Make root system interface a bit clearer

experimental/LieAlgebras/src/LieAlgebra.jl

@@ -9,14 +9,19 @@ abstract type LieAlgebra{C<:FieldElem} end
 abstract type LieAlgebraElem{C<:FieldElem} end
 
 # To be implemented by subtypes:
-# parent_type(::Type{MyLieAlgebraElem{C}})
-# elem_type(::Type{MyLieAlgebra{C}})
-# parent(x::MyLieAlgebraElem{C})
-# coefficient_ring(L::MyLieAlgebra{C})
-# dim(L::MyLieAlgebra{C})
-# Base.show(io::IO, x::MyLieAlgebra{C})
-# symbols(L::MyLieAlgebra{C})
-# bracket(x::MyLieAlgebraElem{C}, y::MyLieAlgebraElem{C})
+# Mandatory:
+#   parent_type(::Type{MyLieAlgebraElem{C}}) = MyLieAlgebra{C}
+#   elem_type(::Type{MyLieAlgebra{C}}) = MyLieAlgebraElem{C}
+#   parent(x::MyLieAlgebraElem{C}) -> MyLieAlgebra{C}
+#   coefficient_ring(L::MyLieAlgebra{C}) -> parent_type(C)
+#   dim(L::MyLieAlgebra) -> Int
+#   symbols(L::MyLieAlgebra) -> Vector{Symbol}
+#   bracket(x::MyLieAlgebraElem{C}, y::MyLieAlgebraElem{C}) -> MyLieAlgebraElem{C}
+#   Base.show(io::IO, x::MyLieAlgebra)
+# If the subtype supports root systems:
+#   has_root_system(::MyLieAlgebra) -> Bool
+#   root_system(::MyLieAlgebra) -> RootSystem
+#   chevalley_basis(L::MyLieAlgebra) -> NTuple{3,Vector{elem_type(L)}}
 
 ###############################################################################
 #
@@ -447,8 +452,6 @@ end
     has_root_system(L::LieAlgebra) -> Bool
 
 Return whether a root system for `L` is known.
-
-This function should be implemented by subtypes that support root systems.
 """
 has_root_system(L::LieAlgebra) = false # to be implemented by subtypes
 
@@ -457,9 +460,9 @@ has_root_system(L::LieAlgebra) = false # to be implemented by subtypes
 
 Return the root system of `L`.
 
-This function should be implemented by subtypes that support root systems.
+This function will error if no root system is known (see [`has_root_system(::LieAlgebra)`](@ref)).
 """
-function root_system(L::LieAlgebra)
+function root_system(L::LieAlgebra) # to be implemented by subtypes
   @req has_root_system(L) "root system of `L` not known."
   throw(Hecke.NotImplemented())
 end
@@ -470,8 +473,10 @@ end
 Return the Chevalley basis of the Lie algebra `L` in three vectors, stating first the positive root vectors, 
 then the negative root vectors, and finally the basis of the Cartan subalgebra. The order of root vectors corresponds
 to the order of the roots in [`root_system(::LieAlgebra)`](@ref).
+
+This function will error if no root system is known (see [`has_root_system(::LieAlgebra)`](@ref)).
 """
-function chevalley_basis(L::LieAlgebra)
+function chevalley_basis(L::LieAlgebra) # to be implemented by subtypes
   @req has_root_system(L) "root system of `L` not known."
   throw(Hecke.NotImplemented())
 end