fix doctests

README.md

@@ -30,22 +30,22 @@ julia> using NiceNumbers
 
 julia> n = NiceNumber(2,3,5);
 Nice number:
-   2//1 + 3//1 ⋅ √5
+   2 + 3 ⋅ √5
 
 julia> n^2
 Nice number:
-   49//1 + 12//1 ⋅ √5
+   49 + 12 ⋅ √5
 
 julia> m = NiceNumber(3//5)
 Nice number:
    3//5
 
 julia> n+m, n-m, n*m, n/m
-(13//5 + 3//1 ⋅ √5, 7//5 + 3//1 ⋅ √5, 6//5 + 9//5 ⋅ √5, 10//3 + 5//1 ⋅ √5)
+(13//5 + 3 ⋅ √5, 7//5 + 3 ⋅ √5, 6//5 + 9//5 ⋅ √5, 10//3 + 5 ⋅ √5)
 
 julia> sqrt(m)
 Nice number:
-   0//1 + 1//5 ⋅ √15
+   1//5 ⋅ √15
 
 julia> sqrt(n)
 ERROR: That's not nice anymore!
@@ -54,12 +54,14 @@ ERROR: That's not nice anymore!
 
 There is also a macro to simplify working with nice numbers:
 ```julia
+julia> using LinearAlgebra
+
 julia> n = norm([4,12,3] * √2)
 18.38477631085024
 
 julia> @nice m = norm([4,12,3] * √2)
 Nice number:
-   0//1 + 13//1 ⋅ √2
+   13 ⋅ √2
 
 julia> n == m
 true

docs/make.jl

@@ -7,6 +7,7 @@ makedocs(
              "Index" => "functions.md",
              "Example: SVD" => "example_svd.md"],
     format = Documenter.HTML(prettyurls = get(ENV, "CI", nothing) == "true"),
+    strict = true
 )
 
 deploydocs(repo = "github.com/fkastner/NiceNumbers.jl.git")

docs/src/example_svd.md

@@ -23,35 +23,35 @@ Decide on an orthogonal basis in ``\mathbb{R}^m`` (here ``m=3``)
 ```jldoctest SVD
 julia> u1 = NiceNumber[3,12,4]
 3-element Array{NiceNumber,1}:
-  3//1
- 12//1
-  4//1
+  3
+ 12
+  4
 
 julia> u2 = NiceNumber[-4,0,3]
 3-element Array{NiceNumber,1}:
- -4//1
-  0//1
-  3//1
+ -4
+  0
+  3
 
 julia> u3 = cross(u1,u2)
 3-element Array{NiceNumber,1}:
-  36//1
- -25//1
-  48//1
+  36
+ -25
+  48
 ```
 and take note of their norms
 ```jldoctest SVD
 julia> n1 = norm(u1)
 Nice number:
-   13//1
+   13
 
 julia> n2 = norm(u2)
 Nice number:
-   5//1
+   5
 
 julia> n3 = norm(u3)
 Nice number:
-   65//1
+   65
 
 julia> n3 == n1*n2
 true
@@ -61,7 +61,7 @@ to construct ``U``:
 julia> U = 1/n3 * [u1*n2 u2*n1 u3]
 3×3 Array{NiceNumber,2}:
   3//13  -4//5  36//65
- 12//13   0//1  -5//13
+ 12//13      0  -5//13
   4//13   3//5  48//65
 ```
 The same procedure can in principle be used to construct a second unitary matrix in
@@ -77,33 +77,33 @@ Now we fix the singular values and construct some auxiliary matrices:
 ```jldoctest SVD
 julia> Σ = diagm(NiceNumber[13,5])
 2×2 Array{NiceNumber,2}:
- 13//1  0//1
-  0//1  5//1
+ 13  0
+  0  5
 
 julia> S = [Σ;0 0]
 3×2 Array{NiceNumber,2}:
- 13//1  0//1
-  0//1  5//1
-  0//1  0//1
+ 13  0
+  0  5
+  0  0
 
 julia> R = pinv(S)
 2×3 Array{NiceNumber,2}:
- 1//13  0//1  0//1
-  0//1  1//5  0//1
+ 1//13     0  0
+     0  1//5  0
 ```
 And we're ready to construct our matrix ``A`` and it's pseudoinverse ``A^\dagger``:
 ```jldoctest SVD
 julia> A = U*S*V'
 3×2 Array{NiceNumber,2}:
-  -5//1   0//1
+     -5      0
  -36//5  48//5
-   0//1   5//1
+      0      5
 
 julia> A⁺ = V*R*U'
 2×3 Array{NiceNumber,2}:
  -2929//21125  -36//845  1728//21125
  -1728//21125   48//845  1921//21125
 
-julia> A⁺ ≈ pinv(A)
+julia> float(A⁺) ≈ pinv(float(A))
 true
 ```

docs/src/index.md

@@ -25,22 +25,22 @@ julia> using NiceNumbers
 
 julia> n = NiceNumber(2,3,5)
 Nice number:
-   2//1 + 3//1 ⋅ √5
+   2 + 3 ⋅ √5
 
 julia> n^2
 Nice number:
-   49//1 + 12//1 ⋅ √5
+   49 + 12 ⋅ √5
 
 julia> m = NiceNumber(3//5)
 Nice number:
    3//5
 
 julia> n+m, n-m, n*m, n/m
-(13//5 + 3//1 ⋅ √5, 7//5 + 3//1 ⋅ √5, 6//5 + 9//5 ⋅ √5, 10//3 + 5//1 ⋅ √5)
+(13//5 + 3 ⋅ √5, 7//5 + 3 ⋅ √5, 6//5 + 9//5 ⋅ √5, 10//3 + 5 ⋅ √5)
 
 julia> sqrt(m)
 Nice number:
-   0//1 + 1//5 ⋅ √15
+   1//5 ⋅ √15
 
 julia> sqrt(n)
 ERROR: That's not nice anymore!
@@ -49,12 +49,14 @@ ERROR: That's not nice anymore!
 
 There is also a macro to simplify working with nice numbers:
 ```jldoctest index
+julia> using LinearAlgebra
+
 julia> n = norm([4,12,3] * √2)
 18.38477631085024
 
 julia> @nice m = norm([4,12,3] * √2)
 Nice number:
-   0//1 + 13//1 ⋅ √2
+   13 ⋅ √2
 
 julia> n == m
 true

src/NiceNumbers.jl

@@ -116,6 +116,12 @@ inv(n::NiceNumber) = NiceNumber(n.a, -n.coeff, n.radicand) * inv(n.a^2 - n.coeff
 /(n::NiceNumber, m::NiceNumber) = n * inv(m)
 
 sqrt(n::NiceNumber) = isrational(n) ? NiceNumber(0, 1, n.a) : error("That's not nice anymore!")
+"""
+    nthroot(m::NiceNumber, n)
+
+Returns the nth root of `m`. Works by repeatedly determining the square root and thus only for
+powers of two.
+"""
 function nthroot(m::NiceNumber, n)
     !ispow2(n) && error("That's not nice anymore!")
     while n > 1
@@ -130,6 +136,7 @@ end
 <(n::NiceNumber, m::NiceNumber) = float(n) < float(m)
 <=(n::NiceNumber, m::NiceNumber) = n === m || n < m
 ==(n::NiceNumber, m::AbstractFloat) = float(n) == m
+==(m::AbstractFloat, n::NiceNumber) = n == m
 
 //(n::S, m::T) where {S<:Union{NiceNumber,Integer,Rational},T<:Union{NiceNumber,Integer,Rational}} =
     n / m