Merge pull request #1 from daviddelaat/patch-1

Update README.md

Author: Keno

README.md

@@ -1,73 +1,62 @@
 # Polynomial
 
-Basic arithmetic, integration, differentiation, evaluation, and root finding over dense polynomials.
+Basic arithmetic, integration, differentiation, evaluation, and root finding over dense univariate polynomials.
 
 [![Build Status](https://travis-ci.org/vtjnash/Polynomial.jl.png?branch=master)](https://travis-ci.org/vtjnash/Polynomial.jl)
 
 #### Poly{T<:Number}(a::Vector)
-Construct a polynomial from its coefficients, highest order first.
-
+Construct a polynomial from its coefficients, lowest order first.
 ```julia
 julia> Poly([1,0,3,4])
-Poly(1x^3 + 3x^1 + 4)
-```
-
-Leading zeros are stripped.
-
-```julia
-julia> Poly([0,1,2,3])
-Poly(1x^2 + 2x^1 + 3)
+Poly(1 + 3x^2 + 4x^3)
 ```
 
 An optional variable parameter can be added.
-
 ```julia
-julia> Poly([1,2,3], 's')
-Poly(s^2 + 2 s + 3)
+julia> Poly([1,2,3], :s)
+Poly(1 + 2s + 3s^2)
 ```
 
 #### poly(r::AbstractVector)
 Construct a polynomial from its roots. This is in contrast to the `Poly` constructor, which constructs a polynomial from its coefficients.
-
 ```julia
-// Represents (x - 1)*(x-2)*(x-3)
+// Represents (x-1)*(x-2)*(x-3)
 julia> poly([1,2,3])
-Poly(1x^3 + -6x^2 + 11x^1 + -6)
+Poly(-6 + 11x - 6x^2 + x^3)
 ```
 
 #### +, -, *, /, ==
 
 The usual arithmetic operators are overloaded to work on polynomials, and combinations of polynomials and scalars.
-
 ```julia
-julia> a = Poly([1,2])
-Poly(1x^1 + 2)
+julia> p = Poly([1,2])
+Poly(1 + 2x)
 
-julia> b = Poly([1, 0, -1])
-Poly(1x^2 + -1)
+julia> q = Poly([1, 0, -1])
+Poly(1 - x^2)
 
-julia> 2*a
-Poly(2x^1 + 4)
+julia> 2p
+Poly(2 + 4x)
 
-julia> 2 + a
-Poly(1x^1 + 4)
+julia> 2+p
+Poly(3 + 2x)
 
-julia> a - b
-Poly(-1x^2 + 1x^1 + 3)
+julia> p - q
+Poly(2x + x^2)
 
-julia> a*b
-Poly(1x^3 + 2x^2 + -1x^1 + -2)
+julia> p*q
+Poly(1 + 2x - x^2 - 2x^3)
 
-julia> b/2
-Poly(0.5x^2 + -0.5)
+julia> q/2
+Poly(0.5 - 0.5x^2)
 ```
 
 Note that operations involving polynomials with different variables will error.
 
 ```julia
-julia> a = Poly([1,2,3], 'x');
-julia> b = Poly([1,2,3], 's');
-julia> a + b
+julia> p = Poly([1, 2, 3], :x)
+julia> q = Poly([1, 2, 3], :s)
+julia> p + q
 ERROR: Polynomials must have same variable.
 ```
 
@@ -76,26 +65,24 @@ Evaluate the polynomial `p` at `x`.
 
 ```julia
 julia> polyval(Poly([1, 0, -1]), 0.1)
--0.99
+0.99
 ```
 
 #### polyint(p::Poly, k::Number=0)
 Integrate the polynomial `p` term by term, optionally adding constant term `k`. The order of the resulting polynomial is one higher than the order of `p`.
-
 ```julia
 julia> polyint(Poly([1, 0, -1]))
-Poly(0.3333333333333333x^3 + -1.0x^1)
+Poly(x - 0.3333333333333333x^3)
 
 julia> polyint(Poly([1, 0, -1]), 2)
-Poly(0.3333333333333333x^3 + -1.0x^1 + 2.0)
+Poly(2.0 + x - 0.3333333333333333x^3)
 ```
 
 #### polyder(p::Poly)
 Differentiate the polynomial `p` term by term. The order of the resulting polynomial is one lower than the order of `p`.
-
 ```julia
 julia> polyder(Poly([1, 3, -1]))
-Poly(2x^1 + 3)
+Poly(3 - 2x)
 ```
 
 #### roots(p::Poly)
@@ -109,10 +96,10 @@ julia> roots(Poly([1, 0, -1]))
 
 julia> roots(Poly([1, 0, 1]))
 2-element Array{Complex{Float64},1}:
- 0.0-1.0im
  0.0+1.0im
+ 0.0-1.0im
 
-julia> roots(Poly([1, 0, 0]))
+julia> roots(Poly([0, 0, 1]))
 2-element Array{Float64,1}:
  0.0
  0.0