Lazy imports for WeylGroup, root systems, crystals and other combinatorics features

src/sage/algebras/affine_nil_temperley_lieb.py

@@ -9,7 +9,6 @@
 # ****************************************************************************
 from sage.categories.algebras_with_basis import AlgebrasWithBasis
 from sage.combinat.root_system.cartan_type import CartanType
-from sage.combinat.root_system.weyl_group import WeylGroup
 from sage.rings.ring import Ring
 from sage.rings.integer_ring import ZZ
 from sage.combinat.free_module import CombinatorialFreeModule
@@ -57,6 +56,7 @@ def __init__(self, n, R=ZZ, prefix='a'):
             raise TypeError("argument R must be a ring")
         self._cartan_type = CartanType(['A', n - 1, 1])
         self._n = n
+        from sage.combinat.root_system.weyl_group import WeylGroup
         W = WeylGroup(self._cartan_type)
         self._prefix = prefix
         self._index_set = W.index_set()

src/sage/algebras/iwahori_hecke_algebra.py

@@ -36,7 +36,6 @@
 from sage.rings.integer_ring import ZZ
 from sage.rings.polynomial.laurent_polynomial_ring import LaurentPolynomialRing
 from sage.arith.misc import is_square
-from sage.combinat.root_system.coxeter_group import CoxeterGroup
 from sage.sets.family import Family
 from sage.combinat.free_module import CombinatorialFreeModule
 
@@ -445,6 +444,7 @@ def __classcall_private__(cls, W, q1, q2=-1, base_ring=None):
             True
         """
         if W not in CoxeterGroups():
+            from sage.combinat.root_system.coxeter_group import CoxeterGroup
             W = CoxeterGroup(W)
         if base_ring is None:
             base_ring = q1.parent()
@@ -2018,6 +2018,7 @@ def __init__(self, IHAlgebra, prefix=None):
             if isinstance(IHAlgebra._W, Coxeter3Group):
                 self._W_Coxeter3 = IHAlgebra._W
             else:
+                from sage.combinat.root_system.coxeter_group import CoxeterGroup
                 self._W_Coxeter3 = CoxeterGroup(IHAlgebra._W.coxeter_type(), implementation='coxeter3')
 
         def hash_involution_on_basis(self, w):
@@ -2751,6 +2752,7 @@ def __classcall_private__(cls, W):
             True
         """
         if W not in CoxeterGroups():
+            from sage.combinat.root_system.coxeter_group import CoxeterGroup
             W = CoxeterGroup(W)
         return super().__classcall__(cls, W)
 

src/sage/combinat/all.py

@@ -95,7 +95,7 @@
 
 # Permutations
 from .permutation import Permutation, Permutations, Arrangements, CyclicPermutations, CyclicPermutationsOfPartition
-from .affine_permutation import AffinePermutationGroup
+lazy_import('sage.combinat.affine_permutation', 'AffinePermutationGroup')
 lazy_import('sage.combinat.colored_permutations', ['ColoredPermutations',
                                                    'SignedPermutation',
                                                    'SignedPermutations'])
@@ -203,10 +203,10 @@
             ['ParkingFunctions', 'ParkingFunction'])
 
 # Trees and Tamari interval posets
-from .ordered_tree import (OrderedTree, OrderedTrees,
-                          LabelledOrderedTree, LabelledOrderedTrees)
-from .binary_tree import (BinaryTree, BinaryTrees,
-                         LabelledBinaryTree, LabelledBinaryTrees)
+lazy_import('sage.combinat.ordered_tree', ['OrderedTree', 'OrderedTrees',
+                                           'LabelledOrderedTree', 'LabelledOrderedTrees'])
+lazy_import('sage.combinat.binary_tree', ['BinaryTree', 'BinaryTrees',
+                                          'LabelledBinaryTree', 'LabelledBinaryTrees'])
 lazy_import('sage.combinat.interval_posets', ['TamariIntervalPoset', 'TamariIntervalPosets'])
 lazy_import('sage.combinat.rooted_tree', ('RootedTree', 'RootedTrees',
                          'LabelledRootedTree', 'LabelledRootedTrees'))

src/sage/combinat/k_tableau.py

@@ -37,7 +37,6 @@
 from sage.misc.inherit_comparison import InheritComparisonClasscallMetaclass
 from sage.combinat.skew_tableau import SkewTableau, SemistandardSkewTableaux
 from sage.combinat.partition import Partition, Partitions
-from sage.combinat.root_system.weyl_group import WeylGroup
 from sage.combinat.core import Core
 from sage.rings.integer_ring import ZZ
 from sage.functions.generalized import sgn
@@ -1826,6 +1825,7 @@ def straighten_input(t, k):
             ...
             ValueError: inconsistent number of rows: should be 4 but got 5
         """
+        from sage.combinat.root_system.weyl_group import WeylGroup
         W = WeylGroup(['A', k, 1], prefix='s')
         if len(t) > 0:
             if isinstance(t[0], (list, tuple)):
@@ -1864,6 +1864,7 @@ def __classcall_private__(cls, t, k, inner_shape = []):
         """
         if isinstance(t, cls):
             return t
+        from sage.combinat.root_system.weyl_group import WeylGroup
         W = WeylGroup(['A', k, 1], prefix='s')
         w = cls.straighten_input(t, k)
         weight = tuple(w[i].length() for i in range(len(w) - 1, -1, -1))

src/sage/combinat/partition.py

@@ -320,7 +320,6 @@
 from sage.combinat.integer_lists.invlex import IntegerListsBackend_invlex
 from sage.combinat.integer_vector_weighted import iterator_fast as weighted_iterator_fast
 from sage.combinat.combinat_cython import conjugate
-from sage.combinat.root_system.weyl_group import WeylGroup
 from sage.combinat.combinatorial_map import combinatorial_map
 from sage.groups.perm_gps.permgroup import PermutationGroup
 from sage.graphs.dot2tex_utils import have_dot2tex
@@ -4633,6 +4632,7 @@ def from_kbounded_to_grassmannian(self, k):
             [0 1 0]
             [0 0 1]
         """
+        from sage.combinat.root_system.weyl_group import WeylGroup
         return WeylGroup(['A', k,1 ]).from_reduced_word(self.from_kbounded_to_reduced_word(k))
 
     def to_list(self):

src/sage/combinat/root_system/all.py

@@ -121,12 +121,13 @@
 
 from sage.misc.lazy_import import lazy_import
 
-from .cartan_type import CartanType
-from .dynkin_diagram import DynkinDiagram
-from .cartan_matrix import CartanMatrix
-from .coxeter_matrix import CoxeterMatrix
-from .coxeter_type import CoxeterType
-from .root_system import RootSystem, WeylDim
+lazy_import('sage.combinat.root_system.cartan_type', 'CartanType')
+lazy_import('sage.combinat.root_system.dynkin_diagram', 'DynkinDiagram')
+lazy_import('sage.combinat.root_system.cartan_matrix', 'CartanMatrix')
+lazy_import('sage.combinat.root_system.coxeter_matrix', 'CoxeterMatrix')
+lazy_import('sage.combinat.root_system.coxeter_type', 'CoxeterType')
+lazy_import('sage.combinat.root_system.root_system', 'RootSystem')
+lazy_import('sage.combinat.root_system.root_system', 'WeylDim')
 lazy_import('sage.combinat.root_system.weyl_group', ['WeylGroup',
                                                      'WeylGroupElement'])
 lazy_import('sage.combinat.root_system.reflection_group_real',

src/sage/groups/perm_gps/permgroup.py

@@ -150,7 +150,8 @@
 from sage.groups.perm_gps.constructor import PermutationGroupElement as PermutationConstructor, standardize_generator
 from sage.groups.abelian_gps.abelian_group import AbelianGroup
 from sage.misc.cachefunc import cached_method
-from sage.groups.class_function import ClassFunction_libgap
+from sage.misc.lazy_import import lazy_import
+lazy_import('sage.groups.class_function', 'ClassFunction_libgap')
 from sage.sets.finite_enumerated_set import FiniteEnumeratedSet
 from sage.categories.finite_enumerated_sets import FiniteEnumeratedSets
 from sage.groups.conjugacy_classes import ConjugacyClassGAP

src/sage/modular/arithgroup/congroup_gamma.py

@@ -298,6 +298,7 @@ def image_mod_n(self):
             [0 1]
             )
         """
+        from sage.groups.matrix_gps.finitely_generated import MatrixGroup
         return MatrixGroup([matrix(Zmod(self.level()), 2, 2, 1)])
 
 

src/sage/modular/arithgroup/congroup_gammaH.py

@@ -28,7 +28,6 @@
 from sage.misc.cachefunc import cached_method
 from sage.rings.integer_ring import ZZ
 from sage.rings.finite_rings.integer_mod_ring import Zmod
-from sage.groups.matrix_gps.finitely_generated import MatrixGroup
 from sage.matrix.constructor import matrix
 from sage.structure.richcmp import richcmp_method, richcmp
 
@@ -1289,6 +1288,7 @@ def image_mod_n(self):
             raise NotImplementedError("matrix groups over ring of integers modulo 1 not implemented")
         gens = [matrix(Zmod(N), 2, 2, [x, 0, 0, Zmod(N).one() / x]) for x in self._generators_for_H()]
         gens += [matrix(Zmod(N), 2, 2, [1, 1, 0, 1])]
+        from sage.groups.matrix_gps.finitely_generated import MatrixGroup
         return MatrixGroup(gens)
 
     def atkin_lehner_matrix(self, Q):

src/sage/modular/hecke/ambient_module.py

@@ -30,8 +30,6 @@
 import sage.matrix.matrix_space as matrix_space
 from sage.matrix.constructor import matrix
 
-from sage.modular.arithgroup.all import Gamma0  # for Sturm bound
-
 
 def is_AmbientHeckeModule(x) -> bool:
     r"""
@@ -488,6 +486,7 @@ def free_module(self):
             sage: ModularForms(59, 2).free_module()
             Vector space of dimension 6 over Rational Field
         """
+        from sage.modular.arithgroup.all import Gamma0
         try:
             return self.__free_module
         except AttributeError:
@@ -518,6 +517,8 @@ def hecke_bound(self):
             15
         """
         from sage.misc.verbose import verbose
+        from sage.modular.arithgroup.all import Gamma0
+
         try:
             if self.is_cuspidal():
                 return Gamma0(self.level()).sturm_bound(self.weight())