Trac #29881: sage.categories: Replace imports from sage.rings.all by more specific imports

`sage.rings.all` has a mixture of generic classes and implementation
classes. Some of the generic and/or basic ones will probably have to be
included in `sage-objects` (#29865). We prepare this by getting rid of
imports from `sage.rings.all` throughout `sage.categories`.

URL: https://trac.sagemath.org/29881
Reported by: mkoeppe
Ticket author(s): Matthias Koeppe
Reviewer(s): Travis Scrimshaw, Frédéric Chapoton

Author: Release Manager

src/sage/categories/bimodules.py

@@ -107,7 +107,8 @@ def an_instance(cls):
             sage: Bimodules.an_instance()
             Category of bimodules over Rational Field on the left and Real Field with 53 bits of precision on the right
         """
-        from sage.rings.all import QQ, RR
+        from sage.rings.rational_field import QQ
+        from sage.rings.real_mpfr import RR
         return cls(QQ, RR)
 
     def _repr_object_names(self):

src/sage/categories/coalgebras_with_basis.py

@@ -197,7 +197,7 @@ def coproduct_iterated(self, n=1):
             if n == 1:
                 return self.coproduct()
             from sage.functions.all import floor, ceil
-            from sage.rings.all import Integer
+            from sage.rings.integer import Integer
 
             # Use coassociativity of `\Delta` to perform many coproducts simultaneously.
             fn = floor(Integer(n-1)/2); cn = ceil(Integer(n-1)/2)

src/sage/categories/complex_reflection_or_generalized_coxeter_groups.py

@@ -339,7 +339,7 @@ def simple_reflection_orders(self):
             """
             one = self.one()
             s = self.simple_reflections()
-            from sage.rings.all import ZZ
+            from sage.rings.integer_ring import ZZ
 
             def mult_order(x):
                 ct = ZZ.one()

src/sage/categories/euclidean_domains.py

@@ -148,7 +148,7 @@ def _test_euclidean_degree(self, **options):
 
             min_degree = self.one().euclidean_degree()
 
-            from sage.rings.all import NN
+            from sage.rings.semirings.non_negative_integer_semiring import NN
             for a in S:
                 tester.assertIn(a.euclidean_degree(), NN)
                 tester.assertGreaterEqual(a.euclidean_degree(), min_degree)

src/sage/categories/fields.py

@@ -559,7 +559,7 @@ def euclidean_degree(self):
             """
             if self.is_zero():
                 raise ValueError("euclidean degree not defined for the zero element")
-            from sage.rings.all import ZZ
+            from sage.rings.integer_ring import ZZ
             return ZZ.zero()
 
         def quo_rem(self, other):

src/sage/categories/finite_complex_reflection_groups.py

@@ -324,7 +324,7 @@ def number_of_reflection_hyperplanes(self):
                 sage: W.number_of_reflection_hyperplanes()  # optional - gap3
                 15
             """
-            from sage.rings.all import ZZ
+            from sage.rings.integer_ring import ZZ
             return ZZ.sum(codeg + 1 for codeg in self.codegrees())
 
         @cached_method
@@ -358,7 +358,7 @@ def number_of_reflections(self):
                 sage: W.number_of_reflections()            # optional - gap3
                 15
             """
-            from sage.rings.all import ZZ
+            from sage.rings.integer_ring import ZZ
             return ZZ.sum(deg - 1 for deg in self.degrees())
 
         @cached_method
@@ -413,7 +413,7 @@ def cardinality(self):
                 sage: W.cardinality()                      # optional - gap3
                 192
             """
-            from sage.rings.all import ZZ
+            from sage.rings.integer_ring import ZZ
             return ZZ.prod(self.degrees())
 
         def is_well_generated(self):

src/sage/categories/finite_coxeter_groups.py

@@ -13,9 +13,6 @@
 from sage.misc.lazy_attribute import lazy_attribute
 from sage.categories.category_with_axiom import CategoryWithAxiom
 from sage.categories.coxeter_groups import CoxeterGroups
-from sage.rings.all import AA, UniversalCyclotomicField, QQbar
-from sage.rings.integer_ring import ZZ
-
 
 class FiniteCoxeterGroups(CategoryWithAxiom):
     r"""
@@ -742,9 +739,12 @@ def permutahedron(self, point=None, base_ring=None):
             n = self.one().canonical_matrix().rank()
             weights = self.fundamental_weights()
             if point is None:
+                from sage.rings.integer_ring import ZZ
                 point = [ZZ.one()] * n
             v = sum(point[i-1] * weights[i] for i in weights.keys())
             from sage.geometry.polyhedron.constructor import Polyhedron
+            from sage.rings.qqbar import AA, QQbar
+            from sage.rings.universal_cyclotomic_field import UniversalCyclotomicField
             vertices = [v*w for w in self]
             if base_ring is None and v.base_ring() in [UniversalCyclotomicField(), QQbar]:
                 vertices = [v.change_ring(AA) for v in vertices]

src/sage/categories/groups.py

@@ -78,7 +78,7 @@ def free(index_set=None, names=None, **kwds):
             sage: F.<x,y,z> = Groups().free(); F
             Free Group on generators {x, y, z}
         """
-        from sage.rings.all import ZZ
+        from sage.rings.integer_ring import ZZ
         if index_set in ZZ or (index_set is None and names is not None):
             from sage.groups.free_group import FreeGroup
             if names is None:

src/sage/categories/highest_weight_crystals.py

@@ -330,7 +330,7 @@ def q_dimension(self, q=None, prec=None, use_product=False):
                  + 36*q^12 + 44*q^13 + 57*q^14 + 70*q^15 + O(x^16)
 
             """
-            from sage.rings.all import ZZ
+            from sage.rings.integer_ring import ZZ
             WLR = self.weight_lattice_realization()
             I = self.index_set()
             mg = self.highest_weight_vectors()

src/sage/categories/lie_algebras.py

@@ -166,7 +166,7 @@ def example(self, gens=None):
         """
         if gens is None:
             from sage.combinat.symmetric_group_algebra import SymmetricGroupAlgebra
-            from sage.rings.all import QQ
+            from sage.rings.rational_field import QQ
             gens = SymmetricGroupAlgebra(QQ, 3).algebra_generators()
         from sage.categories.examples.lie_algebras import Example
         return Example(gens)

src/sage/categories/loop_crystals.py

@@ -22,8 +22,6 @@
 from sage.categories.map import Map
 from sage.graphs.dot2tex_utils import have_dot2tex
 from sage.functions.other import ceil
-from sage.rings.all import ZZ
-
 
 class LoopCrystals(Category_singleton):
     r"""
@@ -534,6 +532,7 @@ def is_perfect(self, ell=None):
 
                 Implement a version for tensor products of KR crystals.
             """
+            from sage.rings.integer_ring import ZZ
             if ell is None:
                 if (self.cartan_type().dual().type() == 'BC'
                     and self.cartan_type().rank() - 1 == self.r()):
@@ -978,6 +977,7 @@ def energy_function(self, algorithm=None):
 
                 if algorithm == 'definition':
                     # Setup
+                    from sage.rings.integer_ring import ZZ
                     energy = ZZ.zero()
                     R_mats = [[K.R_matrix(Kp) for Kp in self.parent().crystals[i+1:]]
                               for i,K in enumerate(self.parent().crystals)]
@@ -1179,6 +1179,7 @@ def __init__(self, B, Bp, normalization=0):
             sage: [H(x) for x in hw]
             [0, 1, 2, 1]
         """
+        from sage.rings.integer_ring import ZZ
         self._B = B
         self._Bp = Bp
         self._R_matrix = self._B.R_matrix(self._Bp)

src/sage/categories/monoids.py

@@ -102,7 +102,7 @@ def free(index_set=None, names=None, **kwds):
         """
         if names is not None:
             if isinstance(names, str):
-                from sage.rings.all import ZZ
+                from sage.rings.integer_ring import ZZ
                 if ',' not in names and index_set in ZZ:
                     names = [names + repr(i) for i in range(index_set)]
                 else:
@@ -349,7 +349,7 @@ def free(index_set=None, names=None, **kwds):
             """
             if names is not None:
                 if isinstance(names, str):
-                    from sage.rings.all import ZZ
+                    from sage.rings.integer_ring import ZZ
                     if ',' not in names and index_set in ZZ:
                         names = [names + repr(i) for i in range(index_set)]
                     else:

src/sage/categories/regular_crystals.py

@@ -259,7 +259,7 @@ def demazure_subcrystal(self, element, reduced_word, only_support=True):
                  ([[2, 2]], [[1, 2]], 0)]
             """
             from sage.combinat.free_module import CombinatorialFreeModule
-            from sage.rings.all import QQ
+            from sage.rings.rational_field import QQ
             C = CombinatorialFreeModule(QQ, self)
             D = self.demazure_operator(C(element), reduced_word)
             if only_support:

src/sage/categories/supercrystals.py

@@ -257,7 +257,7 @@ def character(self):
                     B[(1, 0, 0, 0, 0)] + B[(0, 1, 0, 0, 0)] + B[(0, 0, 1, 0, 0)]
                      + B[(0, 0, 0, 1, 0)] + B[(0, 0, 0, 0, 1)]
                 """
-                from sage.rings.all import ZZ
+                from sage.rings.integer_ring import ZZ
                 A = self.weight_lattice_realization().algebra(ZZ)
                 return A.sum(A(x.weight()) for x in self)