Name examples section in docstrings consistently (#4376)

The Julia style guide suggest to use '# Examples' uniformly, even if
there is just one example.

experimental/BasisLieHighestWeight/src/UserFunctions.jl

@@ -6,7 +6,7 @@ together with their index.
 Operators $f_\alpha$ of negative roots are shown as the coefficients of the corresponding positive root.
 w.r.t. the simple roots $\alpha_i$.
 
-# Example
+# Examples
 ```jldoctest
 julia> basis_lie_highest_weight_operators(:B, 2)
 4-element Vector{Tuple{Int64, Vector{QQFieldElem}}}:
@@ -407,7 +407,7 @@ A birational sequence of type `Vector{Vector{Int}}` is a sequence of weights in
 `monomial_ordering` describes the monomial ordering used for the basis.
 If this is a weighted ordering, the height of the corresponding root is used as weight.
 
-# Example
+# Examples
 ```jldoctest
 julia> bases = basis_coordinate_ring_kodaira(:G, 2, [1,0], 6; monomial_ordering = :invlex)
 6-element Vector{Tuple{MonomialBasis, Vector{ZZMPolyRingElem}}}:
@@ -510,7 +510,7 @@ The the birational sequence used consists of all operators in descening height o
 
 The monomial ordering is fixed to `degrevlex`. 
 
-# Example
+# Examples
 ```jldoctest
 julia> bases = basis_coordinate_ring_kodaira_ffl(:G, 2, [1,0], 6)
 6-element Vector{Tuple{MonomialBasis, Vector{ZZMPolyRingElem}}}:

experimental/LieAlgebras/src/LieAlgebra.jl

@@ -854,7 +854,7 @@ Return the abelian Lie algebra of dimension `n` over the field `R`.
 The first argument can be optionally provided to specify the type of the returned
 Lie algebra.
 
-# Example
+# Examples
 ```jldoctest
 julia> abelian_lie_algebra(LinearLieAlgebra, QQ, 3)
 Linear Lie algebra with 3x3 matrices

experimental/LieAlgebras/src/LieAlgebraModule.jl

@@ -1412,7 +1412,7 @@ Compute the dimension of the simple module of the Lie algebra `L` with highest w
 using Weyl's dimension formula.
 The return value is of type `T`.
 
-# Example
+# Examples
 ```jldoctest
 julia> L = lie_algebra(QQ, :A, 3);
 
@@ -1445,7 +1445,7 @@ sorted ascendingly by the total height of roots needed to reach them from `hw`.
 
 See [MP82](@cite) for details and the implemented algorithm.
 
-# Example
+# Examples
 ```jldoctest
 julia> L = lie_algebra(QQ, :B, 3);
 
@@ -1477,7 +1477,7 @@ together with their multiplicities.
 
 This function uses an optimized version of the Freudenthal formula, see [MP82](@cite) for details.
 
-# Example
+# Examples
 ```jldoctest
 julia> L = lie_algebra(QQ, :A, 3);
 
@@ -1513,7 +1513,7 @@ Computes all weights occurring in the simple module of the Lie algebra `L` with
 together with their multiplicities.
 This is achieved by acting with the Weyl group on the [`dominant_character`](@ref dominant_character(::LieAlgebra, ::Vector{<:IntegerUnion})).
 
-# Example
+# Examples
 ```jldoctest
 julia> L = lie_algebra(QQ, :A, 3);
 
@@ -1557,7 +1557,7 @@ This function uses Klimyk's formula (see [Hum72; Exercise 24.9](@cite)).
 
 The return type may change in the future.
 
-# Example
+# Examples
 ```jldoctest
 julia> L = lie_algebra(QQ, :A, 2);
 
@@ -1599,7 +1599,7 @@ with extremal weight `x*w`, together with their multiplicities.
 Instead of a Weyl group element `x`, a reduced expression for `x` can be supplied.
 This function may return arbitrary results if the provided expression is not reduced.
 
-# Example
+# Examples
 ```jldoctest
 julia> L = lie_algebra(QQ, :A, 2);
 

experimental/LieAlgebras/src/RootSystem.jl

@@ -1468,7 +1468,7 @@ Compute the dimension of the simple module of the Lie algebra defined by the roo
 with highest weight `hw` using Weyl's dimension formula.
 The return value is of type `T`.
 
-# Example
+# Examples
 ```jldoctest
 julia> R = root_system(:B, 2);
 
@@ -1512,7 +1512,7 @@ sorted ascendingly by the total height of roots needed to reach them from `hw`.
 
 See [MP82](@cite) for details and the implemented algorithm.
 
-# Example
+# Examples
 ```jldoctest
 julia> R = root_system(:B, 3);
 
@@ -1575,7 +1575,7 @@ with highest weight `hw`, together with their multiplicities.
 
 This function uses an optimized version of the Freudenthal formula, see [MP82](@cite) for details.
 
-# Example
+# Examples
 ```jldoctest
 julia> R = root_system(:B, 3);
 
@@ -1667,7 +1667,7 @@ Computes all weights occurring in the simple module of the Lie algebra defined b
 with highest weight `hw`, together with their multiplicities.
 This is achieved by acting with the Weyl group on the [`dominant_character`](@ref dominant_character(::RootSystem, ::WeightLatticeElem)).
 
-# Example
+# Examples
 ```jldoctest
 julia> R = root_system(:B, 3);
 
@@ -1720,7 +1720,7 @@ This function uses Klymik's formula.
 
 The return type may change in the future.
 
-# Example
+# Examples
 ```jldoctest
 julia> R = root_system(:B, 2);
 
@@ -1845,7 +1845,7 @@ with extremal weight `x*w`, together with their multiplicities.
 Instead of a Weyl group element `x`, a reduced expression for `x` can be supplied.
 This function may return arbitrary results if the provided expression is not reduced.
 
-# Example
+# Examples
 ```jldoctest
 julia> R = root_system(:B, 3);
 

experimental/MatrixGroups/src/MatrixGroups.jl

@@ -19,7 +19,7 @@ end
 
 Compute the JuliaMatrixRep of `m` in GAP.
 
-# Example
+# Examples
 ```jldoctest
 julia> m = matrix(ZZ, [0 1 ; -1 0]);
 
@@ -43,7 +43,7 @@ A nice monomorphism from `G` to a GAP matrix group `G2` over a finite field
 is stored in `G`, such that calculations in `G` can be handled automatically
 by transferring them to `G2`.
 
-# Example
+# Examples
 ```jldoctest
 julia> m1 = matrix(QQ, [0 1 ; -1 0]);
 

experimental/Schemes/src/Resolution_structure.jl

@@ -55,7 +55,7 @@ end
 Return a `CartierDivisor` on the `domain` of `f` which is the
 exceptional divisor of the sequence of blow-ups `f`.
 
-# Example
+# Examples
 ```jldoctest
 julia> R,(x,y) = polynomial_ring(QQ,2);
 
@@ -90,7 +90,7 @@ end
 Return a `WeilDivisor` on the `domain` of `f` which is the
 exceptional divisor of the sequence of blow-ups `f`.
 
-# Example
+# Examples
 ```jldoctest
 julia> R,(x,y) = polynomial_ring(QQ,2);
 

experimental/Schemes/src/Resolution_tools.jl

@@ -19,7 +19,7 @@ Return a tuple `M`, `v`, `M2`, `m` where
 !!! note
   The intersection matrix referred to in textbooks is `M2`, as these usually restrict to the case of algebraically closed fields, but computations are usually performed over suitable subfields, e.g. `QQ` instead of `CC`. 
 
-# Example
+# Examples
 ```jldoctest
 julia> R,(x,y,z) = polynomial_ring(QQ,3);
 

src/AlgebraicGeometry/Schemes/CoveredProjectiveScheme/CoveredProjectiveScheme.jl

@@ -132,7 +132,7 @@ end
 Given a ring `R`, return the empty relative projective scheme over the
 empty covered scheme over `R`.
 
-# Example
+# Examples
 ```jldoctest
 julia> R, (x,y,z) = QQ[:x, :y, :z];
 

src/AlgebraicGeometry/Schemes/Divisors/WeilDivisor.jl

@@ -67,7 +67,7 @@ end
 Given an ideal sheaf `I` of pure codimension ``1``, return the weil divisor $D = 1 ⋅ I$ with
 coefficients in the integer ring.
 
-# Example
+# Examples
 ```jldoctest
 julia> P, (x, y, z) = graded_polynomial_ring(QQ, [:x, :y, :z]);
 

src/AlgebraicGeometry/Schemes/ProjectiveSchemes/Objects/Attributes.jl

@@ -24,7 +24,7 @@ base_scheme(P::AbsProjectiveScheme) =base_scheme(underlying_scheme(P))
 On a projective scheme ``P = Proj(S)`` for a standard
 graded finitely generated algebra ``S`` this returns ``S``.
 
-# Example
+# Examples
 ```jldoctest
 julia> S, _ = grade(QQ[:x, :y, :z][1]);
 
@@ -52,7 +52,7 @@ homogeneous_coordinate_ring(P::AbsProjectiveScheme) = homogeneous_coordinate_rin
 
 On ``X ⊂ ℙʳ_A`` this returns ``r``.
 
-# Example
+# Examples
 ```jldoctest
 julia> S, _ = grade(QQ[:x, :y, :z][1]);
 
@@ -89,7 +89,7 @@ On a projective scheme ``P = Proj(S)`` with ``S = P/I``
 for a standard graded polynomial ring ``P`` and a
 homogeneous ideal ``I`` this returns ``P``.
 
-# Example
+# Examples
 ```jldoctest
 julia> S, _ = grade(QQ[:x, :y, :z][1])
 (Graded multivariate polynomial ring in 3 variables over QQ, MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}[x, y, z])
@@ -133,7 +133,7 @@ end
 
 On ``X ⊂ ℙʳ_A`` this returns ``ℙʳ_A``.
 
-# Example
+# Examples
 ```jldoctest
 julia> S, _ = grade(QQ[:x, :y, :z][1]);
 
@@ -229,7 +229,7 @@ end
 On ``X ⊂ ℙʳ_A`` this returns the homogeneous
 ideal ``I ⊂ A[s₀,…,sᵣ]`` defining ``X``.
 
-# Example
+# Examples
 ```jldoctest
 julia> R, (u, v) = QQ[:u, :v];
 
@@ -265,7 +265,7 @@ from the `homogeneous_coordinate_ring` to the `coordinate_ring` of the affine co
 
 
 Note that if the base scheme is not affine, then the affine cone is not affine.
-# Example
+# Examples
 ```jldoctest
 julia> R, (u, v) = QQ[:u, :v];
 
@@ -388,7 +388,7 @@ On ``X ⊂ ℙʳ_A`` this returns a vector with the homogeneous
 coordinates ``[s₀,…,sᵣ]`` as entries where each one of the
 ``sᵢ`` is a function on the `affine cone` of ``X``.
 
-# Example
+# Examples
 ```jldoctest
 julia> R, (u, v) = QQ[:u, :v];
 

src/AlgebraicGeometry/Surfaces/duValSing.jl

@@ -3,7 +3,7 @@
 
 Return whether the given ``X`` has at most du Val (surface) singularities.
 
-# Example:
+# Examples
 ```jldoctest
 julia> R,(x,y,z,w) = QQ[:x, :y, :z, :w]
 (Multivariate polynomial ring in 4 variables over QQ, QQMPolyRingElem[x, y, z, w])
@@ -67,7 +67,7 @@ Return whether the given ``X`` has at most du Val (surface) singularities at the
 
 **Note**: For the ideal ``I`` in a ring ``R``, `dim(R/I) = 0` is asserted
 
-# Example:
+# Examples
 ```jldoctest
 julia> R,(x,y,z,w) = QQ[:x, :y, :z, :w]
 (Multivariate polynomial ring in 4 variables over QQ, QQMPolyRingElem[x, y, z, w])
@@ -147,7 +147,7 @@ If ``X`` has a least one singularity which is not du Val, the returned vector co
 
 **Note**: For the ideal ``I`` in a ring ``R``, `dim(R/I) = 0` is asserted
 
-# Example:
+# Examples
 ```jldoctest
 julia> R,(x,y,z,w) = QQ[:x, :y, :z, :w]
 (Multivariate polynomial ring in 4 variables over QQ, QQMPolyRingElem[x, y, z, w])

src/Combinatorics/EnumerativeCombinatorics/partitions.jl

@@ -489,7 +489,7 @@ order.
 
 The implemented algorithm is "partb" in [RJ76](@cite).
 
-# Example
+# Examples
 The number of partitions of 100 where the parts are from {1, 2, 5, 10, 20, 50}:
 ```jldoctest
 julia> length(collect(partitions(100, [1, 2, 5, 10, 20, 50])))

src/Combinatorics/Matroids/quantum_automorphism_groups.jl

@@ -10,7 +10,7 @@ The relations are:
   - idempotent relations: `n^2` relations
   - relations of type `u[i,j]*u[i,k]` and `u[j,i]*u[k,i]` for `k != j`: `2*n*n*(n-1)` relations
 
-# Example
+# Examples
 
 ```jldoctest
 julia> S4 = quantum_symmetric_group(4);

src/PolyhedralGeometry/Cone/properties.jl

@@ -379,7 +379,7 @@ lineality_dim(C::Cone) = pm_object(C).LINEALITY_DIM::Int
 Facet degrees of the cone. The degree of a facet is the number of adjacent facets. 
 In particular a general $2$-dimensional cone has two facets (rays) that meet at the origin. 
 
-# Example
+# Examples
 Produce the facet degrees of a cone over a square and a cone over a square pyramid. 
 ```jldoctest
 julia> c = positive_hull([1 1 0; 1 -1 0; 1 0 1; 1 0 -1])

src/PolyhedralGeometry/Polyhedron/properties.jl

@@ -900,7 +900,7 @@ codim(P::Polyhedron) = ambient_dim(P) - dim(P)
 
 Number of vertices in each facet. 
 
-# Example
+# Examples
 ```jldoctest
 julia> p = johnson_solid(4) 
 Polytope in ambient dimension 3 with EmbeddedAbsSimpleNumFieldElem type coefficients
@@ -929,7 +929,7 @@ end
 
 Number of incident facets for each vertex.
 
-# Example
+# Examples
 ```jldoctest
 julia> vertex_sizes(bipyramid(simplex(2)))
 5-element Vector{Int64}: