ x )"
+f(x) == eval('f(x).to_s')
+=> true
 
-```
+# Differentiate
+g(x) <= d/dx(f(x))
 
-You may wonder why undefined `x` , `e` and `z` are handleable?
+g(3)
+=> 6
 
-`method_missing` solve this problem by converting undefine variable into internal class object.
+g(x).to_s
+=> '2 * x'
 
-Like this.
-
+# Integrate
+S(f(x), dx)[0, 1]
+=> 0.3333333333333334
 ```
- x + x
-=> #<Dydx::Algebra::Formula:0x007fb0a4039fb0 @f=#<Dydx::Algebra::Set::Num:0x007fb0a48169e0 @n=2>, @operator=:*, @g=:x>
 
-e
-=> #<Dydx::Algebra::Set::E:0x007fb0a383e9f0>
 
-log(sin(x))
-=> #<Dydx::Algebra::Set::Log:0x007fe7cd971528 @f=#<Dydx::Algebra::Set::Sin:0x007fe7cd971550 @x=:x>>
-```
+#### limit, trigonometric functions and logarithmic.
+```ruby:
 
-And this DSL has strong simplify.
+f(z) <= log(z)
+S(f(z), dz)[0,1]
+=> -Infinity
 
-```
-((x * y) + (z * x)).to_s
-=> "( x * ( y + z ) )"
+( d/dx(log(x)) ).to_s
+=> "( 1 / x )"
 
-((x ^ y) / (x ^ z)).to_s
-=> "( x ^ ( y - z ) )"
+( d/dx(cos(x)) ).to_s
+=> "( - sin( x ) )"
 
-(x + x).to_s
-=> "( 2 * x )"
-```
+( d/dx(e ^ x) ).to_s
+=> "( e ^ x )"
 
-I show some differential calculus.
+f(x) <= sin(x)
+S(f(x), dx)[0, Math::PI/2]
+=> 1.000000000021139
 
+# standard normal distribution;
+f(x) <= (1.0 / ( ( 2.0 * pi ) ^ 0.5 ) ) * ( e ^ (- (x ^ 2) / 2) )
+S(f(x), dx)[-oo, oo]
+=> 0.9952054164466917
 ```
-# pretermit '#to_s'
 
-d/dz(log(z))
-=> "( 1 / z )"
+#### it's like a magic...
 
-d/dx(x^n)
-=> "( n * ( x ^ ( n - 1 ) ) )"
+```ruby:
+f(x) <= x ^ 2
 
-$y = cos(x)
-dy/dx
-=> "( - sin( x ) )"
+f(a + b).to_s
+=> "( ( a + b ) ^ 2 )"
 
-$x = a * ( (t ^ 2) / 2 )
-dx/dt
-=> "( a * t )"
+#↓it"s magic!!!
+g(a, b) <= f(a + b)
 
-d/dt(dx/dt)
-=>"a"
+g(a, b).to_s
+=> "( ( a + b ) ^ 2 )"
 
-((x ^ 2) * y).d(x)
-=> "( ( 2 * x ) * y )"
+g(2, 2)
+=> 16
 
-((x ^ 2) * y).d(x).d(y)
-=> "( 2 * x )"
+( d/da(g(a, b)) ).to_s
+=> "( 2 * ( a + b ) )"
 
+# 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 )"
 ```
 
 
-(That's wonderful!!!!! ..............)
+## Documents
+I'm going to write now...cominng soon....
 
+### Module, class configuration
+
+```
+Dydx
+  |- Algebra
+  |      |- Set
+  |      |   |- Num
+  |      |   |- ....
+  |      |
+  |      |- Operator
+  |      |   |- Interface
+  |      |   |- ....
+  |      |
+  |      |- Formula
+  |      |- inverse
+  |
+  |- Function
+  |- Delta
+  |- Integrand
+```
+
 ## Installation
 
 Add this line to your application's Gemfile:
 
     gem 'dydx'
@@ -113,8 +154,8 @@
 ## Test
 
 run `bundle exec rake spec`
 
 ```
-Finished in 0.11282 seconds
-231 examples, 0 failures
+Finished in 3.23 seconds
+309 examples, 0 failures
 ```