sage.{algebras,combinat}: Consolidate imports from the same module

Matthias Koeppe · Matthias Koeppe · commit 8e77597c00f4 · 2023-01-29T18:15:43.000-08:00
diff --git a/src/sage/algebras/quatalg/quaternion_algebra.py b/src/sage/algebras/quatalg/quaternion_algebra.py
@@ -35,12 +35,12 @@
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
-from sage.arith.misc import hilbert_conductor_inverse
-from sage.arith.misc import hilbert_conductor
-from sage.arith.misc import factor
-from sage.arith.misc import GCD as gcd
-from sage.arith.misc import kronecker as kronecker_symbol
-from sage.arith.misc import valuation
+from sage.arith.misc import (hilbert_conductor_inverse,
+                             hilbert_conductor,
+                             factor,
+                             GCD as gcd,
+                             kronecker as kronecker_symbol,
+                             valuation)
 from sage.rings.real_mpfr import RR
 from sage.rings.integer import Integer
 from sage.rings.integer_ring import ZZ
diff --git a/src/sage/combinat/binary_recurrence_sequences.py b/src/sage/combinat/binary_recurrence_sequences.py
@@ -66,10 +66,7 @@
 from sage.rings.finite_rings.finite_field_constructor import GF
 from sage.rings.integer import Integer
 from sage.arith.functions import lcm
-from sage.arith.misc import next_prime
-from sage.arith.misc import is_prime
-from sage.arith.misc import next_prime_power
-from sage.arith.misc import legendre_symbol
+from sage.arith.misc import is_prime, next_prime, next_prime_power, legendre_symbol
 from sage.functions.log import log
 from sage.misc.functional import sqrt
 
diff --git a/src/sage/combinat/cluster_algebra_quiver/quiver.py b/src/sage/combinat/cluster_algebra_quiver/quiver.py
@@ -558,8 +558,7 @@ def plot(self, circular=True, center=(0, 0), directed=True, mark=None,
         """
         from sage.plot.colors import rainbow
         from sage.graphs.graph_generators import GraphGenerators
-        from sage.symbolic.constants import e
-        from sage.symbolic.constants import pi
+        from sage.symbolic.constants import e, pi
         from sage.rings.imaginary_unit import I
         graphs = GraphGenerators()
         # returns positions for graph vertices on two concentric cycles with radius 1 and 2
diff --git a/src/sage/combinat/cluster_algebra_quiver/quiver_mutation_type.py b/src/sage/combinat/cluster_algebra_quiver/quiver_mutation_type.py
@@ -27,8 +27,7 @@
 from sage.rings.infinity import infinity
 from sage.graphs.digraph import DiGraph
 from sage.graphs.graph import Graph
-from sage.arith.misc import binomial
-from sage.arith.misc import euler_phi
+from sage.arith.misc import binomial, euler_phi
 from sage.misc.misc_c import prod
 from sage.matrix.constructor import matrix
 
diff --git a/src/sage/combinat/combinat.py b/src/sage/combinat/combinat.py
@@ -167,12 +167,11 @@
 from __future__ import annotations
 from typing import Iterator
 
+from sage.arith.misc import bernoulli, factorial
 from sage.rings.integer_ring import ZZ
 from sage.rings.rational_field import QQ
 from sage.rings.integer import Integer
 from sage.rings.infinity import infinity
-from sage.arith.misc import bernoulli
-from sage.arith.misc import factorial
 from sage.rings.polynomial.polynomial_element import Polynomial
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.libs.pari.all import pari
diff --git a/src/sage/combinat/designs/bibd.py b/src/sage/combinat/designs/bibd.py
@@ -53,8 +53,7 @@
 from sage.categories.sets_cat import EmptySetError
 from sage.misc.unknown import Unknown
 from .design_catalog import transversal_design  # type:ignore
-from sage.arith.misc import binomial
-from sage.arith.misc import is_prime_power
+from sage.arith.misc import binomial, is_prime_power
 from .group_divisible_designs import GroupDivisibleDesign
 from .designs_pyx import is_pairwise_balanced_design
 
diff --git a/src/sage/combinat/designs/block_design.py b/src/sage/combinat/designs/block_design.py
@@ -52,15 +52,13 @@
 # (at your option) any later version.
 #                  https://www.gnu.org/licenses/
 #*****************************************************************************
+from sage.arith.misc import binomial, integer_floor, is_prime_power
+from sage.categories.sets_cat import EmptySetError
 from sage.modules.free_module import VectorSpace
 from sage.rings.integer import Integer
 from sage.rings.integer_ring import ZZ
-from sage.arith.misc import binomial
-from sage.arith.misc import integer_floor
-from sage.arith.misc import is_prime_power
 from .incidence_structures import IncidenceStructure
 from sage.rings.finite_rings.finite_field_constructor import FiniteField
-from sage.categories.sets_cat import EmptySetError
 from sage.misc.unknown import Unknown
 from sage.matrix.matrix_space import MatrixSpace
 from sage.libs.gap.libgap import libgap
diff --git a/src/sage/combinat/designs/difference_matrices.py b/src/sage/combinat/designs/difference_matrices.py
@@ -10,12 +10,11 @@
 ---------
 """
 
+from sage.arith.misc import divisors, is_prime_power
 from sage.misc.unknown import Unknown
 from sage.misc.cachefunc import cached_function
 from sage.categories.sets_cat import EmptySetError
 from sage.rings.finite_rings.finite_field_constructor import FiniteField
-from sage.arith.misc import is_prime_power
-from sage.arith.misc import divisors
 from .designs_pyx import is_difference_matrix
 from .database import DM as DM_constructions
 
diff --git a/src/sage/combinat/matrices/hadamard_matrix.py b/src/sage/combinat/matrices/hadamard_matrix.py
@@ -54,22 +54,23 @@
 #                  https://www.gnu.org/licenses/
 #*****************************************************************************
 
+from math import sqrt
 from urllib.request import urlopen
-from sage.combinat.designs.difference_family import skew_supplementary_difference_set
 
+from sage.arith.misc import divisors, is_prime_power, is_square
+from sage.combinat.designs.difference_family import skew_supplementary_difference_set
+from sage.combinat.t_sequences import T_sequences_smallcases
+from sage.cpython.string import bytes_to_str
 from sage.rings.integer_ring import ZZ
-from sage.matrix.constructor import matrix, block_matrix, block_diagonal_matrix, diagonal_matrix
-from sage.arith.misc import is_square
-from sage.arith.misc import is_prime_power
-from sage.arith.misc import divisors
-from math import sqrt
-from sage.matrix.constructor import identity_matrix as I
-from sage.matrix.constructor import ones_matrix as J
-from sage.matrix.constructor import zero_matrix
+from sage.matrix.constructor import (block_matrix,
+                                     block_diagonal_matrix,
+                                     diagonal_matrix,
+                                     identity_matrix as I,
+                                     ones_matrix as J,
+                                     matrix,
+                                     zero_matrix)
 from sage.misc.unknown import Unknown
-from sage.cpython.string import bytes_to_str
 from sage.modules.free_module_element import vector
-from sage.combinat.t_sequences import T_sequences_smallcases
 
 
 def normalise_hadamard(H):
diff --git a/src/sage/combinat/necklace.py b/src/sage/combinat/necklace.py
@@ -22,18 +22,14 @@
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
-from sage.combinat.composition import Composition
+from sage.arith.misc import divisors, euler_phi, factorial, GCD as gcd
 from sage.categories.finite_enumerated_sets import FiniteEnumeratedSets
-from sage.structure.parent import Parent
-from sage.structure.unique_representation import UniqueRepresentation
-from sage.arith.misc import euler_phi
-from sage.arith.misc import factorial
-from sage.arith.misc import divisors
-from sage.arith.misc import GCD as gcd
-from sage.rings.integer_ring import ZZ
+from sage.combinat.composition import Composition
+from sage.combinat.misc import DoublyLinkedList
 from sage.rings.integer import Integer
 from sage.misc.misc_c import prod
-from sage.combinat.misc import DoublyLinkedList
+from sage.structure.parent import Parent
+from sage.structure.unique_representation import UniqueRepresentation
 
 
 def Necklaces(content):
diff --git a/src/sage/combinat/partition.py b/src/sage/combinat/partition.py
@@ -283,10 +283,9 @@
 from copy import copy
 from itertools import accumulate
 
+from sage.arith.misc import binomial, factorial, GCD as gcd, multinomial
 from sage.libs.pari.all import pari
 from sage.libs.flint.arith import number_of_partitions as flint_number_of_partitions
-
-from sage.arith.misc import multinomial
 from sage.structure.global_options import GlobalOptions
 from sage.structure.parent import Parent
 from sage.structure.unique_representation import UniqueRepresentation
@@ -308,8 +307,6 @@
 from sage.rings.integer_ring import ZZ
 from sage.rings.rational_field import QQ
 from sage.rings.semirings.non_negative_integer_semiring import NN
-from sage.arith.misc import factorial
-from sage.arith.misc import GCD as gcd
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.rings.integer import Integer
 from sage.rings.infinity import infinity
@@ -327,7 +324,6 @@
 from sage.combinat.combinatorial_map import combinatorial_map
 from sage.groups.perm_gps.permgroup import PermutationGroup
 from sage.graphs.dot2tex_utils import have_dot2tex
-from sage.arith.misc import binomial
 
 
 class Partition(CombinatorialElement):
diff --git a/src/sage/combinat/partition_algebra.py b/src/sage/combinat/partition_algebra.py
@@ -15,19 +15,19 @@
 #
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
-from .combinat import catalan_number
-from sage.combinat.free_module import CombinatorialFreeModule
+from sage.arith.misc import binomial, factorial
 from sage.categories.algebras_with_basis import AlgebrasWithBasis
-from sage.combinat.set_partition import SetPartition, SetPartitions, SetPartitions_set
-from sage.sets.set import Set, Set_generic
+from sage.functions.all import ceil
 from sage.graphs.graph import Graph
-from sage.arith.misc import factorial
-from sage.arith.misc import binomial
-from .permutation import Permutations
 from sage.rings.integer_ring import ZZ
 from sage.rings.rational_field import QQ
+from sage.sets.set import Set, Set_generic
+
+from .combinat import catalan_number
+from .free_module import CombinatorialFreeModule
+from .permutation import Permutations
+from .set_partition import SetPartition, SetPartitions, SetPartitions_set
 from .subset import Subsets
-from sage.functions.all import ceil
 
 
 def _int_or_half_int(k):
diff --git a/src/sage/combinat/permutation.py b/src/sage/combinat/permutation.py
@@ -239,38 +239,38 @@
 # ****************************************************************************
 from __future__ import annotations
 from typing import Iterator
+import itertools
 
-from sage.structure.parent import Parent
-from sage.structure.unique_representation import UniqueRepresentation
-from sage.categories.infinite_enumerated_sets import InfiniteEnumeratedSets
+from sage.arith.misc import factorial, multinomial
 from sage.categories.finite_enumerated_sets import FiniteEnumeratedSets
-from sage.categories.sets_with_grading import SetsWithGrading
-from sage.categories.finite_weyl_groups import FiniteWeylGroups
 from sage.categories.finite_permutation_groups import FinitePermutationGroups
-from sage.structure.list_clone import ClonableArray
-from sage.structure.global_options import GlobalOptions
+from sage.categories.finite_weyl_groups import FiniteWeylGroups
+from sage.categories.infinite_enumerated_sets import InfiniteEnumeratedSets
+from sage.categories.sets_with_grading import SetsWithGrading
+from sage.graphs.digraph import DiGraph
+from sage.groups.perm_gps.permgroup_element import PermutationGroupElement
+from sage.groups.perm_gps.permgroup_named import SymmetricGroup
 from sage.libs.gap.libgap import libgap
+from sage.matrix.matrix_space import MatrixSpace
+from sage.misc.cachefunc import cached_method
+from sage.misc.prandom import sample
 from sage.rings.integer import Integer
 from sage.rings.integer_ring import ZZ
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-from sage.arith.misc import factorial
-from sage.arith.misc import multinomial
-from sage.matrix.matrix_space import MatrixSpace
-from sage.combinat.tools import transitive_ideal
-from sage.combinat.composition import Composition
-from sage.groups.perm_gps.permgroup_named import SymmetricGroup
-from sage.groups.perm_gps.permgroup_element import PermutationGroupElement
-from sage.misc.prandom import sample
-from sage.graphs.digraph import DiGraph
-import itertools
-from .combinat import CombinatorialElement, catalan_number
-from sage.misc.cachefunc import cached_method
+from sage.structure.global_options import GlobalOptions
+from sage.structure.list_clone import ClonableArray
+from sage.structure.parent import Parent
+from sage.structure.unique_representation import UniqueRepresentation
+
 from .backtrack import GenericBacktracker
-from sage.combinat.combinatorial_map import combinatorial_map
-from sage.combinat.rsk import RSK, RSK_inverse
-from sage.combinat.permutation_cython import (left_action_product,
-             right_action_product, left_action_same_n, right_action_same_n,
-             map_to_list, next_perm)
+from .combinat import CombinatorialElement, catalan_number
+from .combinatorial_map import combinatorial_map
+from .composition import Composition
+from .permutation_cython import (left_action_product, right_action_product,
+                                 left_action_same_n, right_action_same_n,
+                                 map_to_list, next_perm)
+from .rsk import RSK, RSK_inverse
+from .tools import transitive_ideal
 
 
 class Permutation(CombinatorialElement):
diff --git a/src/sage/combinat/set_partition_ordered.py b/src/sage/combinat/set_partition_ordered.py
@@ -24,8 +24,7 @@
 #
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
-from sage.arith.misc import factorial
-from sage.arith.misc import multinomial
+from sage.arith.misc import factorial, multinomial
 from sage.categories.cartesian_product import cartesian_product
 from sage.categories.finite_enumerated_sets import FiniteEnumeratedSets
 from sage.categories.infinite_enumerated_sets import InfiniteEnumeratedSets
diff --git a/src/sage/combinat/sf/character.py b/src/sage/combinat/sf/character.py
@@ -27,13 +27,11 @@
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
-from sage.combinat.sf.sfa import SymmetricFunctionAlgebra_generic as SFA_generic
-from sage.misc.cachefunc import cached_method
+from sage.arith.misc import binomial, divisors, moebius
 from sage.categories.homset import Hom
 from sage.categories.morphism import SetMorphism
-from sage.arith.misc import divisors
-from sage.arith.misc import moebius
-from sage.arith.misc import binomial
+from sage.combinat.sf.sfa import SymmetricFunctionAlgebra_generic as SFA_generic
+from sage.misc.cachefunc import cached_method
 from sage.rings.integer import Integer
 
 
diff --git a/src/sage/combinat/sf/elementary.py b/src/sage/combinat/sf/elementary.py
@@ -17,13 +17,14 @@
 #
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
-from . import multiplicative, classical
+from sage.arith.misc import binomial, factorial
 from sage.combinat.partition import Partition
 from sage.misc.misc_c import prod
-from sage.arith.misc import factorial
-from sage.arith.misc import binomial
 from sage.rings.infinity import infinity
 
+from . import multiplicative, classical
+
+
 ###################################
 #                                 #
 # Elementary Symmetric Functions  #
diff --git a/src/sage/combinat/sf/homogeneous.py b/src/sage/combinat/sf/homogeneous.py
@@ -25,12 +25,12 @@
 # Homogeneous Symmetric Functions  #
 #                                  #
 ####################################
-from . import multiplicative, classical
+from sage.arith.misc import binomial, factorial
 from sage.combinat.partition import Partition
-from sage.rings.infinity import infinity
 from sage.misc.misc_c import prod
-from sage.arith.misc import factorial
-from sage.arith.misc import binomial
+from sage.rings.infinity import infinity
+
+from . import multiplicative, classical
 
 
 class SymmetricFunctionAlgebra_homogeneous(multiplicative.SymmetricFunctionAlgebra_multiplicative):
diff --git a/src/sage/combinat/sf/sfa.py b/src/sage/combinat/sf/sfa.py
@@ -1013,8 +1013,7 @@ def gessel_reutenauer(self, lam):
                 m = lam.to_exp_dict() # == {i: m_i | i occurs in lam}
                 p = self.realization_of().power()
                 h = self.realization_of().complete()
-                from sage.arith.misc import moebius
-                from sage.arith.misc import squarefree_divisors
+                from sage.arith.misc import moebius, squarefree_divisors
                 mu = moebius
 
                 def component(i, g):  # == h_g[L_i]
diff --git a/src/sage/combinat/similarity_class_type.py b/src/sage/combinat/similarity_class_type.py
@@ -189,23 +189,24 @@ class type, it is also possible to compute the number of classes of that type
 # ****************************************************************************
 
 from itertools import chain, product
-from sage.misc.misc_c import prod
-from sage.arith.misc import factorial
-from sage.arith.misc import moebius
-from sage.arith.misc import divisors
-from sage.misc.inherit_comparison import InheritComparisonClasscallMetaclass
-from sage.structure.element import Element, is_Matrix
-from sage.structure.parent import Parent
-from sage.structure.unique_representation import UniqueRepresentation
+
+from sage.arith.misc import divisors, factorial, moebius
 from sage.categories.finite_enumerated_sets import FiniteEnumeratedSets
-from sage.combinat.combinat import CombinatorialElement
-from sage.combinat.partition import Partitions, Partition
+from sage.misc.cachefunc import cached_in_parent_method, cached_function
+from sage.misc.inherit_comparison import InheritComparisonClasscallMetaclass
+from sage.misc.misc_c import prod
 from sage.rings.fraction_field import FractionField
 from sage.rings.integer_ring import ZZ
-from sage.rings.rational_field import QQ
-from sage.misc.cachefunc import cached_in_parent_method, cached_function
-from sage.combinat.misc import IterableFunctionCall
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
+from sage.rings.rational_field import QQ
+from sage.structure.element import Element, is_Matrix
+from sage.structure.parent import Parent
+from sage.structure.unique_representation import UniqueRepresentation
+
+from .combinat import CombinatorialElement
+from .misc import IterableFunctionCall
+from .partition import Partitions, Partition
+
 
 @cached_function
 def fq(n, q=None):
diff --git a/src/sage/combinat/species/cycle_species.py b/src/sage/combinat/species/cycle_species.py
diff --git a/src/sage/combinat/tableau.py b/src/sage/combinat/tableau.py
diff --git a/src/sage/combinat/words/lyndon_word.py b/src/sage/combinat/words/lyndon_word.py
