gh-35012: Issue #34949: sage.{categories,matrix,structure}: Replace i…

…mports from sage.*.all for namespace packages

    
Closes #34949
    
URL: #35012
Reported by: Matthias Köppe
Reviewer(s): Tobias Diez

src/sage/arith/long.pxd

@@ -1,3 +1,4 @@
+# sage.doctest: optional - sage.misc.cython
 r"""
 Fast conversion of Python objects to C long
 """
@@ -113,7 +114,7 @@ cdef inline bint integer_check_long(x, long* value, int* err) except -1:
 
     We create a pure Python wrapper of this function::
 
-        sage: cython('''  # optional - sage.misc.cython
+        sage: cython('''
         ....: from sage.arith.long cimport *
         ....: from sage.rings.integer cimport smallInteger
         ....: def check_long(x):
@@ -246,7 +247,7 @@ cdef inline bint integer_check_long_py(x, long* value, int* err):
 
     We create a pure Python wrapper of this function::
 
-        sage: cython('''  # optional - sage.misc.cython
+        sage: cython('''
         ....: from sage.arith.long cimport *
         ....: def check_long_py(x):
         ....:     cdef long value
@@ -387,7 +388,7 @@ cdef inline bint is_small_python_int(obj):
 
     EXAMPLES::
 
-        sage: cython('''  # optional - sage.misc.cython
+        sage: cython('''
         ....: from sage.arith.long cimport is_small_python_int
         ....: def is_small_wrapper(x):
         ....:     return is_small_python_int(x)

src/sage/categories/bialgebras.py

@@ -10,7 +10,8 @@
 # *****************************************************************************
 
 from sage.categories.category_types import Category_over_base_ring
-from sage.categories.all import Algebras, Coalgebras
+from sage.categories.algebras import Algebras
+from sage.categories.coalgebras import Coalgebras
 from sage.categories.super_modules import SuperModulesCategory
 from sage.misc.lazy_import import LazyImport
 

src/sage/categories/category.py

@@ -153,7 +153,7 @@ class Category(UniqueRepresentation, SageObject):
 
     This is achieved as follows::
 
-        sage: from sage.categories.all import Category
+        sage: from sage.categories.category import Category
         sage: class EuclideanDomains(Category):
         ....:     # operations on the category itself
         ....:     def super_categories(self):
@@ -201,7 +201,7 @@ class inheritance from ``C.parent_class``.
 
     ::
 
-        sage: from sage.categories.all import Category
+        sage: from sage.categories.category import Category
         sage: from sage.misc.lazy_attribute import lazy_attribute
         sage: class As (Category):
         ....:     def super_categories(self):

src/sage/categories/chain_complexes.py

@@ -46,7 +46,9 @@ def super_categories(self):
             [Category of modules over Ring of integers modulo 9]
 
         """
-        from sage.categories.all import Fields, Modules, VectorSpaces
+        from sage.categories.fields import Fields
+        from sage.categories.modules import Modules
+        from sage.categories.vector_spaces import VectorSpaces
         base_ring = self.base_ring()
         if base_ring in Fields():
             return [VectorSpaces(base_ring)]

src/sage/categories/coalgebras.py

@@ -10,7 +10,7 @@
 # *****************************************************************************
 
 from .category_types import Category_over_base_ring
-from sage.categories.all import Modules
+from sage.categories.modules import Modules
 from sage.categories.category_with_axiom import CategoryWithAxiom_over_base_ring
 from sage.categories.tensor import TensorProductsCategory
 from sage.categories.dual import DualObjectsCategory

src/sage/categories/coalgebras_with_basis.py

@@ -13,7 +13,9 @@
 from sage.misc.lazy_attribute import lazy_attribute
 from sage.misc.lazy_import import LazyImport
 from sage.categories.category_with_axiom import CategoryWithAxiom_over_base_ring
-from sage.categories.all import ModulesWithBasis, tensor, Hom
+from sage.categories.modules_with_basis import ModulesWithBasis
+from sage.categories.tensor import tensor
+from sage.categories.homset import Hom
 from sage.categories.super_modules import SuperModulesCategory
 from sage.categories.filtered_modules import FilteredModulesCategory
 

src/sage/categories/examples/algebras_with_basis.py

@@ -10,7 +10,7 @@
 
 from sage.misc.cachefunc import cached_method
 from sage.sets.family import Family
-from sage.categories.all import AlgebrasWithBasis
+from sage.categories.algebras_with_basis import AlgebrasWithBasis
 from sage.combinat.free_module import CombinatorialFreeModule
 from sage.combinat.words.words import Words
 

src/sage/categories/examples/commutative_additive_monoids.py

@@ -10,7 +10,7 @@
 
 from sage.misc.cachefunc import cached_method
 from sage.structure.parent import Parent
-from sage.categories.all import CommutativeAdditiveMonoids
+from sage.categories.commutative_additive_monoids import CommutativeAdditiveMonoids
 from .commutative_additive_semigroups import FreeCommutativeAdditiveSemigroup
 
 class FreeCommutativeAdditiveMonoid(FreeCommutativeAdditiveSemigroup):

src/sage/categories/examples/commutative_additive_semigroups.py

@@ -12,7 +12,7 @@
 from sage.structure.parent import Parent
 from sage.structure.element_wrapper import ElementWrapper
 from sage.structure.unique_representation import UniqueRepresentation
-from sage.categories.all import CommutativeAdditiveSemigroups
+from sage.categories.commutative_additive_semigroups import CommutativeAdditiveSemigroups
 from sage.sets.family import Family
 
 class FreeCommutativeAdditiveSemigroup(UniqueRepresentation, Parent):

src/sage/categories/examples/finite_coxeter_groups.py

@@ -11,7 +11,7 @@
 from sage.misc.cachefunc import cached_method
 from sage.structure.parent import Parent
 from sage.structure.element_wrapper import ElementWrapper
-from sage.categories.all import FiniteCoxeterGroups
+from sage.categories.finite_coxeter_groups import FiniteCoxeterGroups
 from sage.structure.unique_representation import UniqueRepresentation
 from sage.misc.functional import is_odd, is_even
 from sage.combinat.root_system.coxeter_matrix import CoxeterMatrix

src/sage/categories/examples/finite_dimensional_algebras_with_basis.py

@@ -9,7 +9,7 @@
 #*****************************************************************************
 
 from sage.misc.cachefunc import cached_method
-from sage.categories.all import FiniteDimensionalAlgebrasWithBasis
+from sage.categories.finite_dimensional_algebras_with_basis import FiniteDimensionalAlgebrasWithBasis
 from sage.combinat.free_module import CombinatorialFreeModule
 
 

src/sage/categories/examples/finite_dimensional_lie_algebras_with_basis.py

@@ -10,7 +10,7 @@
 
 from sage.misc.cachefunc import cached_method
 from sage.sets.family import Family
-from sage.categories.all import LieAlgebras
+from sage.categories.lie_algebras import LieAlgebras
 from sage.modules.free_module import FreeModule
 from sage.structure.parent import Parent
 from sage.structure.unique_representation import UniqueRepresentation

src/sage/categories/examples/finite_monoids.py

@@ -13,7 +13,7 @@
 from sage.structure.parent import Parent
 from sage.structure.unique_representation import UniqueRepresentation
 from sage.structure.element_wrapper import ElementWrapper
-from sage.categories.all import Monoids
+from sage.categories.monoids import Monoids
 from sage.rings.integer import Integer
 from sage.rings.integer_ring import ZZ
 

src/sage/categories/examples/finite_weyl_groups.py

@@ -11,7 +11,7 @@
 from sage.misc.cachefunc import cached_method
 from sage.structure.parent import Parent
 from sage.structure.element_wrapper import ElementWrapper
-from sage.categories.all import FiniteWeylGroups
+from sage.categories.finite_weyl_groups import FiniteWeylGroups
 from sage.structure.unique_representation import UniqueRepresentation
 
 class SymmetricGroup(UniqueRepresentation, Parent):

src/sage/categories/examples/hopf_algebras_with_basis.py

@@ -10,9 +10,9 @@
 
 from sage.misc.cachefunc import cached_method
 from sage.sets.family import Family
-from sage.categories.all import HopfAlgebrasWithBasis
+from sage.categories.hopf_algebras_with_basis import HopfAlgebrasWithBasis
 from sage.combinat.free_module import CombinatorialFreeModule
-from sage.categories.all import tensor
+from sage.categories.tensor import tensor
 
 class MyGroupAlgebra(CombinatorialFreeModule):
     r"""

src/sage/categories/examples/lie_algebras.py

@@ -10,7 +10,7 @@
 
 #from sage.misc.cachefunc import cached_method
 from sage.sets.family import Family
-from sage.categories.all import LieAlgebras
+from sage.categories.lie_algebras import LieAlgebras
 from sage.structure.parent import Parent
 from sage.structure.unique_representation import UniqueRepresentation
 from sage.structure.element_wrapper import ElementWrapper

src/sage/categories/examples/magmas.py

@@ -15,7 +15,7 @@
 from sage.structure.parent import Parent
 from sage.structure.unique_representation import UniqueRepresentation
 from sage.structure.element_wrapper import ElementWrapper
-from sage.categories.all import Magmas
+from sage.categories.magmas import Magmas
 from sage.sets.family import Family
 
 

src/sage/categories/examples/monoids.py

@@ -11,7 +11,7 @@
 from sage.misc.cachefunc import cached_method
 from sage.structure.parent import Parent
 from sage.structure.element_wrapper import ElementWrapper
-from sage.categories.all import Monoids
+from sage.categories.monoids import Monoids
 from .semigroups import FreeSemigroup
 from sage.sets.family import Family
 

src/sage/categories/examples/posets.py

@@ -10,7 +10,7 @@
 
 from sage.structure.parent import Parent
 from sage.structure.unique_representation import UniqueRepresentation
-from sage.categories.all import Posets
+from sage.categories.posets import Posets
 from sage.structure.element_wrapper import ElementWrapper
 from sage.sets.set import Set, Set_object_enumerated
 from sage.sets.positive_integers import PositiveIntegers

src/sage/categories/examples/semigroups.py

@@ -12,7 +12,7 @@
 from sage.structure.parent import Parent
 from sage.structure.unique_representation import UniqueRepresentation
 from sage.structure.element_wrapper import ElementWrapper
-from sage.categories.all import Semigroups
+from sage.categories.semigroups import Semigroups
 from sage.sets.family import Family
 
 class LeftZeroSemigroup(UniqueRepresentation, Parent):

src/sage/categories/examples/semigroups_cython.pyx

@@ -4,7 +4,8 @@ Examples of semigroups in cython
 
 from sage.structure.parent cimport Parent
 from sage.structure.element cimport Element
-from sage.categories.all import Category, Semigroups
+from sage.categories.category import Category
+from sage.categories.semigroups import Semigroups
 from sage.categories.examples.semigroups import LeftZeroSemigroup as LeftZeroSemigroupPython
 from cpython.object cimport PyObject_RichCompare
 

src/sage/categories/examples/sets_cat.py

@@ -13,7 +13,7 @@
 from sage.categories.sets_cat import Sets
 from sage.rings.integer import Integer, IntegerWrapper
 from sage.rings.integer_ring import IntegerRing
-from sage.arith.all import is_prime
+from sage.arith.misc import is_prime
 from sage.structure.unique_representation import UniqueRepresentation
 
 

src/sage/categories/examples/with_realizations.py

@@ -10,7 +10,9 @@
 
 from sage.misc.cachefunc import cached_method
 from sage.misc.bindable_class import BindableClass
-from sage.categories.all import Rings, Algebras, AlgebrasWithBasis
+from sage.categories.rings import Rings
+from sage.categories.algebras import Algebras
+from sage.categories.algebras_with_basis import AlgebrasWithBasis
 from sage.categories.realizations import Category_realization_of_parent
 from sage.structure.unique_representation import UniqueRepresentation
 from sage.structure.parent import Parent

src/sage/categories/finite_complex_reflection_groups.py

@@ -523,7 +523,7 @@ def base_change_matrix(self):
                 [   1    0]
                 [E(4)    1]
             """
-            from sage.matrix.all import Matrix
+            from sage.matrix.constructor import Matrix
             return Matrix(list(self.independent_roots())).inverse()
 
     class ElementMethods:
@@ -1187,7 +1187,7 @@ def rational_catalan_number(self, p, polynomial=False):
                         sage: W.rational_catalan_number(3, polynomial=True)
                         q^6 + q^4 + q^3 + q^2 + 1
                     """
-                    from sage.arith.all import gcd
+                    from sage.arith.misc import GCD as gcd
                     from sage.combinat.q_analogues import q_int
 
                     h = self.coxeter_number()

src/sage/categories/finite_dimensional_bialgebras_with_basis.py

@@ -27,5 +27,5 @@ def FiniteDimensionalBialgebrasWithBasis(base_ring):
 
         sage: TestSuite(C).run()
     """
-    from sage.categories.all import BialgebrasWithBasis
+    from sage.categories.bialgebras_with_basis import BialgebrasWithBasis
     return BialgebrasWithBasis(base_ring).FiniteDimensional()

src/sage/categories/finite_dimensional_coalgebras_with_basis.py

@@ -27,5 +27,5 @@ def FiniteDimensionalCoalgebrasWithBasis(base_ring):
 
         sage: TestSuite(C).run()
     """
-    from sage.categories.all import CoalgebrasWithBasis
+    from sage.categories.coalgebras_with_basis import CoalgebrasWithBasis
     return CoalgebrasWithBasis(base_ring).FiniteDimensional()

src/sage/categories/graded_bialgebras.py

@@ -26,5 +26,5 @@ def GradedBialgebras(base_ring):
 
         sage: TestSuite(C).run()
     """
-    from sage.categories.all import Bialgebras
+    from sage.categories.bialgebras import Bialgebras
     return Bialgebras(base_ring).Graded()

src/sage/categories/graded_bialgebras_with_basis.py

@@ -26,5 +26,5 @@ def GradedBialgebrasWithBasis(base_ring):
 
         sage: TestSuite(C).run()
     """
-    from sage.categories.all import BialgebrasWithBasis
+    from sage.categories.bialgebras_with_basis import BialgebrasWithBasis
     return BialgebrasWithBasis(base_ring).Graded()

src/sage/categories/graded_hopf_algebras.py

@@ -35,5 +35,5 @@ def GradedHopfAlgebras(base_ring):
         :class:`super Hopf algebras
         <sage.categories.hopf_algebras.HopfAlgebras.Super>`.
     """
-    from sage.categories.all import HopfAlgebras
+    from sage.categories.hopf_algebras import HopfAlgebras
     return HopfAlgebras(base_ring).Graded()

src/sage/categories/map.pyx

@@ -1331,7 +1331,7 @@ cdef class Section(Map):
               To:   Multivariate Polynomial Ring in x, y over Rational Field
         """
         from sage.categories.homset import Hom
-        from sage.categories.all import SetsWithPartialMaps
+        from sage.categories.sets_with_partial_maps import SetsWithPartialMaps
         Map.__init__(self, Hom(map.codomain(), map.domain(), SetsWithPartialMaps()))
         self._inverse = map    # TODO: Use this attribute somewhere!
 

src/sage/categories/monoid_algebras.py

@@ -33,5 +33,5 @@ def MonoidAlgebras(base_ring):
 
         sage: TestSuite(MonoidAlgebras(ZZ)).run()
     """
-    from sage.categories.all import Monoids
+    from sage.categories.monoids import Monoids
     return Monoids().Algebras(base_ring)

src/sage/categories/schemes.py

@@ -140,7 +140,7 @@ def _call_(self, x):
         from sage.categories.commutative_rings import CommutativeRings
         from sage.schemes.generic.spec import Spec
         from sage.categories.map import Map
-        from sage.categories.all import Rings
+        from sage.categories.rings import Rings
         if x in CommutativeRings():
             return Spec(x)
         elif isinstance(x, Map) and x.category_for().is_subcategory(Rings()):

src/sage/cpython/cython_metaclass.pyx

@@ -61,7 +61,8 @@ In Python, this would be ``meta.__init__(cls, name, bases, dict)``.
 
 EXAMPLES::
 
-    sage: cython('''  # optional - sage.misc.cython
+    sage: cython(                                                               # optional - sage.misc.cython
+    ....: '''
     ....: cimport sage.cpython.cython_metaclass
     ....: cdef class MyCustomType():
     ....:     def __getmetaclass__(_):
@@ -75,9 +76,9 @@ EXAMPLES::
     ....: ''')
     Calling MyMetaclass.__init__(<class '...MyCustomType'>, None, None, None)
     Calling MyMetaclass.__init__(<class '...MyDerivedType'>, None, None, None)
-    sage: MyCustomType.__class__
+    sage: MyCustomType.__class__                                                # optional - sage.misc.cython
     <class '...MyMetaclass'>
-    sage: class MyPythonType(MyDerivedType):
+    sage: class MyPythonType(MyDerivedType):                                    # optional - sage.misc.cython
     ....:     pass
     Calling MyMetaclass.__init__(<class '...MyPythonType'>, 'MyPythonType', (<class '...MyDerivedType'>,), {...})
 
@@ -98,7 +99,8 @@ TESTS:
 Check that a proper exception is raised if ``__getmetaclass__``
 returns a non-type::
 
-    sage: cython('''  # optional - sage.misc.cython
+    sage: cython(                                                               # optional - sage.misc.cython
+    ....: '''
     ....: cimport sage.cpython.cython_metaclass
     ....: cdef class MyCustomType():
     ....:     def __getmetaclass__(_):

src/sage/cpython/string.pyx

@@ -6,7 +6,8 @@ TESTS:
 
 Check that this can be used outside of Sage (see :trac:`25549`)::
 
-    sage: cython('''  # optional - sage.misc.cython
+    sage: cython(                                               # optional - sage.misc.cython
+    ....: '''
     ....: from sage.cpython.string cimport char_to_str
     ....: print(char_to_str("hello world!"))
     ....: ''')