Trac #34947: sage.{rings,modules,geometry}: Replace imports from sage…

….*.all for namespace packages

Using `./sage -fiximports` from #34945.

Also remove trailing whitespace in the affected files.

Part of Meta-ticket #32414

URL: https://trac.sagemath.org/34947
Reported by: mkoeppe
Ticket author(s): Alex Chandler
Reviewer(s): Travis Scrimshaw, Matthias Koeppe

src/sage/geometry/cone.py

@@ -205,7 +205,8 @@
 from copy import copy
 from warnings import warn
 
-from sage.arith.all import gcd, lcm
+from sage.arith.misc import GCD as gcd
+from sage.arith.functions import lcm
 from sage.combinat.posets.posets import FinitePoset
 from sage.geometry.point_collection import PointCollection
 from sage.geometry.polyhedron.constructor import Polyhedron

src/sage/geometry/hyperplane_arrangement/library.py

@@ -22,7 +22,7 @@
 from sage.combinat.combinat import stirling_number2
 from sage.combinat.root_system.cartan_type import CartanType
 from sage.combinat.root_system.root_system import RootSystem
-from sage.arith.all import binomial
+from sage.arith.misc import binomial
 from sage.rings.polynomial.polynomial_ring import polygen
 
 from sage.geometry.hyperplane_arrangement.arrangement import HyperplaneArrangements

src/sage/geometry/integral_points.pyx

@@ -22,7 +22,8 @@ from sage.rings.integer_ring import ZZ
 from sage.rings.rational_field import QQ
 from sage.rings.real_mpfr import RR
 from sage.rings.integer cimport Integer
-from sage.arith.all import gcd, lcm
+from sage.arith.misc import GCD as gcd
+from sage.arith.functions import lcm
 from sage.combinat.permutation import Permutation
 from sage.misc.misc_c import prod
 from sage.modules.free_module import FreeModule

src/sage/geometry/lattice_polytope.py

@@ -103,7 +103,7 @@
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
-from sage.arith.all import gcd
+from sage.arith.misc import GCD as gcd
 from sage.combinat.posets.posets import FinitePoset
 from sage.env import POLYTOPE_DATA_DIR
 from sage.geometry.cone import _ambient_space_point, integral_length

src/sage/geometry/point_collection.pyx

@@ -955,23 +955,23 @@ def read_palp_point_collection(f, lattice=None, permutation=False):
     Read and return a point collection from an opened file.
 
     Data must be in PALP format:
-   
+
         * the first input line starts with two integers `m` and `n`, the number
           of points and the number of components of each;
-    
+
         * the rest of the first line may contain a permutation;
-    
+
         * the next `m` lines contain `n` numbers each.
-        
+
     .. NOTE::
-    
+
         If `m` < `n`, it is assumed (for compatibility with PALP) that the
         matrix is transposed, i.e. that each column is a point.
 
     INPUT:
 
     - ``f`` -- an opened file with PALP output.
-    
+
     - ``lattice`` -- the lattice for points. If not given, the
       :class:`toric lattice <sage.geometry.toric_lattice.ToricLatticeFactory>`
       `M` of dimension `n` will be used.

src/sage/geometry/polyhedron/generating_function.py

@@ -1492,7 +1492,7 @@ def generate_mods(equations):
             sage: _TransformMod.generate_mods([(0, 1, 1, -2)])
             ({0: (2, 0), 1: (2, 0)}, {0: (2, 1), 1: (2, 1)})
         """
-        from sage.arith.all import lcm
+        from sage.arith.functions import lcm
         from sage.matrix.constructor import matrix
         from sage.rings.integer_ring import ZZ
         from sage.rings.rational_field import QQ

src/sage/geometry/triangulation/element.py

@@ -878,7 +878,7 @@ def normal_cone(self):
             raise NotImplementedError('Only base rings ZZ and QQ are supported')
         from ppl import Constraint_System, Linear_Expression, C_Polyhedron
         from sage.matrix.constructor import matrix
-        from sage.arith.all import lcm
+        from sage.arith.functions import lcm
         pc = self.point_configuration()
         cs = Constraint_System()
         for facet in self.interior_facets():

src/sage/modules/fg_pid/fgp_element.py

@@ -448,7 +448,7 @@ def additive_order(self):
         from sage.rings.infinity import infinity
         from sage.rings.finite_rings.integer_mod import Mod
         from sage.rings.integer import Integer
-        from sage.arith.all import lcm
+        from sage.arith.functions import lcm
         n = Integer(1)
         for i, a in enumerate(I):
             if a == 0:

src/sage/modules/fg_pid/fgp_morphism.py

@@ -510,7 +510,7 @@ def __init__(self, X, Y, category=None):
                 from sage.categories.modules_with_basis import ModulesWithBasis
                 category = ModulesWithBasis(X.base_ring())
             else:
-                from sage.categories.all import Modules
+                from sage.categories.modules import Modules
                 category = Modules(X.base_ring())
         Homset.__init__(self, X, Y, category)
 

src/sage/modules/filtered_vector_space.py

@@ -108,7 +108,11 @@
 #                  https://www.gnu.org/licenses/
 # ***************************************************************************
 
-from sage.rings.all import QQ, ZZ, RDF, RR, Integer
+from sage.rings.rational_field import QQ
+from sage.rings.integer_ring import ZZ
+from sage.rings.real_double import RDF
+from sage.rings.real_mpfr import RR
+from sage.rings.integer import Integer
 from sage.rings.infinity import InfinityRing, infinity, minus_infinity
 from sage.categories.fields import Fields
 from sage.modules.free_module import FreeModule_ambient_field, VectorSpace

src/sage/modules/free_module.py

@@ -6718,7 +6718,7 @@ def _denominator(self, B):
         if not B:
             return 1
         d = B[0].denominator()
-        from sage.arith.all import lcm
+        from sage.arith.functions import lcm
         for x in B[1:]:
             d = lcm(d,x.denominator())
         return d

src/sage/modules/free_module_element.pyx

@@ -1602,7 +1602,7 @@ cdef class FreeModuleElement(Vector):   # abstract base class
             if isinstance(ord, AnInfinity):
                 return ord
             v.append(ord)
-        from sage.arith.all import lcm
+        from sage.arith.functions import lcm
         return lcm(v)
 
     def items(self):

src/sage/modules/module.pyx

@@ -254,7 +254,7 @@ cdef class Module(Parent):
             sage: M.endomorphism_ring()
             Set of Morphisms from <sage.modules.module.Module object at ...> to <sage.modules.module.Module object at ...> in Category of modules over Integer Ring
         """
-        from sage.categories.all import End
+        from sage.categories.homset import End
         return End(self)
 
 def is_Module(x):

src/sage/modules/multi_filtered_vector_space.py

@@ -39,7 +39,9 @@
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
-from sage.rings.all import QQ, ZZ, Integer
+from sage.rings.rational_field import QQ
+from sage.rings.integer_ring import ZZ
+from sage.rings.integer import Integer
 from sage.rings.infinity import infinity, minus_infinity
 from sage.categories.fields import Fields
 from sage.modules.free_module import FreeModule_ambient_field, VectorSpace

src/sage/modules/torsion_quadratic_module.py

@@ -20,7 +20,10 @@
 from sage.modules.fg_pid.fgp_element import FGP_Element
 from sage.modules.free_quadratic_module import FreeQuadraticModule
 from sage.arith.misc import gcd
-from sage.rings.all import ZZ, Zp, QQ, IntegerModRing
+from sage.rings.integer_ring import ZZ
+from sage.rings.padics.factory import Zp
+from sage.rings.rational_field import QQ
+from sage.rings.finite_rings.integer_mod_ring import IntegerModRing
 from sage.groups.additive_abelian.qmodnz import QmodnZ
 from sage.matrix.constructor import matrix
 from sage.matrix.special import diagonal_matrix

src/sage/modules/with_basis/cell_module.py

@@ -12,7 +12,7 @@
 #*****************************************************************************
 
 from sage.misc.cachefunc import cached_method
-from sage.categories.all import ModulesWithBasis
+from sage.categories.modules_with_basis import ModulesWithBasis
 from sage.structure.element import Element
 from sage.combinat.free_module import CombinatorialFreeModule
 from sage.data_structures.blas_dict import linear_combination

src/sage/modules/with_basis/indexed_element.pyx

@@ -28,7 +28,9 @@ from sage.misc.lazy_attribute import lazy_attribute
 from sage.misc.superseded import deprecation
 from sage.typeset.ascii_art import AsciiArt, empty_ascii_art, ascii_art
 from sage.typeset.unicode_art import UnicodeArt, empty_unicode_art, unicode_art
-from sage.categories.all import Category, Sets, ModulesWithBasis
+from sage.categories.category import Category
+from sage.categories.sets_cat import Sets
+from sage.categories.modules_with_basis import ModulesWithBasis
 from sage.data_structures.blas_dict cimport add, negate, scal, axpy
 
 

src/sage/modules/with_basis/subquotient.py

@@ -12,7 +12,7 @@
 from sage.sets.family import Family
 from sage.combinat.free_module import CombinatorialFreeModule
 from sage.misc.lazy_attribute import lazy_attribute
-from sage.categories.all import ModulesWithBasis
+from sage.categories.modules_with_basis import ModulesWithBasis
 
 
 class QuotientModuleWithBasis(CombinatorialFreeModule):

src/sage/rings/algebraic_closure_finite_field.py

@@ -956,7 +956,7 @@ def _roots_univariate_polynomial(self, p, ring=None, multiplicities=None, algori
             ....:         assert p(r).is_zero(), "r={} is not a root of p={}".format(r,p)
 
         """
-        from sage.arith.all import lcm
+        from sage.arith.functions import lcm
         from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 
         # first build a polynomial over some finite field

src/sage/rings/asymptotic/asymptotic_expansion_generators.py

@@ -363,7 +363,7 @@ def _log_StirlingNegativePowers_(var, precision):
             return A.zero()
         n = A.gen()
 
-        from sage.arith.all import bernoulli
+        from sage.arith.misc import bernoulli
         from sage.arith.srange import srange
 
         result = sum((bernoulli(k) / k / (k-1) / n**(k-1)
@@ -462,7 +462,7 @@ def HarmonicNumber(var, precision=None, skip_constant_summand=False):
             result += 1 / (2 * n)
 
         from sage.arith.srange import srange
-        from sage.arith.all import bernoulli
+        from sage.arith.misc import bernoulli
         for k in srange(2, 2*precision - 4, 2):
             result += -bernoulli(k) / k / n**k
 
@@ -912,7 +912,7 @@ def SingularityAnalysis(var, zeta=1, alpha=0, beta=0, delta=0,
         from .asymptotic_ring import AsymptoticRing
         from .growth_group import ExponentialGrowthGroup, \
                 MonomialGrowthGroup, GenericNonGrowthGroup
-        from sage.arith.all import falling_factorial
+        from sage.arith.misc import falling_factorial
         from sage.categories.cartesian_product import cartesian_product
         from sage.functions.other import binomial
         from sage.functions.gamma import gamma

src/sage/rings/asymptotic/asymptotics_multivariate_generating_functions.py

@@ -1345,7 +1345,7 @@ def cohomology_decomposition(self):
             (1/3, [(x*y - 1, 1), (x^2 + y^2 - 1, 1)])
         """
         from sage.calculus.functions import jacobian
-        from sage.arith.all import xgcd
+        from sage.arith.misc import XGCD as xgcd
         from sage.sets.set import Set
 
         R = self.denominator_ring

src/sage/rings/cfinite_sequence.py

@@ -851,7 +851,7 @@ def closed_form(self, n='n'):
             sage: CFiniteSequence((x/(1-x-x^2))^2).closed_form()
             1/5*(n - sqrt(1/5))*(1/2*sqrt(5) + 1/2)^n + 1/5*(n + sqrt(1/5))*(-1/2*sqrt(5) + 1/2)^n
         """
-        from sage.arith.all import binomial
+        from sage.arith.misc import binomial
         from sage.rings.qqbar import QQbar
 
         from sage.symbolic.ring import SR

src/sage/rings/complex_double.pyx

@@ -2482,7 +2482,7 @@ cdef class ComplexDoubleElement(FieldElement):
             sage: CDF(1,5).algdep(2)
             x^2 - 2*x + 26
         """
-        from sage.arith.all import algdep
+        from sage.arith.misc import algdep
         return algdep(self, n)
 
 cdef class FloatToCDF(Morphism):

src/sage/rings/complex_mpc.pyx

@@ -1371,7 +1371,7 @@ cdef class MPComplexNumber(sage.structure.element.FieldElement):
             sage: p(z)
             1.11022302462516e-16
         """
-        from sage.arith.all import algdep
+        from sage.arith.misc import algdep
         return algdep(self, n, **kwds)
 
     ################################

src/sage/rings/complex_mpfr.pyx

@@ -3279,7 +3279,7 @@ cdef class ComplexNumber(sage.structure.element.FieldElement):
             sage: p(z)
             1.11022302462516e-16
         """
-        from sage.arith.all import algdep
+        from sage.arith.misc import algdep
         return algdep(self, n, **kwds)
 
     # Alias

src/sage/rings/factorint.pyx

@@ -75,7 +75,7 @@ cpdef aurifeuillian(n, m, F=None, bint check=True):
         There is no need to set `F`. It's only for increasing speed
         of :meth:`factor_aurifeuillian()`.
     """
-    from sage.arith.all import euler_phi
+    from sage.arith.misc import euler_phi
     from sage.rings.real_mpfi import RealIntervalField
     if check:
         if not n.is_squarefree():

src/sage/rings/fast_arith.pyx

@@ -207,7 +207,7 @@ cpdef prime_range(start, stop=None, algorithm=None, bint py_ints=False):
         res = pari_prime_range(start, stop, py_ints)
 
     elif (algorithm == "pari_isprime") or (algorithm == "pari_primes"):
-        from sage.arith.all import primes
+        from sage.arith.misc import primes
         res = list(primes(start, stop))
     else:
         raise ValueError('algorithm must be "pari_primes" or "pari_isprime"')

src/sage/rings/finite_rings/finite_field_base.pyx

@@ -762,7 +762,7 @@ cdef class FiniteField(Field):
             a + 12
         """
         if self.degree() == 1:
-            from sage.arith.all import primitive_root
+            from sage.arith.misc import primitive_root
             return self(primitive_root(self.order()))
         F, = self.factored_unit_order()
         return self._element_of_factored_order(F)

src/sage/rings/finite_rings/integer_mod.pyx

@@ -108,7 +108,8 @@ from sage.misc.persist import register_unpickle_override
 
 from sage.structure.parent cimport Parent
 
-from sage.arith.all import crt, lcm
+from sage.arith.misc import CRT as crt
+from sage.arith.functions import lcm
 from sage.groups.generic import discrete_log
 
 
@@ -1298,7 +1299,7 @@ cdef class IntegerMod_abstract(FiniteRingElement):
                     vmod.append(w)
                     moduli.append(k)
                 # Now combine in all possible ways using the CRT
-                from sage.arith.all import CRT_basis
+                from sage.arith.misc import CRT_basis
                 basis = CRT_basis(moduli)
                 from sage.misc.mrange import cartesian_product_iterator
                 v = []
@@ -4464,7 +4465,7 @@ cdef class IntegerMod_to_Integer(Map):
             Set of Morphisms from Finite Field of size 2 to Integer Ring in Category of sets
         """
         import sage.categories.homset
-        from sage.categories.all import Sets
+        from sage.categories.sets_cat import Sets
         Morphism.__init__(self, sage.categories.homset.Hom(R, integer_ring.ZZ, Sets()))
 
     cpdef Element _call_(self, x):

src/sage/rings/finite_rings/integer_mod_ring.py

@@ -62,7 +62,9 @@
 
 import sage.misc.prandom as random
 
-from sage.arith.all import factor, primitive_root, CRT_basis
+from sage.arith.misc import factor
+from sage.arith.misc import primitive_root
+from sage.arith.misc import CRT_basis
 import sage.rings.ring as ring
 import sage.rings.abc
 from . import integer_mod

src/sage/rings/finite_rings/residue_field.pyx

@@ -870,7 +870,7 @@ cdef class ReductionMap(Map):
         self._PBinv = PBinv
         self._to_order = to_order # used for lift
         self._PB = PB # used for lift
-        from sage.categories.all import SetsWithPartialMaps
+        from sage.categories.sets_with_partial_maps import SetsWithPartialMaps
         self._repr_type_str = "Partially defined reduction"
         Map.__init__(self, Hom(K, F, SetsWithPartialMaps()))
 

src/sage/rings/fraction_field.py

@@ -1138,7 +1138,7 @@ def section(self):
 
         """
         from sage.categories.sets_with_partial_maps import SetsWithPartialMaps
-        from sage.categories.all import Hom
+        from sage.categories.homset import Hom
         parent = Hom(self.codomain(), self.domain(), SetsWithPartialMaps())
         return parent.__make_element_class__(FractionFieldEmbeddingSection)(self)
 

src/sage/rings/function_field/divisor.py

@@ -51,7 +51,7 @@
 from sage.misc.cachefunc import cached_method
 from sage.misc.latex import latex
 
-from sage.arith.all import lcm
+from sage.arith.functions import lcm
 
 from sage.structure.unique_representation import UniqueRepresentation
 from sage.structure.parent import Parent

src/sage/rings/function_field/function_field.py

@@ -225,7 +225,7 @@
 
 from sage.interfaces.singular import singular
 
-from sage.arith.all import lcm
+from sage.arith.functions import lcm
 
 from sage.rings.integer import Integer
 from sage.rings.ring import Field

src/sage/rings/function_field/order.py

@@ -108,7 +108,8 @@
 from sage.misc.cachefunc import cached_method
 
 from sage.modules.free_module_element import vector
-from sage.arith.all import lcm, gcd
+from sage.arith.functions import lcm
+from sage.arith.misc import GCD as gcd
 
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.algebras.all import FiniteDimensionalAlgebra

src/sage/rings/function_field/place.py

@@ -57,7 +57,7 @@
 
 from sage.misc.cachefunc import cached_method
 
-from sage.arith.all import lcm
+from sage.arith.functions import lcm
 
 from sage.rings.integer_ring import ZZ
 from sage.rings.qqbar import QQbar