Merge sagemath#34189

src/sage/rings/asymptotic/asymptotic_ring.py

@@ -419,7 +419,7 @@
 from sage.structure.unique_representation import UniqueRepresentation
 from sage.misc.defaults import series_precision
 import sage.rings.abc
-from sage.rings.all import RIF
+from sage.rings.real_mpfi import RIF
 from .misc import WithLocals
 
 

src/sage/rings/asymptotic/misc.py

@@ -141,9 +141,14 @@ def parent_to_repr_short(P):
         sage: parent_to_repr_short(Zmod(3)['g'])
         'Univariate Polynomial Ring in g over Ring of integers modulo 3'
     """
-    from sage.rings.all import RR, CC, RIF, CIF, RBF, CBF
+    from sage.rings.cc import CC
+    from sage.rings.cif import CIF
+    from sage.rings.complex_arb import CBF
     from sage.rings.integer_ring import ZZ
     from sage.rings.rational_field import QQ
+    from sage.rings.real_arb import RBF
+    from sage.rings.real_mpfi import RIF
+    from sage.rings.real_mpfr import RR
     from sage.symbolic.ring import SR
     from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
     from sage.rings.polynomial.multi_polynomial_ring_base import is_MPolynomialRing

src/sage/rings/complex_arb.pyx

@@ -567,7 +567,9 @@ class ComplexBallField(UniqueRepresentation, sage.rings.abc.ComplexBallField):
             emb = other.coerce_embedding()
             return emb is not None and self.has_coerce_map_from(emb.codomain())
 
-        from sage.rings.all import QQ, AA, QQbar, RLF, CLF
+        from sage.rings.qqbar import AA, QQbar
+        from sage.rings.real_lazy import RLF, CLF
+
         if other in [AA, QQbar, RLF, CLF]:
             return True
 

src/sage/rings/finite_rings/residue_field.pyx

@@ -151,7 +151,9 @@ from sage.rings.rational cimport Rational
 from sage.categories.homset import Hom
 from sage.categories.basic import Fields, Rings
 from sage.categories.pushout import AlgebraicExtensionFunctor
-from sage.rings.all import ZZ, QQ, Integers
+from sage.rings.finite_rings.integer_mod_ring import Integers
+from sage.rings.integer_ring import ZZ
+from sage.rings.rational_field import QQ
 from sage.rings.finite_rings.finite_field_constructor import zech_log_bound, FiniteField as GF
 from sage.rings.finite_rings.finite_field_givaro import FiniteField_givaro
 from sage.rings.finite_rings.finite_field_ntl_gf2e import FiniteField_ntl_gf2e

src/sage/rings/fraction_field.py

@@ -1036,7 +1036,7 @@ def function_field(self):
             :meth:`sage.rings.function_field.RationalFunctionField.field`
 
         """
-        from sage.rings.all import FunctionField
+        from sage.rings.function_field.constructor import FunctionField
         return FunctionField(self.base_ring(), names=self.variable_name())
 
     def _coerce_map_from_(self, R):
@@ -1058,7 +1058,7 @@ def _coerce_map_from_(self, R):
         """
         from sage.rings.function_field.function_field import RationalFunctionField
         if isinstance(R, RationalFunctionField) and self.variable_name() == R.variable_name() and self.base_ring() is R.constant_base_field():
-            from sage.categories.all import Hom
+            from sage.categories.homset import Hom
             parent = Hom(R, self)
             from sage.rings.function_field.maps import FunctionFieldToFractionField
             return parent.__make_element_class__(FunctionFieldToFractionField)(parent)
@@ -1138,7 +1138,7 @@ def section(self):
 
         """
         from sage.categories.sets_with_partial_maps import SetsWithPartialMaps
-        from sage.all import Hom
+        from sage.categories.all import Hom
         parent = Hom(self.codomain(), self.domain(), SetsWithPartialMaps())
         return parent.__make_element_class__(FractionFieldEmbeddingSection)(self)
 

src/sage/rings/function_field/function_field.py

@@ -3436,7 +3436,7 @@ def number_of_rational_places(self, r=1):
             sage: [F.number_of_rational_places(r) for r in [1..10]]
             [4, 8, 4, 16, 44, 56, 116, 288, 508, 968]
         """
-        from sage.rings.all import IntegerRing
+        from sage.rings.integer_ring import IntegerRing
 
         q = self.constant_field().order()
         L = self.L_polynomial()

src/sage/rings/lazy_series.py

@@ -2973,12 +2973,12 @@ def approximate_series(self, prec, name=None):
             name = S.variable_name()
 
         if self.valuation() < 0:
-            from sage.rings.all import LaurentSeriesRing
+            from sage.rings.laurent_series_ring import LaurentSeriesRing
             R = LaurentSeriesRing(S.base_ring(), name=name)
             n = self.valuation()
             return R([self[i] for i in range(n, prec)], n).add_bigoh(prec)
         else:
-            from sage.rings.all import PowerSeriesRing
+            from sage.rings.power_series_ring import PowerSeriesRing
             R = PowerSeriesRing(S.base_ring(), name=name)
             return R([self[i] for i in range(prec)]).add_bigoh(prec)
 

src/sage/rings/number_field/S_unit_solver.py

@@ -54,7 +54,7 @@
 # ****************************************************************************
 
 
-from sage.rings.all import Infinity
+from sage.rings.infinity import Infinity
 from sage.misc.lazy_import import lazy_import
 lazy_import("sage.symbolic.ring", "SR")
 from sage.rings.integer import Integer
@@ -71,11 +71,11 @@
 from sage.rings.padics.factory import Qp
 from sage.combinat.combination import Combinations
 from sage.misc.misc_c import prod
-from sage.arith.all import factorial
+from sage.arith.functions import lcm
+from sage.arith.misc import gcd, CRT, factorial
 from sage.matrix.constructor import matrix, identity_matrix, vector, block_matrix, zero_matrix
 from sage.modules.free_module_element import zero_vector
 from itertools import combinations_with_replacement
-from sage.arith.all import gcd, lcm, CRT
 from copy import copy
 import itertools
 

src/sage/rings/number_field/bdd_height.py

@@ -35,7 +35,8 @@
 from sage.modules.free_module_element import vector
 from sage.matrix.constructor import column_matrix
 from sage.rings.rational_field import QQ
-from sage.rings.all import RR, Infinity
+from sage.rings.infinity import Infinity
+from sage.rings.real_mpfr import RR
 from sage.geometry.polyhedron.constructor import Polyhedron
 
 

src/sage/rings/number_field/class_group.py

@@ -288,7 +288,7 @@ def representative_prime(self, norm_bound=1000):
         # otherwise we just search:
         Cl = self.parent()
         K = Cl.number_field()
-        from sage.rings.all import RR
+        from sage.rings.real_mpfr import RR
         for P in K.primes_of_bounded_norm_iter(RR(norm_bound)):
             if Cl(P)==c:
                 return P

src/sage/rings/number_field/number_field.py

@@ -128,7 +128,7 @@
 from sage.misc.functional import is_odd, lift
 
 from sage.misc.misc_c import prod
-from sage.rings.all import Infinity
+from sage.rings.infinity import Infinity
 from sage.categories.number_fields import NumberFields
 
 import sage.rings.ring
@@ -1635,7 +1635,7 @@ def construction(self):
 
         """
         from sage.categories.pushout import AlgebraicExtensionFunctor
-        from sage.all import QQ
+        from sage.rings.rational_field import QQ
         names = self.variable_names()
         polys = []
         embeddings = []
@@ -3293,7 +3293,8 @@ def algebraic_closure(self):
             sage: K.algebraic_closure()
             Algebraic Field
         """
-        return sage.rings.all.QQbar
+        from sage.rings.qqbar import QQbar
+        return QQbar
 
     @cached_method
     def conductor(self, check_abelian=True):
@@ -6810,7 +6811,7 @@ def regulator(self, proof=None):
         try:
             return self.__regulator
         except AttributeError:
-            from sage.rings.all import RealField
+            from sage.rings.real_mpfr import RealField
             k = self.pari_bnf(proof)
             self.__regulator = RealField(53)(k.bnf_get_reg())
             return self.__regulator
@@ -8119,7 +8120,8 @@ def _coerce_from_other_number_field(self, x):
 
         # Do not use CDF or RDF because of constraints on the
         # exponent of floating-point numbers
-        from sage.rings.all import RealField, ComplexField
+        from sage.rings.complex_mpfr import ComplexField
+        from sage.rings.real_mpfr import RealField
         CC = ComplexField(53)
         RR = RealField(53)
 
@@ -9372,8 +9374,9 @@ def places(self, all_complex=False, prec=None):
             C = sage.rings.complex_double.CDF
 
         elif prec == Infinity:
-            R = sage.rings.all.AA
-            C = sage.rings.all.QQbar
+            from sage.rings.qqbar import AA, QQbar
+            R = AA
+            C = QQbar
 
         else:
             R = sage.rings.real_mpfr.RealField(prec)
@@ -9670,7 +9673,8 @@ def relativize(self, alpha, names, structure=None):
         # step 1: construct the abstract field generated by alpha.w
         # step 2: make a relative extension of it.
         # step 3: construct isomorphisms
-        from sage.all import vector, matrix
+        from sage.matrix.constructor import matrix
+        from sage.modules.free_module_element import vector
 
         from sage.categories.map import is_Map
         if is_Map(alpha):
@@ -9680,7 +9684,7 @@ def relativize(self, alpha, names, structure=None):
             L = alpha.domain()
             alpha = alpha(L.gen()) # relativize over phi's domain
             if L is QQ:
-                from sage.rings.all import polygen
+                from sage.rings.polynomial.polynomial_ring import polygen
                 f = polygen(QQ)
             else:
                 f = L.defining_polynomial() # = alpha.minpoly()
@@ -10036,13 +10040,13 @@ def hilbert_symbol(self, a, b, P = None):
             return pari(self).nfhilbert(a, b)
 
         from sage.categories.map import Map
-        from sage.categories.all import Rings
+        from sage.categories.rings import Rings
         if isinstance(P, Map) and P.category_for().is_subcategory(Rings()):
             # P is a morphism of Rings
             if P.domain() is not self:
                 raise ValueError("Domain of P (=%s) should be self (=%s) in self.hilbert_symbol" % (P, self))
             codom = P.codomain()
-            from sage.rings.all import (AA, QQbar)
+            from sage.rings.qqbar import AA, QQbar
             if isinstance(codom, (sage.rings.abc.ComplexField, sage.rings.abc.ComplexDoubleField, sage.rings.abc.ComplexIntervalField)) or \
                                          codom is QQbar:
                 if P(self.gen()).imag() == 0:

src/sage/rings/number_field/number_field_element.pyx

@@ -2948,7 +2948,11 @@ cdef class NumberFieldElement(FieldElement):
         from .number_field import NumberField_cyclotomic
         if isinstance(K, NumberField_cyclotomic):
             # solution by radicals may be difficult, but we have a closed form
-            from sage.all import exp, I, pi, ComplexField, RR
+            from sage.functions.log import exp
+            from sage.rings.complex_mpfr import ComplexField
+            from sage.rings.imaginary_unit import I
+            from sage.rings.real_mpfr import RR
+            from sage.symbolic.constants import pi
             CC = ComplexField(53)
             two_pi_i = 2 * pi * I
             k = ( K._n()*CC(K.gen()).log() / CC(two_pi_i) ).real().round() # n ln z / (2 pi i)

src/sage/rings/number_field/number_field_ideal.py

@@ -2731,7 +2731,7 @@ def ideallog(self, x, gens=None, check=True):
         ans = N.hermite_form()[0, 1:].list()
 
         if check:
-            from sage.rings.all import Zmod
+            from sage.rings.finite_rings.integer_mod_ring import Zmod
             Z_norm = Zmod(self.norm().numerator())  # norm is an integer ?
             t = 1
             for gi, ai in zip(gens, ans):

src/sage/rings/number_field/order.py

@@ -1786,13 +1786,13 @@ def _assume_maximal(self, is_maximal=True, p=None):
                 self.__is_maximal = False
             elif is_maximal:
                 if self._is_maximal() is False:
-                    raise ValueError(f"cannot assume this order to be maximal because we already found it to be a non-maximal order")
+                    raise ValueError("cannot assume this order to be maximal because we already found it to be a non-maximal order")
                 self.__is_maximal = True
                 # No need to keep information at specific primes anymore.
                 self.__is_maximal_at = {}
             else:
                 if self._is_maximal() is True:
-                    raise ValueError(f"cannot assume this order to be non-maximal because we already found it to be a maximal order")
+                    raise ValueError("cannot assume this order to be non-maximal because we already found it to be a maximal order")
                 self.__is_maximal = False
         else:
             p = ZZ(p).abs()
@@ -2752,7 +2752,8 @@ def GaussianIntegers(names="I", latex_name="i"):
         sage: GaussianIntegers().basis()
         [1, I]
     """
-    from sage.rings.all import CDF, NumberField
+    from sage.rings.complex_double import CDF
+    from sage.rings.number_field.number_field import NumberField
     f = ZZ['x']([1, 0, 1])
     nf = NumberField(f, names, embedding=CDF(0, 1), latex_name=latex_name)
     return nf.ring_of_integers()
@@ -2780,7 +2781,8 @@ def EisensteinIntegers(names="omega"):
         sage: EisensteinIntegers().basis()
         [1, omega]
     """
-    from sage.rings.all import CDF, NumberField
+    from sage.rings.complex_double import CDF
+    from sage.rings.number_field.number_field import NumberField
     f = ZZ['x']([1, 1, 1])
     nf = NumberField(f, names, embedding=CDF(-0.5, 0.8660254037844386))
     return nf.ring_of_integers()

src/sage/rings/padics/local_generic.py

@@ -1459,7 +1459,7 @@ def _test_matrix_smith(self, **options):
         tester.assertEqual(self.residue_field().characteristic(), self.residue_characteristic())
 
         from itertools import chain
-        from sage.all import MatrixSpace
+        from sage.matrix.matrix_space import MatrixSpace
         from .precision_error import PrecisionError
         matrices = chain(*[MatrixSpace(self, n, m).some_elements() for n in (1,3,7) for m in (1,4,7)])
         for M in tester.some_elements(matrices):

src/sage/rings/padics/padic_ZZ_pX_CA_element.pyx

@@ -180,7 +180,7 @@ from sage.rings.padics.padic_generic_element cimport pAdicGenericElement
 from sage.libs.pari.all import pari_gen
 from sage.interfaces.gp import GpElement
 from sage.rings.finite_rings.integer_mod import is_IntegerMod
-from sage.rings.all import IntegerModRing
+from sage.rings.finite_rings.integer_mod_ring import IntegerModRing
 from sage.rings.padics.padic_ext_element cimport pAdicExtElement
 from sage.rings.padics.precision_error import PrecisionError
 

src/sage/rings/padics/padic_ZZ_pX_FM_element.pyx

@@ -149,7 +149,7 @@ from sage.rings.rational cimport Rational
 from sage.libs.pari.all import pari_gen
 from sage.interfaces.gp import GpElement
 from sage.rings.finite_rings.integer_mod import is_IntegerMod
-from sage.rings.all import IntegerModRing
+from sage.rings.finite_rings.integer_mod_ring import IntegerModRing
 from sage.rings.padics.pow_computer_ext cimport PowComputer_ZZ_pX_FM_Eis
 
 

src/sage/rings/padics/padic_valuation.py

@@ -1252,7 +1252,7 @@ def simplify(self, x, error=None, force=False, size_heuristic_bound=32):
             return self.domain().zero()
 
         from sage.rings.rational_field import QQ
-        from sage.rings.all import Qp
+        from sage.rings.padics.factory import Qp
         precision_ring = Qp(self.p(), QQ(error).floor() + 1 - v)
         reduced = precision_ring(x)
         lift = (reduced >> v).lift()

src/sage/rings/polynomial/hilbert.pyx

@@ -464,8 +464,9 @@ def first_hilbert_series(I, grading=None, return_grading=False):
         sage: first_hilbert_series(singular(I))
         0
     """
-    from sage.all import ZZ, PolynomialRing
-    PR = PolynomialRing(ZZ,'t')
+    from sage.rings.integer_ring import ZZ
+    from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
+    PR = PolynomialRing(ZZ, 't')
     cdef Node AN
     # The "active node". If a recursive computation is needed, it will be equipped
     # with a 'Left' and a 'Right' child node, and some 'Multipliers'. Later, the first Hilbert

src/sage/rings/polynomial/infinite_polynomial_element.py

@@ -164,7 +164,7 @@ def InfinitePolynomial(A, p):
         alpha_2^2 + alpha_1^2
 
     """
-    from sage.all import parent
+    from sage.structure.element import parent
     if hasattr(A,'_P'):
         if parent(p) is A._P or (A._P.base_ring().has_coerce_map_from(parent(p))):
             return InfinitePolynomial_dense(A, p)
@@ -826,7 +826,7 @@ def _richcmp_(self, x, op):
         # but of course the underlying polynomial rings
         # may be widely different, and the sage coercion
         # system can't guess what order we want.
-        from sage.all import parent
+        from sage.structure.element import parent
         R1 = parent(self._p)
         R2 = parent(x._p)
         if (hasattr(R1,'has_coerce_map_from') and R1.has_coerce_map_from(R2)) or (hasattr(R2,'has_coerce_map_from') and R2.has_coerce_map_from(R1)):

src/sage/rings/polynomial/infinite_polynomial_ring.py

@@ -1337,7 +1337,7 @@ def krull_dimension(self, *args, **kwds):
             sage: R.krull_dimension()
             +Infinity
         """
-        from sage.rings.all import Infinity
+        from sage.rings.infinity import Infinity
         return Infinity
 
     def order(self):
@@ -1351,7 +1351,7 @@ def order(self):
             sage: R.order()
             +Infinity
         """
-        from sage.rings.all import Infinity
+        from sage.rings.infinity import Infinity
         return Infinity
 
 

src/sage/rings/polynomial/multi_polynomial_ideal.py

@@ -1313,7 +1313,7 @@ def _groebner_basis_ginv(self, algorithm="TQ", criteria='CritPartially', divisio
         except KeyError:
             raise NotImplementedError("Term order '%s' not supported by Sage's GINV interface or GINV"%T.term_order())
 
-        from sage.all import QQ
+        from sage.rings.rational_field import QQ
         if K is QQ:
             ic = ginv.CoeffInterface("GmpQ", st)
         elif K.order() <= 2**16 and K.order().is_prime():

src/sage/rings/polynomial/polynomial_gf2x.pyx

@@ -147,7 +147,7 @@ cdef class Polynomial_GF2X(Polynomial_template):
         from sage.misc.verbose import verbose
         from sage.functions.all import ceil
         from sage.matrix.constructor import Matrix
-        from sage.rings.all import FiniteField as GF
+        from sage.rings.finite_rings.finite_field_constructor import FiniteField as GF
 
         cdef Polynomial_GF2X res
         cdef GF2XModulus_c modulus