Update README.md

* Update description.
* Update installation instructions.
* Add brief tutorial.
* Add lifecycle badge.

README.md

@@ -2,21 +2,64 @@
 
 [![Build Status](https://travis-ci.org/Element-126/LorentzVectors.jl.svg?branch=master)](https://travis-ci.org/Element-126/LorentzVectors.jl)
 [![codecov.io](http://codecov.io/github/Element-126/LorentzVectors.jl/coverage.svg?branch=master)](http://codecov.io/github/Element-126/LorentzVectors.jl?branch=master)
+[![lifecycle](https://img.shields.io/badge/lifecycle-maturing-blue.svg)](https://www.tidyverse.org/lifecycle/#maturing)
 
-This package defines the `LorentzVector{T}` and `SpatialVector{T}` types for use in computations involving Special Relativity.
-It implements the usual algebraic operations as well as some relevant functions such as `boost`.
-The signature of the Minkowski metric (used for the dot product) is `+,-,-,-`.
+This package defines the `LorentzVector{T}` and `SpatialVector{T}` types for use in computations involving Special Relativity. These types are statically allocated and should therefore be very fast.
 
-:floppy_disk: Installing
+The usual algebraic operations are implemented, as well as some domain-specific functions (such as `boost`) and many convenience methods.
+
+The signature of the Minkowski metric (used for the inner product) is `+,-,-,-`.
+
+:arrow_down: Installing
 ---
 
-Install it with:
+From the Julia REPL:
+
+```
+(v1.0) pkg> add https://github.com/Element-126/LorentzVectors.jl.git
+```
+
+:information_source: Usage
+---
 
 ```julia
-Pkg.clone("https://github.com/Element-126/LorentzVectors.jl.git")
+using LorentzVectors
+
+p1 = Vec4(10, 0, 0, 10)
+p2 = Vec4(7, 0, 1, 5)
+
+m1 = √(p1⋅p1)
+@assert m1 == 0 # p1 is lightlike, so its mass must be zero
+m2 = √(p2⋅p2)
+@assert m2 > 0
+
+β1 = Vec3(p1/p1.t)
+@assert norm(β1) ≈ 1 # Check that p1 travels at the speed of light
+
+p2_rest = boost(p2, p2/p2.t) # Boost p2 to its rest frame
+@assert p2_rest.t ≈ m2 # Check that its energy at rest is equal to its mass
+
+@assert boost(p2, zero(Vec3)) ≈ p2 # Identity boost
+
+p_tot = p1 + p2
+β_cm = p_tot/p_tot.t # Compute the velocity of the center of mass (CM)
+p1_cm = boost(p1, β_cm) # Boost p1 and p2 to the CM frame
+p2_cm = boost(p2, β_cm)
+@assert norm(Vec3(p1_cm + p2_cm)) < 1e-12 # Check that the spatial parts cancel in the CM
+
+u1 = rand(Vec3{Float64}) # Generate a random 3-vector on the unit sphere
+@assert norm(u1) ≈ 1
+u2 = normalize(Vec3(p2)) # Extract the spatial direction of p2
+@assert norm(u2) ≈ 1
+
+@assert Vec4 === LorentzVector # Long forms
+@assert Vec3 === SpatialVector
+
+x = Vec3(1f0, 0, 0) # Float64 is used by default, but it can be overriden
+@assert typeof(x) == Vec3{Float32}
 ```
 
-:warning: This package is currently :construction: WIP and may change at any time without prior notice. Use at your own risk !
+For more examples, have a look in the `test` directory.
 
 :heart: Contributing
 ---