Update README.md (#61)

Author: MasonProtter

README.md

@@ -20,6 +20,56 @@ julia> y[-1,-7,-128,-5,-1,-3,-2,-1] += 5
 19.0
 ```
 
+## Example: Relativistic Notation
+Suppose we have a position vector `r = [:x, :y, :z]` which is naturally one-based, ie. `r[1] == :x`, `r[2] == :y`,  `r[3] == :z` and we also want to cosntruct a relativistic position vector which includes time as the 0th component. This can be done with OffsetArrays like 
+```julia
+julia> using OffsetArrays
+
+julia> r = [:x, :y, :z];
+
+julia> x = OffsetVector([:t, r...], 0:3)
+OffsetArray(::Array{Symbol,1}, 0:3) with eltype Symbol with indices 0:3:
+ :t
+ :x
+ :y
+ :z
+
+julia> x[0]
+:t
+
+julia> x[1:3]
+3-element Array{Symbol,1}:
+ :x
+ :y
+ :z
+```
+
+## Example: Polynomials
+Suppose one wants to represent the Laurent polynomial
+```
+6/x + 5 - 2*x + 3*x^2 + x^3
+```
+in julia. The coefficients of this polynomial are a naturally `-1` based list, since the `n`th element of the list 
+(counting from `-1`) `6, 5, -2, 3, 1` is the coefficient corresponding to the `n`th power of `x`. This Laurent polynomial can be evaluated at say `x = 2` as follows.
+```julia
+julia> using OffsetArrays
+
+julia> coeffs = OffsetVector([6, 5, -2, 3, 1], -1:3)
+OffsetArray(::Array{Int64,1}, -1:3) with eltype Int64 with indices -1:3:
+  6
+  5
+ -2
+  3
+  1
+
+julia> polynomial(x, coeffs) = sum(coeffs[n]*x^n for n in eachindex(coeffs))
+polynomial (generic function with 1 method)
+
+julia> polynomial(2.0, coeffs)
+24.0
+```
+Notice our use of the `eachindex` function which does not assume that the given array starts at `1`.
+
 ## Notes on supporting OffsetArrays
 
 Julia supports generic programming with arrays that doesn't require you to assume that indices start with 1, see the [documentation](http://docs.julialang.org/en/latest/devdocs/offset-arrays/).