Add docstrings to documentation

experimental/LieAlgebras/docs/src/root_systems.md

@@ -145,6 +145,8 @@ is_negative_root_with_index(::RootSpaceElem)
 ```@docs
 reflect(::RootSpaceElem, ::Int)
 reflect!(::RootSpaceElem, ::Int)
+reflect(::RootSpaceElem, ::RootSpaceElem)
+reflect!(::RootSpaceElem, ::RootSpaceElem)
 ```
 
 

experimental/LieAlgebras/docs/src/weight_lattices.md

@@ -68,6 +68,8 @@ is_fundamental_weight_with_index(::WeightLatticeElem)
 ```@docs
 reflect(::WeightLatticeElem, ::Int)
 reflect!(::WeightLatticeElem, ::Int)
+reflect(::WeightLatticeElem, ::RootSpaceElem)
+reflect!(::WeightLatticeElem, ::RootSpaceElem)
 ```
 
 ### Conjugate dominant weight

experimental/LieAlgebras/docs/src/weyl_groups.md

@@ -33,8 +33,6 @@ weyl_group(::Vector{Tuple{Symbol,Int}})
 ## Basic properties
 Basic group arithmetic like `*`, and `inv` are defined for `WeylGroupElem` objects.
 
-Using `(W::WeylGroup)(word::Vector{<:Integer})`, one can construct group elements from a word in the generators.
-
 ```@docs
 is_finite(::WeylGroup)
 one(::WeylGroup)
@@ -49,6 +47,19 @@ order(::Type{T}, ::WeylGroup) where {T}
 root_system(::WeylGroup)
 ```
 
+### Element constructors
+
+Using `(W::WeylGroup)(word::Vector{<:Integer})`, one can construct group elements from a word in the generators.
+
+```@docs; canonical=false
+gen(::WeylGroup, ::Int)
+gens(::WeylGroup)
+```
+
+```@docs
+reflection(::RootSpaceElem)
+```
+
 ### Words and length
 ```@docs
 word(::WeylGroupElem)

experimental/LieAlgebras/src/RootSystem.jl

@@ -1101,42 +1101,6 @@ function reflect!(r::RootSpaceElem, s::Int)
   return r
 end
 
-@doc raw"""
-    reflection(beta::RootSpaceElem) -> WeylGroupElem
-
-Return the Weyl group element corresponding to the reflection at the hyperplane orthogonal to root `beta`.
-"""
-function reflection(beta::RootSpaceElem)
-  R = root_system(beta)
-  W = weyl_group(R)
-  rk = number_of_simple_roots(R)
-
-  b, index_of_beta = is_positive_root_with_index(beta)
-  if !b
-    b, index_of_beta = is_negative_root_with_index(beta)
-  end
-  @req b "Not a root"
-
-  found_simple_root = index_of_beta <= rk
-  current_index = index_of_beta
-  list_of_indices = Int[]
-  while !found_simple_root
-    for j in 1:rk
-      next_index = W.refl[j, current_index]
-      if !iszero(next_index) &&
-        next_index < current_index
-        current_index = next_index
-        if current_index <= rk
-          found_simple_root = true
-        end
-        push!(list_of_indices, j)
-        break
-      end
-    end
-  end
-  return W([list_of_indices; current_index; reverse(list_of_indices)])
-end
-
 @doc raw"""
     reflect(r::RootSpaceElem, beta::RootSpaceElem) -> RootSpaceElem
   

experimental/LieAlgebras/src/WeylGroup.jl

@@ -513,6 +513,42 @@ function word(x::WeylGroupElem)
   return x.word
 end
 
+@doc raw"""
+    reflection(beta::RootSpaceElem) -> WeylGroupElem
+
+Return the Weyl group element corresponding to the reflection at the hyperplane orthogonal to root `beta`.
+"""
+function reflection(beta::RootSpaceElem)
+  R = root_system(beta)
+  W = weyl_group(R)
+  rk = number_of_simple_roots(R)
+
+  b, index_of_beta = is_positive_root_with_index(beta)
+  if !b
+    b, index_of_beta = is_negative_root_with_index(beta)
+  end
+  @req b "Not a root"
+
+  found_simple_root = index_of_beta <= rk
+  current_index = index_of_beta
+  list_of_indices = Int[]
+  while !found_simple_root
+    for j in 1:rk
+      next_index = W.refl[j, current_index]
+      if !iszero(next_index) &&
+        next_index < current_index
+        current_index = next_index
+        if current_index <= rk
+          found_simple_root = true
+        end
+        push!(list_of_indices, j)
+        break
+      end
+    end
+  end
+  return W([list_of_indices; current_index; reverse(list_of_indices)])
+end
+
 @doc raw"""
     fp_group(W::WeylGroup) -> FPGroup