gh-35263: sage.topology: Move imports from sage.graphs, `sage.hom…

…ology` into methods

    
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URL: #35263
Reported by: Matthias Köppe
Reviewer(s): David Coudert

src/sage/topology/cubical_complex.py

@@ -74,8 +74,6 @@
 from sage.rings.integer_ring import ZZ
 from sage.rings.rational_field import QQ
 from sage.matrix.constructor import matrix
-from sage.homology.chain_complex import ChainComplex
-from sage.graphs.graph import Graph
 from sage.misc.cachefunc import cached_method
 from sage.misc.superseded import deprecation
 from functools import total_ordering
@@ -1192,6 +1190,8 @@ def chain_complex(self, subcomplex=None, augmented=False,
             sage: Square.homology(subcomplex=EdgesLTR)[2] == Square.homology(subcomplex=EdgesLBR)[2]
             True
         """
+        from sage.homology.chain_complex import ChainComplex
+
         # initialize subcomplex
         if subcomplex is None:
             subcomplex = CubicalComplex()
@@ -1333,6 +1333,8 @@ def graph(self):
             sage: cubical_complexes.Sphere(2).graph()
             Graph on 8 vertices
         """
+        from sage.graphs.graph import Graph
+
         data = {}
         vertex_dict = {}
         i = 0

src/sage/topology/delta_complex.py

@@ -51,14 +51,11 @@
 
 from copy import copy
 from sage.topology.cell_complex import GenericCellComplex
-from sage.homology.chains import Chains, Cochains
 from sage.rings.integer_ring import ZZ
 from sage.rings.rational_field import QQ
 from sage.rings.integer import Integer
 from sage.matrix.constructor import matrix
 from .simplicial_complex import Simplex, lattice_paths, SimplicialComplex
-from sage.homology.chain_complex import ChainComplex
-from sage.graphs.graph import Graph
 from sage.arith.misc import binomial
 from sage.misc.cachefunc import cached_method
 
@@ -630,6 +627,8 @@ def chain_complex(self, subcomplex=None, augmented=False,
             sage: T.homology(subcomplex=A)
             {0: 0, 1: 0, 2: Z}
         """
+        from sage.homology.chain_complex import ChainComplex
+
         if subcomplex is not None:
             # relative chain complex, so don't augment the chain complex
             augmented = False
@@ -776,6 +775,8 @@ def graph(self):
             sage: delta_complexes.Simplex(4).graph() == graphs.CompleteGraph(5)
             True
         """
+        from sage.graphs.graph import Graph
+
         data = {}
         for vertex in range(len(self.n_cells(0))):
             data[vertex] = []
@@ -1523,6 +1524,8 @@ def n_chains(self, n, base_ring=None, cochains=False):
             sage: list(T.n_chains(1, QQ, cochains=True).basis())
             [\chi_(0, (0, 0)), \chi_(1, (0, 0)), \chi_(2, (0, 0))]
         """
+        from sage.homology.chains import Chains, Cochains
+
         n_cells = tuple(enumerate(self.n_cells(n)))
         if cochains:
             return Cochains(self, n, n_cells, base_ring)

src/sage/topology/simplicial_complex_morphism.py

@@ -102,15 +102,13 @@
 #
 # ****************************************************************************
 
-from .simplicial_complex import Simplex, SimplicialComplex
-from sage.matrix.constructor import matrix, zero_matrix
-from sage.rings.integer_ring import ZZ
-from sage.homology.chain_complex_morphism import ChainComplexMorphism
-from sage.combinat.permutation import Permutation
-from sage.algebras.steenrod.steenrod_algebra_misc import convert_perm
-from sage.categories.morphism import Morphism
 from sage.categories.homset import Hom
+from sage.categories.morphism import Morphism
 from sage.categories.simplicial_complexes import SimplicialComplexes
+from sage.matrix.constructor import matrix, zero_matrix
+from sage.rings.integer_ring import ZZ
+
+from .simplicial_complex import Simplex, SimplicialComplex
 
 
 def is_SimplicialComplexMorphism(x):
@@ -252,6 +250,9 @@ def __call__(self,x,orientation=False):
         for j in tup:
             fx.append(self._vertex_dictionary[j])
         if orientation:
+            from sage.algebras.steenrod.steenrod_algebra_misc import convert_perm
+            from sage.combinat.permutation import Permutation
+
             if len(set(fx)) == len(tup):
                 oriented = Permutation(convert_perm(fx)).signature()
             else:
@@ -371,6 +372,8 @@ def associated_chain_complex_morphism(self,base_ring=ZZ,augmented=False,cochain=
             {0: [0 1]
              [1 0], 1: [-1]}
         """
+        from sage.homology.chain_complex_morphism import ChainComplexMorphism
+
         max_dim = max(self.domain().dimension(),self.codomain().dimension())
         min_dim = min(self.domain().dimension(),self.codomain().dimension())
         matrices = {}

src/sage/topology/simplicial_set.py

@@ -254,7 +254,6 @@
 
 import copy
 
-from sage.graphs.graph import Graph
 from sage.matrix.constructor import matrix
 from sage.misc.cachefunc import cached_method
 from sage.misc.fast_methods import WithEqualityById
@@ -263,9 +262,6 @@
 from sage.rings.rational_field import QQ
 from sage.structure.parent import Parent
 from sage.structure.sage_object import SageObject
-from sage.homology.algebraic_topological_model import algebraic_topological_model_delta_complex
-from sage.homology.chain_complex import ChainComplex
-from sage.homology.chains import Chains, Cochains
 
 from .cell_complex import GenericCellComplex
 from .delta_complex import DeltaComplex
@@ -1686,6 +1682,8 @@ def graph(self):
             sage: Sigma3.nerve().is_connected()
             True
         """
+        from sage.graphs.graph import Graph
+
         G = Graph(loops=True, multiedges=True)
         for e in self.n_cells(1):
             G.add_edge(self.face(e,0), self.face(e,1), e)
@@ -2153,6 +2151,9 @@ def n_chains(self, n, base_ring=ZZ, cochains=False):
             return GenericCellComplex.n_chains(self, n=n,
                                                base_ring=base_ring,
                                                cochains=cochains)
+
+        from sage.homology.chains import Chains, Cochains
+
         n_cells = tuple(self.n_cells(n))
         if cochains:
             return Cochains(self, n, n_cells, base_ring)
@@ -3634,6 +3635,8 @@ def chain_complex(self, dimensions=None, base_ring=ZZ, augmented=False,
             sage: RP2.cohomology(base_ring=GF(2)) == SimplicialSet(RP2).cohomology(base_ring=GF(2))
             True
         """
+        from sage.homology.chain_complex import ChainComplex
+
         if dimensions is None:
             if not self.cells(): # Empty
                 if cochain:
@@ -3782,6 +3785,8 @@ def algebraic_topological_model(self, base_ring=None):
              1: Vector space of dimension 2 over Rational Field,
              2: Vector space of dimension 1 over Rational Field}
         """
+        from sage.homology.algebraic_topological_model import algebraic_topological_model_delta_complex
+
         if base_ring is None:
             base_ring = QQ
         return algebraic_topological_model_delta_complex(self, base_ring)

src/sage/topology/simplicial_set_constructions.py

@@ -74,7 +74,6 @@
 
 import itertools
 
-from sage.graphs.graph import Graph
 from sage.misc.latex import latex
 from sage.sets.set import Set
 from sage.structure.parent import Parent
@@ -1417,6 +1416,8 @@ def __init__(self, maps=None, vertex_name=None):
             sage: PushoutOfSimplicialSets_finite([T.base_point_map(), S2.base_point_map()], vertex_name='v').n_cells(0)[0]
             v
         """
+        from sage.graphs.graph import Graph
+
         # Import this here to prevent circular imports.
         from sage.topology.simplicial_set_morphism import SimplicialSetMorphism
         if maps and any(not isinstance(f, SimplicialSetMorphism) for f in maps):

src/sage/topology/simplicial_set_examples.py

@@ -34,7 +34,6 @@
 from pyparsing import OneOrMore, nestedExpr
 
 from sage.env import SAGE_ENV
-from sage.groups.abelian_gps.abelian_group import AbelianGroup
 from sage.misc.cachefunc import cached_method, cached_function
 from sage.misc.latex import latex
 from sage.rings.infinity import Infinity
@@ -363,6 +362,8 @@ def RealProjectiveSpace(n):
         RP^{\infty}
     """
     if n == Infinity:
+        from sage.groups.abelian_gps.abelian_group import AbelianGroup
+
         X = AbelianGroup([2]).nerve()
         X.rename('RP^oo')
         X.rename_latex('RP^{\\infty}')

src/sage/topology/simplicial_set_morphism.py

@@ -39,8 +39,6 @@
 from sage.misc.latex import latex
 from sage.rings.integer_ring import ZZ
 
-from sage.homology.chain_complex_morphism import ChainComplexMorphism
-from sage.homology.homology_morphism import InducedHomologyMorphism
 from .simplicial_set import SimplicialSet_arbitrary
 
 class SimplicialSetHomset(Homset):
@@ -1312,6 +1310,8 @@ def associated_chain_complex_morphism(self, base_ring=ZZ,
             [-+-]
             [0|0]
         """
+        from sage.homology.chain_complex_morphism import ChainComplexMorphism
+
         # One or the other chain complex is trivial between these
         # dimensions:
         max_dim = max(self.domain().dimension(), self.codomain().dimension())
@@ -1394,6 +1394,8 @@ def induced_homology_morphism(self, base_ring=None, cohomology=False):
             [-+-]
             [0|2]
         """
+        from sage.homology.homology_morphism import InducedHomologyMorphism
+
         return InducedHomologyMorphism(self, base_ring, cohomology)
 
     def _repr_type(self):