sagemathgh-36673: capitals to Hopf, Lie, Coxeter by appropriate mecha…

…nism

    
This is adding a proper mechanism to have capitalized proper names in
category names.

This is applied here to Coxeter, Lie and Hopf. Also Hecke and Weyl.

The important changes are in `src/sage/categories/category.py`

### 📝 Checklist

- [x] The title is concise, informative, and self-explanatory.
- [x] The description explains in detail what this PR is about.
- [x] I have updated the documentation accordingly.
    
URL: sagemath#36673
Reported by: Frédéric Chapoton
Reviewer(s): Kwankyu Lee

src/sage/algebras/clifford_algebra.py

@@ -1370,7 +1370,7 @@ def __init__(self, R, names):
             sage: E.<x,y,z> = ExteriorAlgebra(QQ)
             sage: E.category()
             Category of finite dimensional supercommutative supercocommutative
-             super hopf algebras with basis over Rational Field
+             super Hopf algebras with basis over Rational Field
             sage: TestSuite(E).run()
 
             sage: TestSuite(ExteriorAlgebra(GF(3), ['a', 'b'])).run()

src/sage/algebras/lie_algebras/free_lie_algebra.py

@@ -933,7 +933,7 @@ def super_categories(self):
             sage: L.<x, y> = LieAlgebra(QQ)
             sage: bases = FreeLieAlgebraBases(L)
             sage: bases.super_categories()
-            [Category of lie algebras with basis over Rational Field,
+            [Category of Lie algebras with basis over Rational Field,
              Category of realizations of Free Lie algebra generated by (x, y) over Rational Field]
         """
         return [LieAlgebras(self.base().base_ring()).WithBasis(), Realizations(self.base())]

src/sage/algebras/lie_algebras/lie_algebra.py

@@ -322,7 +322,7 @@ class LieAlgebra(Parent, UniqueRepresentation):  # IndexedGenerators):
         sage: L
         Nilpotent Lie algebra on 3 generators (X, Y, Z) over Rational Field
         sage: L.category()
-        Category of finite dimensional nilpotent lie algebras with basis over Rational Field
+        Category of finite dimensional nilpotent Lie algebras with basis over Rational Field
 
     A second example defining the Engel Lie algebra::
 
@@ -530,7 +530,7 @@ def __init__(self, R, names=None, category=None):
 
             sage: L.<x,y> = LieAlgebra(QQ, abelian=True)
             sage: L.category()
-            Category of finite dimensional nilpotent lie algebras with basis over Rational Field
+            Category of finite dimensional nilpotent Lie algebras with basis over Rational Field
         """
         category = LieAlgebras(R).or_subcategory(category)
         Parent.__init__(self, base=R, names=names, category=category)
@@ -805,7 +805,7 @@ def __init__(self, R, names=None, index_set=None, category=None, prefix='L', **k
 
             sage: L.<x,y> = LieAlgebra(QQ, abelian=True)
             sage: L.category()
-            Category of finite dimensional nilpotent lie algebras with basis over Rational Field
+            Category of finite dimensional nilpotent Lie algebras with basis over Rational Field
         """
         self._indices = index_set
         LieAlgebra.__init__(self, R, names, category)
@@ -890,7 +890,7 @@ def __init__(self, R, names=None, index_set=None, category=None):
 
             sage: L.<x,y> = LieAlgebra(QQ, abelian=True)
             sage: L.category()
-            Category of finite dimensional nilpotent lie algebras with basis over Rational Field
+            Category of finite dimensional nilpotent Lie algebras with basis over Rational Field
         """
         LieAlgebraWithGenerators.__init__(self, R, names, index_set, category)
         self.__ngens = len(self._indices)

src/sage/algebras/lie_algebras/morphism.py

@@ -43,7 +43,7 @@ class LieAlgebraHomomorphism_im_gens(Morphism):
       It should be a map from the base ring of the domain to the
       base ring of the codomain.
       Note that if base_map is nontrivial then the result will
-      not be a morphism in the category of lie algebras over
+      not be a morphism in the category of Lie algebras over
       the base ring.
     - ``check`` -- whether to run checks on the validity of the defining data
 
@@ -380,7 +380,7 @@ class LieAlgebraMorphism_from_generators(LieAlgebraHomomorphism_im_gens):
       It should be a map from the base ring of the domain to the
       base ring of the codomain.
       Note that if base_map is nontrivial then the result will
-      not be a morphism in the category of lie algebras over
+      not be a morphism in the category of Lie algebras over
       the base ring.
     - ``check`` -- (default: ``True``) boolean; if ``False`` the
       values  on the Lie brackets implied by ``on_generators`` will

src/sage/algebras/lie_algebras/nilpotent_lie_algebra.py

@@ -243,7 +243,7 @@ class FreeNilpotentLieAlgebra(NilpotentLieAlgebra_dense):
 
         sage: L = LieAlgebra(QQ, 3, step=3)
         sage: L.category()
-        Category of finite dimensional stratified lie algebras with basis over Rational Field
+        Category of finite dimensional stratified Lie algebras with basis over Rational Field
         sage: L in LieAlgebras(QQ).Nilpotent()
         True
 

src/sage/algebras/lie_algebras/quotient.py

@@ -51,7 +51,7 @@ class LieQuotient_finite_dimensional_with_basis(LieAlgebraWithStructureCoefficie
         L: Free Nilpotent Lie algebra on 5 generators (X_1, X_2, X_12, X_112, X_122) over Rational Field
         I: Ideal (X_122)
         sage: E.category()
-        Join of Category of finite dimensional nilpotent lie algebras with basis
+        Join of Category of finite dimensional nilpotent Lie algebras with basis
         over Rational Field and Category of subquotients of sets
         sage: E.basis().list()
         [X_1, X_2, X_12, X_112]

src/sage/algebras/steenrod/steenrod_algebra.py

@@ -556,7 +556,7 @@ def __init__(self, p=2, basis='milnor', **kwds):
             sage: TestSuite(SteenrodAlgebra(basis='woody')).run()   # long time
             sage: A3 = SteenrodAlgebra(3)
             sage: A3.category()
-            Category of supercocommutative super hopf algebras
+            Category of supercocommutative super Hopf algebras
              with basis over Finite Field of size 3
             sage: TestSuite(A3).run()  # long time
             sage: TestSuite(SteenrodAlgebra(basis='adem', p=3)).run()
@@ -3842,7 +3842,7 @@ def SteenrodAlgebra(p=2, basis='milnor', generic='auto', **kwds):
         sage: A.is_division_algebra()
         False
         sage: A.category()
-        Category of supercocommutative super hopf algebras
+        Category of supercocommutative super Hopf algebras
          with basis over Finite Field of size 2
 
     There are methods for constructing elements of the Steenrod

src/sage/categories/category.py

@@ -119,6 +119,9 @@
 _join_cache = WeakValueDictionary()
 
 
+HALL_OF_FAME = ['Coxeter', 'Hopf', 'Weyl', 'Lie', 'Hecke']
+
+
 class Category(UniqueRepresentation, SageObject):
     r"""
     The base class for modeling mathematical categories, like for example:
@@ -513,14 +516,10 @@ def _repr_object_names(self):
             sage: PrincipalIdealDomains()._repr_object_names()
             'principal ideal domains'
         """
-        i = -1
-        s = self._label
-        while i < len(s) - 1:
-            for i in range(len(s)):
-                if s[i].isupper():
-                    s = s[:i] + " " + s[i].lower() + s[i + 1:]
-                    break
-        return s.lstrip()
+        words = "".join(letter if not letter.isupper() else ";" + letter
+                        for letter in self._label).split(";")
+        return " ".join(w if w in HALL_OF_FAME else w.lower()
+                        for w in words).lstrip()
 
     def _short_name(self):
         """
@@ -1235,7 +1234,7 @@ def structure(self):
              Category of right modules over Rational Field,
              Category of left modules over Rational Field)
             sage: structure(HopfAlgebras(QQ).Graded().WithBasis().Connected())
-            (Category of hopf algebras over Rational Field,
+            (Category of Hopf algebras over Rational Field,
              Category of graded modules over Rational Field)
 
         This method is used in :meth:`is_full_subcategory` for
@@ -2018,7 +2017,7 @@ def _with_axiom_as_tuple(self, axiom):
              Category of commutative magmas,
              Category of finite additive groups)
             sage: HopfAlgebras(QQ)._with_axiom_as_tuple('FiniteDimensional')
-            (Category of hopf algebras over Rational Field,
+            (Category of Hopf algebras over Rational Field,
              Category of finite dimensional vector spaces over Rational Field)
         """
         if axiom in self.axioms():
@@ -2595,11 +2594,13 @@ def category_sample():
         [Category of Coxeter groups,
          Category of G-sets for Symmetric group of order 8! as a permutation group,
          Category of Hecke modules over Rational Field,
+         Category of Hopf algebras over Rational Field,
+         Category of Hopf algebras with basis over Rational Field,
          Category of Lie algebras over Rational Field,
          Category of Weyl groups,
          Category of additive magmas, ...,
          Category of fields, ...,
-         Category of graded hopf algebras with basis over Rational Field, ...,
+         Category of graded Hopf algebras with basis over Rational Field, ...,
          Category of modular abelian varieties over Rational Field, ...,
          Category of simplicial complexes, ...,
          Category of vector spaces over Rational Field, ...

src/sage/categories/complex_reflection_groups.py

@@ -45,10 +45,10 @@ class ComplexReflectionGroups(Category_singleton):
         sage: ComplexReflectionGroups()
         Category of complex reflection groups
         sage: ComplexReflectionGroups().super_categories()
-        [Category of complex reflection or generalized coxeter groups]
+        [Category of complex reflection or generalized Coxeter groups]
         sage: ComplexReflectionGroups().all_super_categories()
         [Category of complex reflection groups,
-         Category of complex reflection or generalized coxeter groups,
+         Category of complex reflection or generalized Coxeter groups,
          Category of groups,
          Category of monoids,
          Category of finitely generated semigroups,
@@ -87,7 +87,7 @@ def super_categories(self):
 
             sage: from sage.categories.complex_reflection_groups import ComplexReflectionGroups
             sage: ComplexReflectionGroups().super_categories()
-            [Category of complex reflection or generalized coxeter groups]
+            [Category of complex reflection or generalized Coxeter groups]
         """
         return [ComplexReflectionOrGeneralizedCoxeterGroups()]
 

src/sage/categories/complex_reflection_or_generalized_coxeter_groups.py

@@ -82,7 +82,7 @@ class ComplexReflectionOrGeneralizedCoxeterGroups(Category_singleton):
 
         sage: from sage.categories.complex_reflection_or_generalized_coxeter_groups import ComplexReflectionOrGeneralizedCoxeterGroups
         sage: C = ComplexReflectionOrGeneralizedCoxeterGroups(); C
-        Category of complex reflection or generalized coxeter groups
+        Category of complex reflection or generalized Coxeter groups
         sage: C.super_categories()
         [Category of finitely generated enumerated groups]
 
@@ -108,7 +108,7 @@ def super_categories(self):
 
             sage: from sage.categories.complex_reflection_groups import ComplexReflectionGroups
             sage: ComplexReflectionGroups().super_categories()
-            [Category of complex reflection or generalized coxeter groups]
+            [Category of complex reflection or generalized Coxeter groups]
         """
         return [Groups().FinitelyGenerated()]
 
@@ -117,7 +117,7 @@ def Irreducible(self):
             r"""
             Return the full subcategory of irreducible objects of ``self``.
 
-            A complex reflection group, or generalized coxeter group
+            A complex reflection group, or generalized Coxeter group
             is *reducible* if its simple reflections can be split in
             two sets `X` and `Y` such that the elements of `X` commute
             with that of `Y`. In particular, the group is then direct

src/sage/categories/coxeter_groups.py

@@ -43,7 +43,7 @@ class CoxeterGroups(Category_singleton):
         sage: C = CoxeterGroups(); C
         Category of Coxeter groups
         sage: C.super_categories()
-        [Category of generalized coxeter groups]
+        [Category of generalized Coxeter groups]
 
         sage: W = C.example(); W
         The symmetric group on {0, ..., 3}
@@ -105,7 +105,7 @@ def super_categories(self):
         EXAMPLES::
 
             sage: CoxeterGroups().super_categories()
-            [Category of generalized coxeter groups]
+            [Category of generalized Coxeter groups]
         """
         return [GeneralizedCoxeterGroups()]
 
@@ -128,17 +128,6 @@ def additional_structure(self):
     Finite = LazyImport('sage.categories.finite_coxeter_groups', 'FiniteCoxeterGroups')
     Algebras = LazyImport('sage.categories.coxeter_group_algebras', 'CoxeterGroupAlgebras')
 
-    def _repr_object_names(self):
-        """
-        Return the name of the objects of this category.
-
-        EXAMPLES::
-
-            sage: CoxeterGroups().Finite()
-            Category of finite Coxeter groups
-        """
-        return "Coxeter groups"
-
     class ParentMethods:
         @abstract_method
         def coxeter_matrix(self):

src/sage/categories/examples/hopf_algebras_with_basis.py

@@ -29,7 +29,7 @@ def __init__(self, R, G):
             sage: from sage.categories.examples.hopf_algebras_with_basis import MyGroupAlgebra
             sage: A = MyGroupAlgebra(QQ, DihedralGroup(6))
             sage: A.category()
-            Category of finite dimensional hopf algebras with basis over Rational Field
+            Category of finite dimensional Hopf algebras with basis over Rational Field
             sage: TestSuite(A).run()
         """
         self._group = G

src/sage/categories/filtered_hopf_algebras_with_basis.py

@@ -31,9 +31,9 @@ class FilteredHopfAlgebrasWithBasis(FilteredModulesCategory):
     EXAMPLES::
 
         sage: C = HopfAlgebrasWithBasis(ZZ).Filtered(); C
-        Category of filtered hopf algebras with basis over Integer Ring
+        Category of filtered Hopf algebras with basis over Integer Ring
         sage: C.super_categories()
-        [Category of hopf algebras with basis over Integer Ring,
+        [Category of Hopf algebras with basis over Integer Ring,
          Category of filtered algebras with basis over Integer Ring,
          Category of filtered coalgebras with basis over Integer Ring]
 
@@ -53,7 +53,7 @@ def super_categories(self):
             EXAMPLES::
 
                 sage: HopfAlgebrasWithBasis(QQ).Filtered().WithRealizations().super_categories()
-                [Join of Category of hopf algebras over Rational Field
+                [Join of Category of Hopf algebras over Rational Field
                      and Category of filtered algebras over Rational Field
                      and Category of filtered coalgebras over Rational Field]
 

src/sage/categories/finite_coxeter_groups.py

@@ -27,7 +27,7 @@ class FiniteCoxeterGroups(CategoryWithAxiom):
         sage: CoxeterGroups.Finite()
         Category of finite Coxeter groups
         sage: FiniteCoxeterGroups().super_categories()
-        [Category of finite generalized coxeter groups,
+        [Category of finite generalized Coxeter groups,
          Category of Coxeter groups]
 
         sage: G = CoxeterGroups().Finite().example()
@@ -54,7 +54,7 @@ def extra_super_categories(self):
         EXAMPLES::
 
             sage: CoxeterGroups().Finite().super_categories()
-            [Category of finite generalized coxeter groups,
+            [Category of finite generalized Coxeter groups,
              Category of Coxeter groups]
         """
         from sage.categories.complex_reflection_groups import ComplexReflectionGroups

src/sage/categories/finite_dimensional_graded_lie_algebras_with_basis.py

@@ -29,10 +29,10 @@ class FiniteDimensionalGradedLieAlgebrasWithBasis(CategoryWithAxiom_over_base_ri
     EXAMPLES::
 
         sage: C = LieAlgebras(ZZ).WithBasis().FiniteDimensional().Graded(); C
-        Category of finite dimensional graded lie algebras with basis over Integer Ring
+        Category of finite dimensional graded Lie algebras with basis over Integer Ring
         sage: C.super_categories()
-        [Category of graded lie algebras with basis over Integer Ring,
-         Category of finite dimensional lie algebras with basis over Integer Ring]
+        [Category of graded Lie algebras with basis over Integer Ring,
+         Category of finite dimensional Lie algebras with basis over Integer Ring]
 
         sage: C is LieAlgebras(ZZ).WithBasis().FiniteDimensional().Graded()
         True
@@ -120,7 +120,7 @@ class Stratified(CategoryWithAxiom_over_base_ring):
 
             sage: C = LieAlgebras(QQ).WithBasis().Graded().Stratified().FiniteDimensional()
             sage: C
-            Category of finite dimensional stratified lie algebras with basis over Rational Field
+            Category of finite dimensional stratified Lie algebras with basis over Rational Field
 
         A finite-dimensional stratified Lie algebra is nilpotent::
 

src/sage/categories/finite_dimensional_hopf_algebras_with_basis.py

@@ -1,27 +1,28 @@
 r"""
 Finite dimensional Hopf algebras with basis
 """
-#*****************************************************************************
+# ****************************************************************************
 #  Copyright (C) 2008 Teresa Gomez-Diaz (CNRS) <Teresa.Gomez-Diaz@univ-mlv.fr>
 #                2011 Nicolas M. Thiery <nthiery at users.sf.net>
 #
 #  Distributed under the terms of the GNU General Public License (GPL)
-#                  http://www.gnu.org/licenses/
-#******************************************************************************
+#                  https://www.gnu.org/licenses/
+# *****************************************************************************
 
 from sage.categories.category_with_axiom import CategoryWithAxiom_over_base_ring
 
+
 class FiniteDimensionalHopfAlgebrasWithBasis(CategoryWithAxiom_over_base_ring):
     """
     The category of finite dimensional Hopf algebras with a
     distinguished basis.
 
     EXAMPLES::
 
-        sage: FiniteDimensionalHopfAlgebrasWithBasis(QQ) # fixme: Hopf should be capitalized
-        Category of finite dimensional hopf algebras with basis over Rational Field
+        sage: FiniteDimensionalHopfAlgebrasWithBasis(QQ)
+        Category of finite dimensional Hopf algebras with basis over Rational Field
         sage: FiniteDimensionalHopfAlgebrasWithBasis(QQ).super_categories()
-        [Category of hopf algebras with basis over Rational Field,
+        [Category of Hopf algebras with basis over Rational Field,
          Category of finite dimensional algebras with basis over Rational Field]
 
     TESTS::

src/sage/categories/finitely_generated_lambda_bracket_algebras.py

@@ -95,7 +95,7 @@ class Graded(GradedModulesCategory):
         EXAMPLES::
 
             sage: LieConformalAlgebras(QQbar).FinitelyGenerated().Graded()              # needs sage.rings.number_field
-            Category of H-graded finitely generated lie conformal algebras
+            Category of H-graded finitely generated Lie conformal algebras
              over Algebraic Field
         """
         def _repr_object_names(self):