sage.matroids: Import fixes, # needs copied from #35095

Author: Matthias Koeppe

src/sage/matroids/advanced.py

@@ -59,4 +59,6 @@
 from . import lean_matrix
 from .extension import LinearSubclasses, MatroidExtensions
 from .union_matroid import MatroidUnion, MatroidSum, PartitionMatroid
-from .graphic_matroid import GraphicMatroid
+
+from sage.misc.lazy_import import lazy_import
+lazy_import('sage.matroids.graphic_matroid', 'GraphicMatroid')

src/sage/matroids/catalog.py

@@ -46,6 +46,10 @@
 from sage.misc.lazy_import import lazy_import
 from sage.rings.integer_ring import ZZ
 
+lazy_import('sage.rings.finite_rings.finite_field_constructor', 'GF')
+lazy_import('sage.schemes.projective.projective_space', 'ProjectiveSpace')
+
+
 # The order is the same as in Oxley.
 
 
@@ -134,7 +138,7 @@ def R6():
         True
         sage: M.is_connected()
         True
-        sage: M.is_3connected()
+        sage: M.is_3connected()                                                         # needs sage.graphs
         False
     """
     A = Matrix(GF(3), [
@@ -166,7 +170,7 @@ def Fano():
         sage: setprint(sorted(M.nonspanning_circuits()))
         [{'a', 'b', 'f'}, {'a', 'c', 'e'}, {'a', 'd', 'g'}, {'b', 'c', 'd'},
          {'b', 'e', 'g'}, {'c', 'f', 'g'}, {'d', 'e', 'f'}]
-        sage: M.delete(M.groundset_list()[randrange(0,
+        sage: M.delete(M.groundset_list()[randrange(0,                                  # needs sage.graphs
         ....:                  7)]).is_isomorphic(matroids.CompleteGraphic(4))
         True
     """
@@ -197,9 +201,9 @@ def NonFano():
         sage: setprint(M.nonbases())
         [{'a', 'b', 'f'}, {'a', 'c', 'e'}, {'a', 'd', 'g'}, {'b', 'c', 'd'},
          {'b', 'e', 'g'}, {'c', 'f', 'g'}]
-        sage: M.delete('f').is_isomorphic(matroids.CompleteGraphic(4))
+        sage: M.delete('f').is_isomorphic(matroids.CompleteGraphic(4))                  # needs sage.graphs
         True
-        sage: M.delete('g').is_isomorphic(matroids.CompleteGraphic(4))
+        sage: M.delete('g').is_isomorphic(matroids.CompleteGraphic(4))                  # needs sage.graphs
         False
     """
     A = Matrix(GF(3), [
@@ -226,7 +230,7 @@ def O7():
 
         sage: M = matroids.named_matroids.O7(); M
         O7: Ternary matroid of rank 3 on 7 elements, type 0+
-        sage: M.delete('e').is_isomorphic(matroids.CompleteGraphic(4))
+        sage: M.delete('e').is_isomorphic(matroids.CompleteGraphic(4))                  # needs sage.graphs
         True
         sage: M.tutte_polynomial()
         y^4 + x^3 + x*y^2 + 3*y^3 + 4*x^2 + 5*x*y + 5*y^2 + 4*x + 4*y
@@ -257,7 +261,7 @@ def P7():
         P7: Ternary matroid of rank 3 on 7 elements, type 1+
         sage: M.f_vector()
         [1, 7, 11, 1]
-        sage: M.has_minor(matroids.CompleteGraphic(4))
+        sage: M.has_minor(matroids.CompleteGraphic(4))                                  # needs sage.graphs
         False
         sage: M.is_valid()
         True
@@ -585,7 +589,7 @@ def J():
         [{'a', 'b', 'f'}, {'a', 'c', 'g'}, {'a', 'd', 'h'}]
         sage: M.is_isomorphic(M.dual())
         True
-        sage: M.has_minor(matroids.CompleteGraphic(4))
+        sage: M.has_minor(matroids.CompleteGraphic(4))                                  # needs sage.graphs
         False
         sage: M.is_valid()
         True
@@ -692,6 +696,8 @@ def K33dual():
         sage: M.is_valid()                      # long time, needs sage.graphs
         True
     """
+    from sage.graphs.graph_generators import graphs
+
     E = 'abcdefghi'
     G = graphs.CompleteBipartiteGraph(3, 3)
     M = Matroid(groundset=E, graph=G, regular=True)
@@ -763,6 +769,8 @@ def CompleteGraphic(n):
         sage: M.is_valid()
         True
     """
+    from sage.graphs.graph_generators import graphs
+
     M = Matroid(groundset=list(range((n * (n - 1)) // 2)),
                 graph=graphs.CompleteGraph(n))
     M.rename('M(K' + str(n) + '): ' + repr(M))
@@ -858,7 +866,7 @@ def Whirl(n):
         sage: M.is_isomorphic(matroids.Wheel(5))
         False
         sage: M = matroids.Whirl(3)
-        sage: M.is_isomorphic(matroids.CompleteGraphic(4))
+        sage: M.is_isomorphic(matroids.CompleteGraphic(4))                              # needs sage.graphs
         False
 
     .. TODO::

src/sage/matroids/constructor.py

@@ -103,7 +103,6 @@
 
 from itertools import combinations
 from sage.matrix.constructor import Matrix
-from sage.graphs.graph import Graph
 from sage.structure.element import is_Matrix
 from sage.rings.integer_ring import ZZ
 from sage.rings.rational_field import QQ
@@ -493,7 +492,7 @@ def Matroid(groundset=None, data=None, **kwds):
             ....:         matrix=[[1, 1, 0], [1, 0, 1], [0, 1, 1]],
             ....:         field=GF(4, 'x'))
             Quaternary matroid of rank 3 on 6 elements
-            sage: Matroid([0, 1, 2, 3, 4, 5],
+            sage: Matroid([0, 1, 2, 3, 4, 5],                                           # needs sage.graphs
             ....:         matrix=[[1, 1, 0], [1, 0, 1], [0, 1, 1]],
             ....:         field=GF(2), regular=True)
             Regular matroid of rank 3 on 6 elements with 16 bases
@@ -628,25 +627,25 @@ def Matroid(groundset=None, data=None, **kwds):
     increase speed, this check can be skipped::
 
         sage: M = matroids.named_matroids.Fano()
-        sage: N = Matroid(M, regular=True)
+        sage: N = Matroid(M, regular=True)                                              # needs sage.graphs
         Traceback (most recent call last):
         ...
         ValueError: input is not a valid regular matroid
-        sage: N = Matroid(M, regular=True, check=False); N
+        sage: N = Matroid(M, regular=True, check=False); N                              # needs sage.graphs
         Regular matroid of rank 3 on 7 elements with 32 bases
 
-        sage: N.is_valid()
+        sage: N.is_valid()                                                              # needs sage.graphs
         False
 
     Sometimes the output is regular, but represents a different matroid
     from the one you intended::
 
         sage: M = Matroid(Matrix(GF(3), [[1, 0, 1, 1], [0, 1, 1, 2]]))
-        sage: N = Matroid(Matrix(GF(3), [[1, 0, 1, 1], [0, 1, 1, 2]]),
+        sage: N = Matroid(Matrix(GF(3), [[1, 0, 1, 1], [0, 1, 1, 2]]),                  # needs sage.graphs
         ....:             regular=True)
-        sage: N.is_valid()
+        sage: N.is_valid()                                                              # needs sage.graphs
         True
-        sage: N.is_isomorphic(M)
+        sage: N.is_isomorphic(M)                                                        # needs sage.graphs
         False
 
     TESTS::
@@ -711,7 +710,11 @@ def Matroid(groundset=None, data=None, **kwds):
             groundset = None
 
     if key is None:
-        if isinstance(data, sage.graphs.graph.Graph):
+        try:
+            from sage.graphs.graph import Graph
+        except ImportError:
+            Graph = ()
+        if isinstance(data, Graph):
             key = 'graph'
         elif is_Matrix(data):
             key = 'matrix'
@@ -772,6 +775,8 @@ def Matroid(groundset=None, data=None, **kwds):
     # Graphs:
 
     elif key == 'graph':
+        from sage.graphs.graph import Graph
+
         if isinstance(data, sage.graphs.generic_graph.GenericGraph):
             G = data
         else:

src/sage/matroids/graphic_matroid.py

@@ -89,12 +89,10 @@
 # ****************************************************************************
 from .matroid import Matroid
 
-from sage.graphs.graph import Graph
 from copy import copy, deepcopy
 from .utilities import newlabel, split_vertex, sanitize_contractions_deletions
 from itertools import combinations
 from sage.rings.integer import Integer
-from sage.sets.disjoint_set import DisjointSet
 
 
 class GraphicMatroid(Matroid):
@@ -186,6 +184,7 @@ def __init__(self, G, groundset=None):
             running ._test_not_implemented_methods() . . . pass
             running ._test_pickling() . . . pass
         """
+        from sage.graphs.graph import Graph
 
         if groundset is None:
             # Try to construct a ground set based on the edge labels.
@@ -284,6 +283,8 @@ def _rank(self, X):
             1
 
         """
+        from sage.sets.disjoint_set import DisjointSet
+
         edges = self.groundset_to_edges(X)
         vertices = set([u for (u, v, l) in edges]).union(
             [v for (u, v, l) in edges])
@@ -713,6 +714,8 @@ def _corank(self, X):
             sage: M._corank([1,2,3])
             3
         """
+        from sage.sets.disjoint_set import DisjointSet
+
         all_vertices = self._G.vertices(sort=False)
         not_our_edges = self.groundset_to_edges(self._groundset.difference(X))
         DS_vertices = DisjointSet(all_vertices)
@@ -826,6 +829,8 @@ def _max_independent(self, X):
             sage: sorted(N._max_independent(frozenset(['a'])))
             []
         """
+        from sage.sets.disjoint_set import DisjointSet
+
         edges = self.groundset_to_edges(X)
         vertices = set([u for (u, v, l) in edges])
         vertices.update([v for (u, v, l) in edges])
@@ -861,6 +866,8 @@ def _max_coindependent(self, X):
             sage: sorted(N.max_coindependent([0,1,2,5]))
             [1, 2, 5]
         """
+        from sage.sets.disjoint_set import DisjointSet
+
         edges = self.groundset_to_edges(X)
         all_vertices = self._G.vertices(sort=False)
         not_our_edges = self.groundset_to_edges(self._groundset.difference(X))
@@ -924,6 +931,8 @@ def _circuit(self, X):
             [4, 5]
 
         """
+        from sage.sets.disjoint_set import DisjointSet
+
         edges = self.groundset_to_edges(X)
         vertices = set([u for (u, v, l) in edges]).union(
             set([v for (u, v, l) in edges]))

src/sage/matroids/linear_matroid.pyx

@@ -2844,8 +2844,7 @@ cdef class LinearMatroid(BasisExchangeMatroid):
         EXAMPLES::
 
             sage: M = matroids.Wheel(3)
-            sage: OS = M.orlik_terao_algebra()
-            sage: OS
+            sage: OS = M.orlik_terao_algebra(); OS
             Orlik-Terao algebra of Wheel(3):
              Regular matroid of rank 3 on 6 elements with 16 bases
              over Integer Ring