sage.combinat: Modularization fixes (imports), update # needs

src/sage/algebras/lie_algebras/bch.py

@@ -19,7 +19,7 @@
 from sage.algebras.lie_algebras.lie_algebra import LieAlgebra
 from sage.arith.misc import bernoulli
 from sage.categories.lie_algebras import LieAlgebras
-from sage.combinat.integer_vector import IntegerListsLex
+from sage.combinat.integer_lists import IntegerListsLex
 from sage.arith.misc import factorial
 from sage.rings.rational_field import QQ
 from sage.structure.element import canonical_coercion

src/sage/combinat/affine_permutation.py

@@ -12,23 +12,24 @@
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 from itertools import repeat
+
+from sage.arith.misc import binomial
+from sage.categories.affine_weyl_groups import AffineWeylGroups
+from sage.combinat.composition import Composition
+from sage.combinat.partition import Partition
+from sage.combinat.root_system.cartan_type import CartanType
 from sage.misc.cachefunc import cached_method
-from sage.misc.misc_c import prod
 from sage.misc.constant_function import ConstantFunction
+from sage.misc.lazy_import import lazy_import
+from sage.misc.misc_c import prod
 from sage.misc.prandom import randint
-
-from sage.categories.affine_weyl_groups import AffineWeylGroups
+from sage.rings.integer_ring import ZZ
 from sage.structure.list_clone import ClonableArray
-from sage.structure.unique_representation import UniqueRepresentation
 from sage.structure.parent import Parent
-from sage.rings.integer_ring import ZZ
+from sage.structure.unique_representation import UniqueRepresentation
 
-from sage.groups.perm_gps.permgroup_named import SymmetricGroup
-from sage.arith.misc import binomial
-from sage.combinat.root_system.cartan_type import CartanType
-from sage.combinat.root_system.weyl_group import WeylGroup
-from sage.combinat.composition import Composition
-from sage.combinat.partition import Partition
+lazy_import('sage.combinat.root_system.weyl_group', 'WeylGroup')
+lazy_import('sage.groups.perm_gps.permgroup_named', 'SymmetricGroup')
 
 
 class AffinePermutation(ClonableArray):

src/sage/combinat/alternating_sign_matrix.py

@@ -45,16 +45,18 @@
 from sage.matrix.constructor import matrix
 from sage.modules.free_module_element import zero_vector
 from sage.misc.cachefunc import cached_method
+from sage.misc.lazy_import import lazy_import
 from sage.rings.integer_ring import ZZ
 from sage.arith.misc import factorial
 from sage.rings.integer import Integer
-from sage.combinat.posets.lattices import LatticePoset
 from sage.combinat.gelfand_tsetlin_patterns import GelfandTsetlinPatternsTopRow
 from sage.combinat.combinatorial_map import combinatorial_map
 from sage.combinat.non_decreasing_parking_function import NonDecreasingParkingFunction
 from sage.combinat.permutation import Permutation
 from sage.combinat.six_vertex_model import SquareIceModel
 
+lazy_import('sage.combinat.posets.lattices', 'LatticePoset')
+
 
 def _inplace_height_function_gyration(hf):
     k = hf.nrows() - 1

src/sage/combinat/binary_recurrence_sequences.py

@@ -61,17 +61,19 @@
 
 
 from sage.structure.sage_object import SageObject
-from sage.matrix.constructor import matrix
-from sage.modules.free_module_element import vector
-from sage.rings.number_field.number_field import QuadraticField
 from sage.rings.finite_rings.integer_mod_ring import Integers
 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 is_prime, next_prime, next_prime_power, legendre_symbol
-from sage.functions.log import log
+from sage.misc.lazy_import import lazy_import
 from sage.misc.functional import sqrt
 
+lazy_import("sage.functions.log", "log")
+lazy_import("sage.rings.number_field.number_field", "QuadraticField")
+lazy_import("sage.matrix.constructor", "matrix")
+lazy_import("sage.modules.free_module_element", "vector")
+
 
 class BinaryRecurrenceSequence(SageObject):
 

src/sage/combinat/cluster_complex.py

@@ -49,10 +49,12 @@
 # ****************************************************************************
 
 from sage.categories.coxeter_groups import CoxeterGroups
-from sage.combinat.root_system.coxeter_group import CoxeterGroup
 from sage.combinat.subword_complex import SubwordComplex, SubwordComplexFacet
+from sage.misc.lazy_import import lazy_import
 from sage.rings.semirings.non_negative_integer_semiring import NN
 
+lazy_import('sage.combinat.root_system.coxeter_group', 'CoxeterGroup')
+
 
 class ClusterComplexFacet(SubwordComplexFacet):
     r"""

src/sage/combinat/colored_permutations.py

@@ -14,16 +14,18 @@
 from sage.structure.unique_representation import UniqueRepresentation
 from sage.misc.inherit_comparison import InheritComparisonClasscallMetaclass
 from sage.misc.cachefunc import cached_method
+from sage.misc.lazy_import import lazy_import
 from sage.misc.misc_c import prod
 from sage.arith.functions import lcm
 
 from sage.combinat.permutation import Permutations
-from sage.matrix.constructor import diagonal_matrix
 from sage.rings.finite_rings.integer_mod_ring import IntegerModRing
-from sage.rings.number_field.number_field import CyclotomicField
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.rings.integer_ring import ZZ
 
+lazy_import('sage.matrix.constructor', 'diagonal_matrix')
+lazy_import('sage.rings.number_field.number_field', 'CyclotomicField')
+
 
 class ColoredPermutation(MultiplicativeGroupElement):
     """

src/sage/combinat/constellation.py

@@ -57,13 +57,15 @@
 from sage.structure.richcmp import (op_NE, op_EQ, richcmp_not_equal,
                                     rich_to_bool)
 
-from sage.groups.perm_gps.permgroup_named import SymmetricGroup
 from sage.rings.integer import Integer
 from sage.combinat.partition import Partition
-from sage.graphs.graph import Graph
 from sage.misc.misc_c import prod
+from sage.misc.lazy_import import lazy_import
 from sage.categories.groups import Groups
 
+lazy_import('sage.graphs.graph', 'Graph')
+lazy_import('sage.graphs.digraph', 'DiGraph')
+lazy_import('sage.groups.perm_gps.permgroup_named', 'SymmetricGroup')
 
 # constructors
 
@@ -886,8 +888,6 @@ def braid_group_orbit(self):
             sage: G.num_edges()
             12
         """
-        from sage.graphs.digraph import DiGraph
-
         G = DiGraph(multiedges=True, loops=True)
         waiting = [self.relabel()]
 
@@ -1537,7 +1537,6 @@ def perms_are_connected(g, n):
         sage: perms_are_connected([S([0,1,2]),S([1,2,0])],3)
         True
     """
-    from sage.graphs.graph import Graph
     G = Graph()
     if g:
         G.add_vertices(g[0].domain())

src/sage/combinat/crystals/affine_factorization.py

@@ -10,6 +10,7 @@
 #******************************************************************************
 
 from sage.misc.lazy_attribute import lazy_attribute
+from sage.misc.lazy_import import lazy_import
 from sage.structure.parent import Parent
 from sage.structure.element_wrapper import ElementWrapper
 from sage.structure.unique_representation import UniqueRepresentation
@@ -18,9 +19,10 @@
 from sage.categories.enumerated_sets import EnumeratedSets
 from sage.categories.homset import Hom
 from sage.combinat.root_system.cartan_type import CartanType
-from sage.combinat.root_system.weyl_group import WeylGroup
 from sage.combinat.rsk import RSK
 
+lazy_import('sage.combinat.root_system.weyl_group', 'WeylGroup')
+
 
 class AffineFactorizationCrystal(UniqueRepresentation, Parent):
     r"""

src/sage/combinat/crystals/alcove_path.py

@@ -29,19 +29,21 @@
 from sage.structure.richcmp import richcmp
 from sage.categories.classical_crystals import ClassicalCrystals
 from sage.categories.loop_crystals import LoopCrystals
-from sage.graphs.digraph import DiGraph
 from sage.combinat.root_system.cartan_type import CartanType
 from sage.combinat.root_system.root_system import RootSystem
-from sage.modules.free_module_element import free_module_element as vector
 from sage.rings.integer import Integer
-from sage.combinat.root_system.weyl_group import WeylGroup
 from sage.misc.misc_c import prod
 from sage.categories.sets_cat import Sets
 from sage.misc.cachefunc import cached_method, cached_in_parent_method
+from sage.misc.lazy_import import lazy_import
 from sage.categories.highest_weight_crystals import HighestWeightCrystals
 from copy import copy
 from sage.misc.latex import latex
 
+lazy_import('sage.graphs.digraph', 'DiGraph')
+lazy_import('sage.combinat.root_system.weyl_group', 'WeylGroup')
+lazy_import('sage.modules.free_module_element', 'vector')
+
 
 class CrystalOfAlcovePaths(UniqueRepresentation, Parent):
     r"""

src/sage/combinat/crystals/fully_commutative_stable_grothendieck.py

@@ -32,10 +32,12 @@
 from sage.categories.finite_enumerated_sets import FiniteEnumeratedSets
 from sage.combinat.root_system.cartan_type import CartanType
 from sage.combinat import permutation
-from sage.groups.perm_gps.permgroup_named import SymmetricGroup
 from sage.rings.integer import Integer
 from sage.misc.inherit_comparison import InheritComparisonClasscallMetaclass
 from sage.misc.lazy_attribute import lazy_attribute
+from sage.misc.lazy_import import lazy_import
+
+lazy_import('sage.groups.perm_gps.permgroup_named', 'SymmetricGroup')
 
 
 class DecreasingHeckeFactorization(Element, metaclass=InheritComparisonClasscallMetaclass):

src/sage/combinat/crystals/littelmann_path.py

@@ -28,6 +28,7 @@
 # ***************************************************************************
 
 from sage.misc.cachefunc import cached_in_parent_method, cached_method
+from sage.misc.lazy_import import lazy_import
 from sage.structure.unique_representation import UniqueRepresentation
 from sage.structure.element_wrapper import ElementWrapper
 from sage.structure.parent import Parent
@@ -38,13 +39,14 @@
 from sage.categories.loop_crystals import (RegularLoopCrystals,
                                            KirillovReshetikhinCrystals)
 from sage.combinat.root_system.cartan_type import CartanType
-from sage.combinat.root_system.weyl_group import WeylGroup
 from sage.rings.integer import Integer
 from sage.rings.rational_field import QQ
 from sage.combinat.root_system.root_system import RootSystem
 from sage.arith.misc import integer_floor as floor
 from sage.misc.latex import latex
 
+lazy_import('sage.combinat.root_system.weyl_group', 'WeylGroup')
+
 
 class CrystalOfLSPaths(UniqueRepresentation, Parent):
     r"""

src/sage/combinat/diagram.py

@@ -29,16 +29,17 @@
 from sage.combinat.composition import Composition
 from sage.combinat.partition import Partition
 from sage.combinat.permutation import Permutations
-from sage.combinat.tableau import Tableau
-from sage.combinat.tiling import Polyomino
 from sage.combinat.skew_partition import SkewPartition
 from sage.combinat.skew_tableau import SkewTableaux
-from sage.matrix.matrix_dense import Matrix_dense
-from sage.matrix.matrix_sparse import Matrix_sparse
+from sage.combinat.tableau import Tableau
 from sage.misc.inherit_comparison import InheritComparisonClasscallMetaclass
-from sage.structure.unique_representation import UniqueRepresentation
+from sage.misc.lazy_import import lazy_import
+from sage.structure.element import Matrix
 from sage.structure.list_clone import ClonableArray
 from sage.structure.parent import Parent
+from sage.structure.unique_representation import UniqueRepresentation
+
+lazy_import('sage.combinat.tiling', 'Polyomino')
 
 
 class Diagram(ClonableArray, metaclass=InheritComparisonClasscallMetaclass):
@@ -693,7 +694,7 @@ def _element_constructor_(self, cells, n_rows=None, n_cols=None, check=True):
             return self.from_polyomino(cells)
         if isinstance(cells, Composition):
             return self.from_composition(cells)
-        if isinstance(cells, (Matrix_dense, Matrix_sparse)):
+        if isinstance(cells, Matrix):
             return self.from_zero_one_matrix(cells)
 
         return self.element_class(self, cells, n_rows, n_cols, check)

src/sage/combinat/diagram_algebras.py

@@ -25,6 +25,8 @@
 #                  https://www.gnu.org/licenses/
 # ***************************************************************************
 
+import itertools
+
 from sage.categories.associative_algebras import AssociativeAlgebras
 from sage.categories.finite_enumerated_sets import FiniteEnumeratedSets
 from sage.arith.power import generic_power
@@ -37,19 +39,19 @@
                                            set_partition_composition)
 from sage.combinat.set_partition import SetPartitions, AbstractSetPartition
 from sage.combinat.set_partition_iterator import set_partition_iterator
-from sage.combinat.symmetric_group_algebra import SymmetricGroupAlgebra_n
 from sage.combinat.permutation import Permutations
-from sage.graphs.graph import Graph
 from sage.misc.cachefunc import cached_method
-from sage.misc.lazy_attribute import lazy_attribute
 from sage.misc.flatten import flatten
+from sage.misc.lazy_attribute import lazy_attribute
+from sage.misc.lazy_import import lazy_import
 from sage.misc.misc_c import prod
 from sage.rings.integer_ring import ZZ
 from sage.rings.rational_field import QQ
 from sage.arith.misc import integer_floor as floor
 from sage.arith.misc import integer_ceil as ceil
 
-import itertools
+lazy_import('sage.graphs.graph', 'Graph')
+lazy_import('sage.combinat.symmetric_group_algebra', 'SymmetricGroupAlgebra_n')
 
 
 def partition_diagrams(k):

src/sage/combinat/dyck_word.py

@@ -94,9 +94,12 @@
 from sage.rings.rational_field import QQ
 from sage.combinat.permutation import Permutation, Permutations
 from sage.combinat.words.word import Word
-from sage.combinat.alternating_sign_matrix import AlternatingSignMatrices
 from sage.combinat.set_partition import SetPartitions
 from sage.misc.latex import latex
+from sage.misc.lazy_import import lazy_import
+
+lazy_import('sage.combinat.alternating_sign_matrix', 'AlternatingSignMatrices')
+
 
 open_symbol = 1
 close_symbol = 0

src/sage/combinat/e_one_star.py

@@ -214,8 +214,6 @@
 from sage.misc.functional import det
 from sage.structure.sage_object import SageObject
 from sage.combinat.words.morphism import WordMorphism
-from sage.matrix.constructor import matrix
-from sage.modules.free_module_element import vector
 from sage.misc.lazy_import import lazy_import
 lazy_import("sage.plot.all", "Graphics")
 lazy_import("sage.plot.colors", "Color")
@@ -226,6 +224,10 @@
 from sage.misc.cachefunc import cached_method
 from sage.structure.richcmp import richcmp_by_eq_and_lt, richcmp_method
 
+lazy_import('sage.matrix.constructor', 'matrix')
+lazy_import('sage.modules.free_module_element', 'vector')
+
+
 # matplotlib color maps, loaded on-demand
 cm = None
 

src/sage/combinat/fqsym.py

@@ -20,15 +20,17 @@
 from sage.misc.cachefunc import cached_method
 from sage.misc.bindable_class import BindableClass
 from sage.misc.lazy_attribute import lazy_attribute
+from sage.misc.lazy_import import lazy_import
 from sage.structure.parent import Parent
 from sage.structure.unique_representation import UniqueRepresentation
 from sage.categories.hopf_algebras import HopfAlgebras
 from sage.categories.realizations import Category_realization_of_parent
 from sage.combinat.free_module import CombinatorialFreeModule
 from sage.combinat.permutation import Permutations, Permutation
-from sage.groups.perm_gps.permgroup_element import PermutationGroupElement
-from sage.combinat.words.word import Word
 from sage.combinat.symmetric_group_algebra import SymmetricGroupAlgebra
+from sage.combinat.words.word import Word
+
+lazy_import('sage.groups.perm_gps.permgroup_element', 'PermutationGroupElement')
 
 
 class FQSymBasis_abstract(CombinatorialFreeModule, BindableClass):

src/sage/combinat/fully_commutative_elements.py

@@ -28,15 +28,18 @@
 # (at your option) any later version.
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
-from sage.structure.parent import Parent
-from sage.structure.list_clone import NormalizedClonableList
-from sage.categories.enumerated_sets import EnumeratedSets
-from sage.structure.unique_representation import UniqueRepresentation
-from .root_system.coxeter_matrix import CoxeterMatrix
 from collections import deque
-from sage.combinat.posets.posets import Poset
+
 from sage.categories.coxeter_groups import CoxeterGroups
-from sage.combinat.root_system.coxeter_group import CoxeterGroup
+from sage.categories.enumerated_sets import EnumeratedSets
+from sage.misc.lazy_import import lazy_import
+from sage.structure.list_clone import NormalizedClonableList
+from sage.structure.parent import Parent
+from sage.structure.unique_representation import UniqueRepresentation
+
+lazy_import('sage.combinat.posets.posets', 'Poset')
+lazy_import('sage.combinat.root_system.coxeter_group', 'CoxeterGroup')
+lazy_import('sage.combinat.root_system.coxeter_matrix', 'CoxeterMatrix')
 
 
 class FullyCommutativeElement(NormalizedClonableList):

src/sage/combinat/growth.py

@@ -476,7 +476,6 @@
 
 from sage.structure.sage_object import SageObject
 from sage.structure.unique_representation import UniqueRepresentation
-from sage.combinat.posets.posets import Poset
 from sage.combinat.words.word import Word
 from sage.combinat.words.words import Words
 from sage.combinat.binary_tree import BinaryTree, BinaryTrees, LabelledBinaryTree