Add docstrings for ZZ, QQ, QQBar, algebraic_closure (#1708)

Co-authored-by: Lars Göttgens <[email protected]>

src/Nemo.jl

@@ -570,7 +570,10 @@ const _ecm_nCs = Vector{Int}[_ecm_nC]
 #
 ###############################################################################
 
+@doc zz_ring_doc
 const FlintZZ = ZZ
+
+@doc qq_field_doc
 const FlintQQ = QQ
 
 ###############################################################################
@@ -588,6 +591,7 @@ GaussianRationals() = FlintQQi
 #
 ###############################################################################
 
+@doc qqbar_field_doc
 const QQBar = CalciumQQBar
 
 

src/calcium/CalciumTypes.jl

@@ -59,11 +59,36 @@ end
 #
 ################################################################################
 
+qqbar_field_doc = raw"""
+    QQBarField <: Field
+    QQBarFieldElem <: FieldElem
+
+The algebraic closure $\overline{\mathbb Q}$ of the rationals $\mathbb Q$ and
+its elements. This is a singleton type, meaning that there is a unique global
+instance of this field, which can be obtained via `algebraic_closure(QQ)`.
+
+```jldoctest
+julia> K = algebraic_closure(QQ)
+Field of algebraic numbers
+
+julia> sqrt(K(2))
+Root 1.41421 of x^2 - 2
+
+julia> QQBar(2//3)
+Root 0.666667 of 3x - 2
+
+julia> sinpi(QQBar(2//3))
+Root 0.866025 of 4x^2 - 3
+```
+"""
+
+@doc qq_field_doc
 struct QQBarField <: Field
 end
 
 const CalciumQQBar = QQBarField()
 
+@doc qq_field_doc
 mutable struct QQBarFieldElem <: FieldElem
   coeffs::Ptr{Nothing}
   alloc::Int

src/calcium/qqbar.jl

@@ -1538,4 +1538,20 @@ end
 #
 ###############################################################################
 
+"""
+    algebraic_closure(::QQField)
+
+Return a field representing the algebraic closure of the field of
+rational numbers.
+
+# Examples
+
+```jldoctest
+julia> K = algebraic_closure(QQ)
+Field of algebraic numbers
+
+julia> sqrt(K(2))
+Root 1.41421 of x^2 - 2
+```
+"""
 algebraic_closure(::QQField) = QQBar