Update documentation

README.md

@@ -7,57 +7,7 @@ A Julia implementation of quaternions.
 [![codecov](https://codecov.io/gh/JuliaGeometry/Quaternions.jl/branch/master/graph/badge.svg?token=dJBiR91dCD)](https://codecov.io/gh/JuliaGeometry/Quaternions.jl)
 
 [Quaternions](http://en.wikipedia.org/wiki/Quaternion) are best known for their suitability
-as representations of 3D rotational orientation. They can also be viewed as an extension of complex numbers.
+as representations of 3D rotational orientation.
+They can also be viewed as an extension of complex numbers.
 
-Implemented functions are:
-
-    +-*/^
-    real
-    imag_part  (tuple)
-    conj
-    abs
-    abs2
-    normalize
-    normalizea  (return normalized quaternion and absolute value as a pair)
-    angleaxis  (taken as an orientation, return the angle and axis (3 vector) as a tuple)
-    angle
-    axis
-    sqrt
-    exp
-    exp2
-    exp10
-    expm1
-    log2
-    log10
-    log1p
-    sin
-    cos
-    tan
-    asin
-    acos
-    atan
-    sinh
-    cosh
-    tanh
-    asinh
-    acosh
-    atanh
-    csc
-    sec
-    cot
-    acsc
-    asec
-    acot
-    csch
-    sech
-    coth
-    acsch
-    asech
-    acoth
-    sinpi
-    cospi
-    sincos
-    sincospi
-    slerp
-    rand
-    randn
+In JuliaGeometry organization, there is also [Octonions.jl](https://github.com/JuliaGeometry/Octonions.jl).

docs/make.jl

@@ -14,6 +14,7 @@ makedocs(;
     ),
     pages=[
         "Home" => "index.md",
+        "APIs" => "api.md",
         "Examples" => ["examples/dual_quaternions.md"],
     ],
 )

docs/src/api.md

@@ -0,0 +1,25 @@
+# APIs
+
+```@docs
+Quaternion
+```
+
+```@docs
+quat
+```
+
+```@docs
+real(::Quaternion)
+```
+
+```@docs
+imag_part
+```
+
+```@docs
+conj
+```
+
+```@docs
+Quaternions.extend_analytic
+```

src/Quaternion.jl

@@ -1,3 +1,13 @@
+"""
+    Quaternion{T<:Real} <: Number
+
+Quaternion number type with real and imaginary part of type `T`.
+
+`QuaternionF16`, `QuaternionF32` and `QuaternionF64` are aliases for
+`Quaternion{Float16}`, `Quaternion{Float32}`, and `Quaternion{Float64}`, respectively.
+
+See also: [`quat`](@ref), [`real`](@ref), [`imag_part`](@ref).
+"""
 struct Quaternion{T<:Real} <: Number
     s::T
     v1::T
@@ -29,14 +39,72 @@ quat(p, v1, v2, v3, n) = Quaternion(p, v1, v2, v3, n)
 quat(x) = Quaternion(x)
 quat(s, a) = Quaternion(s, a)
 
+"""
+    real(T::Type)
+
+Return the type that represents the real part of a value of type `T`.
+e.g: for `T == Quaternion{R}`, returns `R`.
+Equivalent to `typeof(real(zero(T)))`.
+
+# Examples
+```jldoctest
+julia> real(Quaternion{Int})
+Int64
+```
+"""
 real(::Type{Quaternion{T}}) where {T} = T
+
+"""
+    real(q::Quaternion)
+
+Return the real part of the quaternion `q`.
+
+See also: [`imag_part`](@ref), [`quat`](@ref), [`isreal`](@ref).
+
+# Examples
+```jldoctest
+julia> real(quat(1,2,3,4))
+1
+
+julia> real([quat(5,6,7,8), 9])
+2-element Vector{Int64}:
+ 5
+ 9
+```
+"""
 real(q::Quaternion) = q.s
+
+"""
+    imag_part(q::Quaternion{T})
+
+Return the imaginary part of the quaternion `q` with type `Tuple{T,T,T}`.
+Note that this function is different from `Base.imag` which returns `Real`.
+
+See also: [`real`](@ref), [`conj`](@ref).
+
+# Examples
+```jldoctest
+julia> imag_part(Quaternion(1,2,3,4))
+(2, 3, 4)
+```
+"""
 imag_part(q::Quaternion) = (q.v1, q.v2, q.v3)
 
 (/)(q::Quaternion, x::Real) = Quaternion(q.s / x, q.v1 / x, q.v2 / x, q.v3 / x)
 (*)(q::Quaternion, x::Real) = Quaternion(q.s * x, q.v1 * x, q.v2 * x, q.v3 * x)
 (*)(x::Real, q::Quaternion) = q * x
 
+"""
+    conj(q::Quaternion)
+
+Compute the quaternion conjugate of a quaternion `q`.
+
+# Examples
+```jldoctest
+julia> conj(Quaternion(1,2,3,4))
+Quaternion{Int64}(1, -2, -3, -4, false)
+```
+"""
 conj(q::Quaternion) = Quaternion(q.s, -q.v1, -q.v2, -q.v3, q.norm)
 abs(q::Quaternion) = sqrt(abs2(q))
 float(q::Quaternion{T}) where T = convert(Quaternion{float(T)}, q)
@@ -129,7 +197,7 @@ See Theorem 5 of [^Sudbery1970] for details.
 
 [^Sudbery1970]
     Sudbery (1979). Quaternionic analysis. Mathematical Proceedings of the Cambridge
-    Philosophical Society,85, pp 199­225
+    Philosophical Society,85, pp 199225
     doi:[10.1017/S030500410005563](https://doi.org/10.1017/S0305004100055638)
 """
 function extend_analytic(f, q::Quaternion)