Revert "Make algebraic sets and varieties internal (#2424)" (#2430)

This reverts commit e2e2c31.

docs/doc.main

@@ -165,6 +165,14 @@
         "AlgebraicGeometry/Schemes/ProjectiveSchemes.md",
         "AlgebraicGeometry/Schemes/MorphismsOfProjectiveSchemes.md",
      ],
+     "Algebraic Sets" => [
+        "AlgebraicGeometry/AlgebraicSets/AffineAlgebraicSet.md",
+        "AlgebraicGeometry/AlgebraicSets/ProjectiveAlgebraicSet.md",
+     ],
+     "Algebraic Varieties" => [
+        "AlgebraicGeometry/AlgebraicVarieties/AffineVariety.md",
+        "AlgebraicGeometry/AlgebraicVarieties/ProjectiveVariety.md",
+     ],
      "Toric Varieties" => [
         "AlgebraicGeometry/ToricVarieties/intro.md",
         "AlgebraicGeometry/ToricVarieties/NormalToricVarieties.md",

src/AlgebraicGeometry/Schemes/AffineAlgebraicSet/Objects/Constructors.jl

@@ -26,10 +26,10 @@ Return the vanishing locus of ``I`` as an algebraic set.
 This computes the radical of ``I`` if `check=true`.
 Otherwise, Oscar takes on faith that ``I`` is radical.
 
-```
+```jldoctest
 julia> R, (x,y) = GF(2)[:x,:y];
 
-julia> X = Oscar.vanishing_locus(ideal([y^2+y+x^3+1,x]))
+julia> X = vanishing_locus(ideal([y^2+y+x^3+1,x]))
 Vanishing locus
   in Affine 2-space over GF(2)
   of ideal(x, y^2 + y + 1)
@@ -56,17 +56,17 @@ Return the vanishing locus of the multivariate polynomial `p`.
 This computes the radical of ``I`` if `check=true`.
 Otherwise Oscar takes on faith that ``I`` is radical.
 
-```
+```jldoctest
 julia> R, (x,y) = QQ[:x,:y];
 
-julia> X = Oscar.vanishing_locus((y^2+y+x^3+1)*x^2)
+julia> X = vanishing_locus((y^2+y+x^3+1)*x^2)
 Vanishing locus
   in Affine 2-space over QQ
   of ideal(x^4 + x*y^2 + x*y + x)
 
 julia> R, (x,y) = GF(2)[:x,:y];
 
-julia> X = Oscar.vanishing_locus((y^2+y+x^3+1)*x^2)
+julia> X = vanishing_locus((y^2+y+x^3+1)*x^2)
 Vanishing locus
   in Affine 2-space over GF(2)
   of ideal(x^4 + x*y^2 + x*y + x)

src/AlgebraicGeometry/Schemes/AffineVariety/Objects/Constructors.jl

@@ -23,11 +23,11 @@ Return the affine variety defined by the prime ideal ``I``.
 Since our varieties are irreducible, we check that ``I`` stays prime when
 viewed over the algebraic closure. This is an expensive check that can be disabled.
 
-```
+```jldoctest
 julia> R, (x,y) = QQ[:x,:y]
 (Multivariate polynomial ring in 2 variables over QQ, QQMPolyRingElem[x, y])
 
-julia> Oscar.affine_variety(ideal([x,y]))
+julia> affine_variety(ideal([x,y]))
 Affine variety
  in Affine 2-space over QQ
 defined by ideal(x, y)
@@ -36,10 +36,10 @@ defined by ideal(x, y)
 Over fields different from `QQ`, currently, we cannot check for irreducibility
 over the algebraic closure. But if you know that the ideal in question defines
 a variety, you can construct it by disabling the check.
-```
+```jldoctest
 julia> R, (x,y) = GF(2)[:x,:y];
 
-julia> Oscar.affine_variety(x^3+y+1,check=false)
+julia> affine_variety(x^3+y+1,check=false)
 Affine variety
  in Affine 2-space over GF(2)
 defined by ideal(x^3 + y + 1)
@@ -57,12 +57,12 @@ We require that ``R`` is a finitely generated algebra over a field ``k`` and
 moreover that the base change of ``R`` to the algebraic closure ``\bar k``
 is an integral domain.
 
-```
+```jldoctest
 julia> R, (x,y) = QQ[:x,:y];
 
 julia> Q,_ = quo(R,ideal([x,y]));
 
-julia> Oscar.affine_variety(Q)
+julia> affine_variety(Q)
 Affine variety
  in Affine 2-space over QQ
 defined by ideal(x, y)
@@ -78,12 +78,12 @@ Return the affine variety defined as the vanishing locus of the multivariate pol
 
 This checks that `f` is irreducible over the algebraic closure.
 
-```
+```jldoctest
 julia> A2 = affine_space(QQ,[:x,:y]);
 
 julia> (x,y) = coordinates(A2);
 
-julia> Oscar.affine_variety(y^2-x^3-1)
+julia> affine_variety(y^2-x^3-1)
 Affine variety
  in Affine 2-space over QQ
 defined by ideal(-x^3 + y^2 - 1)

src/AlgebraicGeometry/Schemes/ProjectiveAlgebraicSet/Objects/Constructors.jl

@@ -9,15 +9,15 @@ Convert `X` to an `ProjectiveAlgebraicSet` by taking the underlying reduced sche
 
 If `check=false`, assumes that `X` is already reduced.
 
-```
+```jldoctest
 julia> P,(x0,x1,x2) = graded_polynomial_ring(QQ,[:x0,:x1,:x2]);
 
 julia> X = projective_scheme(ideal([x0*x1^2, x2]))
 Projective scheme
   over Rational field
   defined by ideal(x0*x1^2, x2)
 
-julia> Y = Oscar.projective_algebraic_set(X)
+julia> Y = projective_algebraic_set(X)
 Vanishing locus
   in Projective 2-space over QQ
   of ideal(x2, x0*x1)
@@ -43,10 +43,10 @@ in projective space.
 This computes the radical of ``I`` if `check=true`.
 Otherwise Oscar takes on faith that ``I`` is radical.
 
-```
+```jldoctest
 julia> P,(x0,x1) = graded_polynomial_ring(QQ,[:x0,:x1]);
 
-julia> Oscar.vanishing_locus(ideal([x0,x1]))
+julia> vanishing_locus(ideal([x0,x1]))
 Vanishing locus
   in Projective 1-space over QQ
   of ideal(x1, x0)
@@ -112,20 +112,20 @@ Return the irreducible components of ``X`` defined over the base field of ``X``.
 
 Note that even if ``X`` is irreducible, there may be several geometrically irreducible components.
 
-```
+```jldoctest
 julia> P1 = projective_space(QQ,1)
 Projective space of dimension 1
   with homogeneous coordinates s0 s1
   over Rational field
 
 julia> (s0,s1) = homogeneous_coordinates(P1);
 
-julia> X = Oscar.vanishing_locus((s0^2+s1^2)*s1)
+julia> X = vanishing_locus((s0^2+s1^2)*s1)
 Vanishing locus
   in Projective 1-space over QQ
   of ideal(s0^2*s1 + s1^3)
 
-julia> (X1,X2) = Oscar.irreducible_components(X)
+julia> (X1,X2) = irreducible_components(X)
 2-element Vector{ProjectiveAlgebraicSet{QQField, MPolyQuoRing{MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}}}}:
  Vanishing locus in IP^1 of ideal(s0^2 + s1^2)
  Vanishing locus in IP^1 of ideal(s1)

src/AlgebraicGeometry/Schemes/ProjectiveVariety/Objects/Constructors.jl

@@ -31,23 +31,23 @@ we check that ``I`` stays prime when viewed over the algebraic closure.
 This is an expensive check that can be disabled.
 Note that the ideal ``I`` must live in a standard graded ring.
 
-```
+```jldoctest
 julia> P3 = projective_space(QQ,3)
 Projective space of dimension 3
   with homogeneous coordinates s0 s1 s2 s3
   over Rational field
 
 julia> (s0,s1,s2,s3) = homogeneous_coordinates(P3);
 
-julia> X = Oscar.projective_variety(s0^3 + s1^3 + s2^3 + s3^3)
+julia> X = projective_variety(s0^3 + s1^3 + s2^3 + s3^3)
 Projective variety
   in Projective 3-space over QQ
   defined by ideal(s0^3 + s1^3 + s2^3 + s3^3)
 
 julia> dim(X)
 2
 
-julia> Y = Oscar.projective_variety(ideal([s0^3 + s1^3 + s2^3 + s3^3, s0]))
+julia> Y = projective_variety(ideal([s0^3 + s1^3 + s2^3 + s3^3, s0]))
 Projective variety
   in Projective 3-space over QQ
   defined by ideal(s0^3 + s1^3 + s2^3 + s3^3, s0)

src/exports.jl

@@ -25,14 +25,14 @@ export AbsProjectiveVariety
 export AbsSpec
 export AbsSpecMor
 export AbstractAlgebra
-#export AffineAlgebraicSet
+export AffineAlgebraicSet
 export AffineHalfspace
 export AffineHyperplane
 export AffineNormalToricVariety
-#export AffineVariety
+export AffineVariety
 export affine_normal_toric_variety
-#export affine_variety
-#export affine_algebraic_set
+export affine_variety
+export affine_algebraic_set
 export AutomorphismGroup
 export AutomorphismGroupElem
 export BorcherdsCtx
@@ -138,8 +138,8 @@ export Polymake
 export PrincipalOpenSubset
 export ProjectiveScheme
 export ProjectiveSchemeMor
-#export ProjectiveVariety
-#export ProjectiveAlgebraicSet
+export ProjectiveVariety
+export ProjectiveAlgebraicSet
 export QQ
 export RationalEquivalenceClass
 export RayVector
@@ -540,7 +540,7 @@ export generic_fraction
 export generic_fractions
 export gens, has_gens
 export gens_of_rational_equivalence_classes
-#export geometric_irreducible_components
+export geometric_irreducible_components
 export girth
 export gkz_vector
 export glueing_domains
@@ -664,7 +664,7 @@ export invariant_symmetric_forms
 export inverse
 export invert
 export inverted_set
-#export irreducible_components
+export irreducible_components
 export irreducible_secondary_invariants
 export irreducibles
 export irrelevant_ideal
@@ -1108,8 +1108,8 @@ export projective_special_orthogonal_group
 export projective_special_unitary_group
 export projective_symplectic_group
 export projective_unitary_group
-#export projective_variety
-#export projective_algebraic_set
+export projective_variety
+export projective_algebraic_set
 export pullback
 export pullback_type
 export pyramid
@@ -1214,7 +1214,7 @@ export set_name!
 export set_power!
 export set_relative_order!
 export set_relative_orders!
-#export set_theoretic_intersection
+export set_theoretic_intersection
 export sets
 export short_right_transversal
 export shortest_path_dijkstra
@@ -1342,7 +1342,7 @@ export valuation_of_roots
 export valued_weighted_degree
 export vamos_matroid
 export vanishing_sets
-#export vanishing_locus
+export vanishing_locus
 export vanishing_ideal
 export vdim
 export vector_matrix

test/AlgebraicGeometry/Schemes/runtests.jl

@@ -1,8 +1,8 @@
 using Test
 
 include("AffineSchemes.jl")
-#include("AffineVariety.jl")
-#include("AffineAlgebraicSet.jl")
+include("AffineVariety.jl")
+include("AffineAlgebraicSet.jl")
 include("CartierDivisor.jl")
 include("CoveredProjectiveSchemes.jl")
 include("CoveredScheme.jl")
@@ -11,9 +11,9 @@ include("FunctionFields.jl")
 include("Glueing.jl")
 include("IdealSheaves.jl")
 include("K3.jl")
-#include("ProjectiveAlgebraicSet.jl")
+include("ProjectiveAlgebraicSet.jl")
 include("ProjectiveSchemes.jl")
-#include("ProjectiveVarieties.jl")
+include("ProjectiveVarieties.jl")
 include("Sheaves.jl")
 include("SpaceGerms.jl")
 include("SpecOpen.jl")