gh-35105: sage.{functions,interfaces,symbolic}: Replace imports from sage.*.all for namespace packages
    
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### 📚 Description
Fixes #34954

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URL: #35105
Reported by: Matthias Köppe
Reviewer(s): Dima Pasechnik, Matthias Köppe, Tobias Diez

Author: Release Manager

src/sage/functions/hypergeometric.py

@@ -162,27 +162,27 @@
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
+from functools import reduce
+
+from sage.arith.misc import binomial, factorial, rising_factorial
+from sage.calculus.functional import derivative
+from sage.functions.error import erf
+from sage.functions.gamma import gamma
+from sage.functions.hyperbolic import cosh, sinh
+from sage.functions.log import exp, log
+from sage.functions.other import sqrt, real_part
+from sage.libs.mpmath import utils as mpmath_utils
+from sage.misc.latex import latex
+from sage.misc.misc_c import prod
+from sage.rings.infinity import Infinity
 from sage.rings.integer import Integer
 from sage.rings.integer_ring import ZZ
 from sage.rings.rational_field import QQ
-from sage.rings.infinity import Infinity
-from sage.arith.all import binomial, rising_factorial, factorial
+from sage.structure.element import get_coercion_model
 from sage.symbolic.constants import pi
+from sage.symbolic.expression import Expression
 from sage.symbolic.function import BuiltinFunction
 from sage.symbolic.ring import SR
-from sage.structure.element import get_coercion_model
-from sage.misc.latex import latex
-from sage.misc.misc_c import prod
-from sage.libs.mpmath import utils as mpmath_utils
-from sage.symbolic.expression import Expression
-from sage.calculus.functional import derivative
-from functools import reduce
-
-from .gamma import gamma
-from .other import sqrt, real_part
-from .log import exp, log
-from .hyperbolic import cosh, sinh
-from .error import erf
 
 
 def rational_param_as_tuple(x):

src/sage/functions/piecewise.py

@@ -1089,7 +1089,9 @@ def laplace(self, parameters, variable, x='x', s='t'):
                 sage: f.laplace(t,s)
                 (s + 1)*e^(-s)/s^2 + 2*e^(-s)/s - 1/s^2
             """
-            from sage.all import assume, exp, forget
+            from sage.symbolic.assumptions import assume, forget
+            from sage.functions.log import exp
+
             x = SR.var(x)
             s = SR.var(s)
             assume(s>0)
@@ -1180,7 +1182,8 @@ def fourier_series_cosine_coefficient(self, parameters,
                 -3/5/pi
 
             """
-            from sage.all import cos, pi
+            from sage.functions.trig import cos
+            from sage.symbolic.constants import pi
             L0 = (self.domain().sup() - self.domain().inf()) / 2
             if not L:
                 L = L0
@@ -1270,7 +1273,8 @@ def fourier_series_sine_coefficient(self, parameters, variable,
                 4/3/pi
 
             """
-            from sage.all import sin, pi
+            from sage.functions.trig import sin
+            from sage.symbolic.constants import pi
             L0 = (self.domain().sup() - self.domain().inf()) / 2
             if not L:
                 L = L0
@@ -1358,7 +1362,10 @@ def fourier_series_partial_sum(self, parameters, variable, N,
                  - 4/9*sin(3*pi*x)/pi^2 + 4*sin(pi*x)/pi^2 + 1/4
 
             """
-            from sage.all import pi, sin, cos, srange
+            from sage.symbolic.constants import pi
+            from sage.functions.trig import cos, sin
+            from sage.arith.srange import srange
+
             if not L:
                 L = (self.domain().sup() - self.domain().inf()) / 2
             x = self.default_variable()

src/sage/interfaces/axiom.py

@@ -836,7 +836,8 @@ def _sage_(self):
             return self._sage_domain()
 
         if type == "Float":
-            from sage.rings.all import RealField, ZZ
+            from sage.rings.real_mpfr import RealField
+            from sage.rings.integer_ring import ZZ
             prec = max(self.mantissa().length()._sage_(), 53)
             R = RealField(prec)
             x,e,b = self.unparsed_input_form().lstrip('float(').rstrip(')').split(',')

src/sage/interfaces/fricas.py

@@ -1217,7 +1217,9 @@ def _get_sage_type(self, domain):
             sage: fricas(0)._get_sage_type(m)                                   # optional - fricas
             Univariate Polynomial Ring in y over Univariate Polynomial Ring in x over Algebraic Field
         """
-        from sage.rings.all import QQbar, RDF, PolynomialRing
+        from sage.rings.qqbar import QQbar
+        from sage.rings.real_double import RDF
+        from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
         from sage.rings.fraction_field import FractionField
         from sage.rings.finite_rings.integer_mod_ring import Integers
         from sage.rings.finite_rings.finite_field_constructor import FiniteField
@@ -1730,7 +1732,8 @@ def convert_rootOf(x, y):
 
         ex, _ = FriCASElement._parse_and_eval(fricas_InputForm)
         # postprocessing of rootOf
-        from sage.rings.all import QQbar, PolynomialRing
+        from sage.rings.qqbar import QQbar
+        from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
         while rootOf:
             for var, poly in rootOf.items():
                 pvars = poly.variables()

src/sage/interfaces/genus2reduction.py

@@ -34,7 +34,9 @@
 # ****************************************************************************
 
 from sage.structure.sage_object import SageObject
-from sage.rings.all import ZZ, QQ, PolynomialRing
+from sage.rings.integer_ring import ZZ
+from sage.rings.rational_field import QQ
+from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.libs.pari.all import pari
 
 roman_numeral = ["", "I", "II", "III", "IV", "V", "VI", "VII"]

src/sage/interfaces/maxima_abstract.py

@@ -1846,7 +1846,7 @@ def _matrix_(self, R):
             [  3 3/2   1 3/4]
             [  4   2 4/3   1]
         """
-        from sage.matrix.all import MatrixSpace
+        from sage.matrix.matrix_space import MatrixSpace
         self._check_valid()
         P = self.parent()
         nrows = int(P.eval('length(%s)'%self.name()))

src/sage/interfaces/octave.py

@@ -508,7 +508,7 @@ def solve_linear_system(self, A, b):
         m = A.nrows()
         if m != len(b):
             raise ValueError("dimensions of A and b must be compatible")
-        from sage.matrix.all import MatrixSpace
+        from sage.matrix.matrix_space import MatrixSpace
         from sage.rings.rational_field import QQ
         MS = MatrixSpace(QQ,m,1)
         b  = MS(list(b)) # converted b to a "column vector"
@@ -707,7 +707,7 @@ def _matrix_(self, R=None):
         if self.iscomplex():
             w = [[to_complex(x,R) for x in row] for row in w]
 
-        from sage.matrix.all import MatrixSpace
+        from sage.matrix.matrix_space import MatrixSpace
         return MatrixSpace(R, nrows, ncols)(w)
 
     def _vector_(self, R=None):

src/sage/interfaces/sage0.py

@@ -159,7 +159,8 @@ def __init__(self,
         if python:
             command = 'python -u'
             prompt = re.compile(b'>>> ')
-            init_code.append('from sage.all import *')
+            environment = 'sage.all'
+            init_code.append(f'from {environment} import *')
         else:
             command = ' '.join([
                 'sage-ipython',

src/sage/interfaces/scilab.py

@@ -486,7 +486,7 @@ def _matrix_(self, R):
             [1.00000000000000 2.00000000000000]
             [3.00000000000000 4.50000000000000]
         """
-        from sage.matrix.all import MatrixSpace
+        from sage.matrix.matrix_space import MatrixSpace
         s = str(self).strip()
         v = s.split('\n ')
         nrows = len(v)

src/sage/interfaces/singular.py

@@ -1656,15 +1656,19 @@ def sage_global_ring(self):
             br = ZZ
             is_extension = False
         elif charstr[0] in ['0', 'QQ']:
-            from sage.all import QQ
+            from sage.rings.rational_field import QQ
             br = QQ
         elif charstr[0].startswith('Float'):
-            from sage.all import RealField, ceil, log
+            from sage.rings.real_mpfr import RealField
+            from sage.functions.other import ceil
+            from sage.misc.functional import log
             prec = singular.eval('ringlist(basering)[1][2][1]')
             br = RealField(ceil((ZZ(prec)+1)/log(2,10)))
             is_extension = False
         elif charstr[0]=='complex':
-            from sage.all import ComplexField, ceil, log
+            from sage.rings.complex_mpfr import ComplexField
+            from sage.functions.other import ceil
+            from sage.misc.functional import log
             prec = singular.eval('ringlist(basering)[1][2][1]')
             br = ComplexField(ceil((ZZ(prec)+1)/log(2,10)))
             is_extension = False
@@ -1684,7 +1688,7 @@ def sage_global_ring(self):
         if is_extension:
             minpoly = singular.eval('minpoly')
             if minpoly == '0':
-                from sage.all import Frac
+                from sage.rings.fraction_field import FractionField as Frac
                 BR = Frac(br[charstr[1]])
             else:
                 is_short = singular.eval('short')
@@ -1701,7 +1705,7 @@ def sage_global_ring(self):
         # Now, we form the polynomial ring over BR with the given variables,
         # using Singular's term order
         from sage.rings.polynomial.term_order import termorder_from_singular
-        from sage.all import PolynomialRing
+        from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
         # Meanwhile Singulars quotient rings are also of 'ring' type, not 'qring' as it was in the past.
         # To find out if a singular ring is a quotient ring or not checking for ring type does not help
         # and instead of that we check if the quotient ring is zero or not: