gh-35951: `sage.combinat.cluster_algebra_quiver`: Modularization fixes, update `# needs`
    
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- `# optional` with standard features are replaced by `# needs`
- Some import fixes needed for separate testing of **sagemath-graphs**
from #35095
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This is:
- done with the help of `sage -fixdoctests` from #35749
- Part of: #29705
- Cherry-picked from: #35095

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- [x] I have linked a relevant issue or discussion.
- [ ] I have created tests covering the changes.
- [ ] I have updated the documentation accordingly.

### ⌛ Dependencies

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URL: #35951
Reported by: Matthias Köppe
Reviewer(s): David Coudert

Author: Release Manager

src/sage/combinat/cluster_algebra_quiver/all.py

@@ -15,3 +15,6 @@
 lazy_import("sage.combinat.cluster_algebra_quiver.quiver_mutation_type", "QuiverMutationType")
 lazy_import("sage.combinat.cluster_algebra_quiver.quiver", "ClusterQuiver")
 lazy_import("sage.combinat.cluster_algebra_quiver.cluster_seed", "ClusterSeed")
+
+del install_doc
+del lazy_import

src/sage/combinat/cluster_algebra_quiver/cluster_seed.py

@@ -1,4 +1,4 @@
-# -*- coding: utf-8 -*-
+# sage.doctest: needs sage.graphs sage.modules
 r"""
 ClusterSeed
 
@@ -44,10 +44,10 @@
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.rings.fraction_field_element import FractionFieldElement
 from sage.sets.set import Set
-from sage.graphs.digraph import DiGraph
 from sage.combinat.cluster_algebra_quiver.quiver_mutation_type import QuiverMutationType_Irreducible, QuiverMutationType_Reducible
 from sage.combinat.cluster_algebra_quiver.mutation_type import is_mutation_finite
 from random import randint
+from sage.misc.lazy_import import lazy_import
 from sage.misc.misc_c import prod
 from sage.matrix.special import identity_matrix
 from sage.matrix.constructor import matrix
@@ -57,6 +57,8 @@
 
 from sage.combinat.cluster_algebra_quiver.interact import cluster_interact
 
+lazy_import('sage.graphs.digraph', 'DiGraph')
+
 
 class ClusterSeed(SageObject):
     r"""
@@ -1040,11 +1042,11 @@ def plot(self, circular=False, mark=None, save_pos=False, force_c=False, with_gr
         EXAMPLES::
 
             sage: S = ClusterSeed(['A',5])
-            sage: S.plot()                                                              # optional - sage.plot sage.symbolic
+            sage: S.plot()                                                              # needs sage.plot sage.symbolic
             Graphics object consisting of 15 graphics primitives
-            sage: S.plot(circular=True)                                                 # optional - sage.plot sage.symbolic
+            sage: S.plot(circular=True)                                                 # needs sage.plot sage.symbolic
             Graphics object consisting of 15 graphics primitives
-            sage: S.plot(circular=True, mark=1)                                         # optional - sage.plot sage.symbolic
+            sage: S.plot(circular=True, mark=1)                                         # needs sage.plot sage.symbolic
             Graphics object consisting of 15 graphics primitives
         """
         greens = []
@@ -1086,7 +1088,7 @@ def show(self, fig_size=1, circular=False, mark=None, save_pos=False, force_c=Fa
         TESTS::
 
             sage: S = ClusterSeed(['A',5])
-            sage: S.show()  # long time                                                 # optional - sage.plot sage.symbolic
+            sage: S.show()                      # long time                             # needs sage.plot sage.symbolic
         """
         greens = []
         if with_greens:
@@ -1120,7 +1122,7 @@ def interact(self, fig_size=1, circular=True):
         TESTS::
 
             sage: S = ClusterSeed(['A',4])
-            sage: S.interact()                                                          # optional - sage.plot sage.symbolic
+            sage: S.interact()                                                          # needs sage.plot sage.symbolic
             ...VBox(children=...
         """
         return cluster_interact(self, fig_size, circular, kind='seed')
@@ -1142,7 +1144,7 @@ def save_image(self, filename, circular=False, mark=None, save_pos=False):
 
             sage: S = ClusterSeed(['F',4,[1,2]])
             sage: import tempfile
-            sage: with tempfile.NamedTemporaryFile(suffix=".png") as f:                 # optional - sage.plot sage.symbolic
+            sage: with tempfile.NamedTemporaryFile(suffix=".png") as f:                 # needs sage.plot sage.symbolic
             ....:     S.save_image(f.name)
         """
         graph_plot = self.plot(circular=circular, mark=mark, save_pos=save_pos)

src/sage/combinat/cluster_algebra_quiver/interact.py

@@ -25,8 +25,8 @@ def cluster_interact(self, fig_size=1, circular=True, kind='seed'):
 
     TESTS::
 
-        sage: S = ClusterSeed(['A',4])                                                  # optional - sage.graphs
-        sage: S.interact()   # indirect doctest                                         # optional - sage.graphs sage.symbolic
+        sage: S = ClusterSeed(['A',4])                                                  # needs sage.graphs sage.modules
+        sage: S.interact()   # indirect doctest                                         # needs sage.graphs sage.modules sage.symbolic
         ...VBox(children=...
     """
     if kind not in ['seed', 'quiver']:

src/sage/combinat/cluster_algebra_quiver/mutation_class.py

@@ -1,3 +1,4 @@
+# sage.doctest: needs sage.graphs
 r"""
 mutation_class
 
@@ -41,11 +42,11 @@ def _principal_part(mat):
     EXAMPLES::
 
         sage: from sage.combinat.cluster_algebra_quiver.mutation_class import _principal_part
-        sage: M = Matrix([[1,2],[3,4],[5,6]]); M
+        sage: M = Matrix([[1,2],[3,4],[5,6]]); M                                        # needs sage.modules
         [1 2]
         [3 4]
         [5 6]
-        sage: _principal_part(M)
+        sage: _principal_part(M)                                                        # needs sage.modules
         [1 2]
         [3 4]
     """
@@ -159,7 +160,7 @@ def _matrix_to_digraph( M ):
     EXAMPLES::
 
         sage: from sage.combinat.cluster_algebra_quiver.mutation_class import _matrix_to_digraph
-        sage: _matrix_to_digraph(matrix(3,[0,1,0,-1,0,-1,0,1,0]))
+        sage: _matrix_to_digraph(matrix(3,[0,1,0,-1,0,-1,0,1,0]))                       # needs sage.modules
         Digraph on 3 vertices
     """
     n = M.ncols()
@@ -452,7 +453,7 @@ def _dig6_to_matrix( dig6 ):
         sage: from sage.combinat.cluster_algebra_quiver.quiver import ClusterQuiver
         sage: dg = ClusterQuiver(['A',4]).digraph()
         sage: data = _digraph_to_dig6(dg)
-        sage: _dig6_to_matrix(data)
+        sage: _dig6_to_matrix(data)                                                     # needs sage.modules
         [ 0  1  0  0]
         [-1  0 -1  0]
         [ 0  1  0  1]

src/sage/combinat/cluster_algebra_quiver/mutation_type.py

@@ -1,3 +1,4 @@
+# sage.doctest: needs sage.graphs
 r"""
 Helper functions for mutation types of quivers
 
@@ -55,20 +56,20 @@ def is_mutation_finite(M, nr_of_checks=None):
         sage: from sage.combinat.cluster_algebra_quiver.mutation_type import is_mutation_finite
 
         sage: Q = ClusterQuiver(['A',10])
-        sage: M = Q.b_matrix()
-        sage: is_mutation_finite(M)
+        sage: M = Q.b_matrix()                                                          # needs sage.modules
+        sage: is_mutation_finite(M)                                                     # needs sage.modules
         (True, None)
 
         sage: Q = ClusterQuiver([(0,1),(1,2),(2,3),(3,4),(4,5),(5,6),(6,7),(7,8),(2,9)])
-        sage: M = Q.b_matrix()
-        sage: is_mutation_finite(M) # random
+        sage: M = Q.b_matrix()                                                          # needs sage.modules
+        sage: is_mutation_finite(M)  # random                                           # needs sage.modules
         (False, [9, 6, 9, 8, 9, 4, 0, 4, 5, 2, 1, 0, 1, 0, 7, 1, 9, 2, 5, 7, 8, 6, 3, 0, 2, 5, 4, 2, 6, 9, 2, 7, 3, 5, 3, 7, 9, 5, 9, 0, 2, 7, 9, 2, 4, 2, 1, 6, 9, 4, 3, 5, 0, 8, 2, 9, 5, 3, 7, 0, 1, 8, 3, 7, 2, 7, 3, 4, 8, 0, 4, 9, 5, 2, 8, 4, 8, 1, 7, 8, 9, 1, 5, 0, 8, 7, 4, 8, 9, 8, 0, 7, 4, 7, 1, 2, 8, 6, 1, 3, 9, 3, 9, 1, 3, 2, 4, 9, 5, 1, 2, 9, 4, 8, 5, 3, 4, 6, 8, 9, 2, 5, 9, 4, 6, 2, 1, 4, 9, 6, 0, 9, 8, 0, 4, 7, 9, 2, 1, 6])
 
     Check that :trac:`19495` is fixed::
 
-        sage: dg = DiGraph(); dg.add_vertex(0); S = ClusterSeed(dg); S
+        sage: dg = DiGraph(); dg.add_vertex(0); S = ClusterSeed(dg); S                  # needs sage.modules
         A seed for a cluster algebra of rank 1
-        sage: S.is_mutation_finite()
+        sage: S.is_mutation_finite()                                                    # needs sage.modules
         True
     """
     import random
@@ -1428,7 +1429,7 @@ def _random_tests(mt, k, mut_class=None, nr_mut=5):
     TESTS::
 
         sage: from sage.combinat.cluster_algebra_quiver.mutation_type import _random_tests
-        sage: _random_tests( ['A',3], 1)
+        sage: _random_tests( ['A',3], 1)                                                # needs sage.modules
         testing ['A', 3]
     """
     from sage.combinat.cluster_algebra_quiver.quiver import ClusterQuiver

src/sage/combinat/cluster_algebra_quiver/quiver.py

@@ -1,4 +1,4 @@
-# -*- coding: utf-8 -*-
+# sage.doctest: needs sage.graphs sage.modules
 r"""
 Quiver
 
@@ -37,19 +37,18 @@
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
-from sage.structure.sage_object import SageObject
 from copy import copy
+
+from sage.structure.sage_object import SageObject
 from sage.rings.integer_ring import ZZ
-from sage.rings.cc import CC
 from sage.rings.infinity import infinity
 from sage.graphs.digraph import DiGraph
 from sage.graphs.graph import Graph
 from sage.graphs.views import EdgesView
 from sage.arith.misc import gcd
-from sage.modules.free_module_element import vector
-from sage.matrix.constructor import matrix
 from sage.categories.cartesian_product import cartesian_product
 from sage.misc.misc_c import prod
+from sage.misc.lazy_import import lazy_import
 from sage.rings.rational_field import QQ
 from sage.rings.polynomial.polynomial_ring import polygen
 from sage.combinat.cluster_algebra_quiver.quiver_mutation_type import QuiverMutationType, QuiverMutationType_Irreducible, QuiverMutationType_Reducible, _edge_list_to_matrix
@@ -58,6 +57,9 @@
 
 from sage.combinat.cluster_algebra_quiver.interact import cluster_interact
 
+lazy_import('sage.modules.free_module_element', 'vector')
+lazy_import('sage.matrix.constructor', 'matrix')
+
 
 class ClusterQuiver(SageObject):
     """
@@ -67,14 +69,14 @@ class ClusterQuiver(SageObject):
 
     - ``data`` -- can be any of the following::
 
-        * QuiverMutationType
-        * str - a string representing a QuiverMutationType or a common quiver type (see Examples)
-        * ClusterQuiver
-        * Matrix - a skew-symmetrizable matrix
-        * DiGraph - must be the input data for a quiver
-        * List of edges - must be the edge list of a digraph for a quiver
+      * :class:`QuiverMutationType`
+      * :class:`str` -- a string representing a :class:`QuiverMutationType` or a common quiver type (see Examples)
+      * :class:`ClusterQuiver`
+      * :class:`Matrix` -- a skew-symmetrizable matrix
+      * :class:`DiGraph` -- must be the input data for a quiver
+      * List of edges -- must be the edge list of a digraph for a quiver
 
-    - ``frozen`` -- (default:``None``) sets the list of frozen variables
+    - ``frozen`` -- (default: ``None``) sets the list of frozen variables
       if the input type is a :class:`DiGraph`, it is ignored otherwise
 
     - ``user_labels`` -- (default:``None``) sets the names of the labels for
@@ -549,16 +551,17 @@ def plot(self, circular=True, center=(0, 0), directed=True, mark=None,
         EXAMPLES::
 
             sage: Q = ClusterQuiver(['A',5])
-            sage: Q.plot()                                                              # optional - sage.plot sage.symbolic
+            sage: Q.plot()                                                              # needs sage.plot sage.symbolic
             Graphics object consisting of 15 graphics primitives
-            sage: Q.plot(circular=True)                                                 # optional - sage.plot sage.symbolic
+            sage: Q.plot(circular=True)                                                 # needs sage.plot sage.symbolic
             Graphics object consisting of 15 graphics primitives
-            sage: Q.plot(circular=True, mark=1)                                         # optional - sage.plot sage.symbolic
+            sage: Q.plot(circular=True, mark=1)                                         # needs sage.plot sage.symbolic
             Graphics object consisting of 15 graphics primitives
         """
         from sage.plot.colors import rainbow
         from sage.graphs.graph_generators import GraphGenerators
         from sage.symbolic.constants import e, pi
+        from sage.rings.cc import CC
         from sage.rings.imaginary_unit import I
         graphs = GraphGenerators()
         # returns positions for graph vertices on two concentric cycles with radius 1 and 2
@@ -699,7 +702,7 @@ def interact(self, fig_size=1, circular=True):
         TESTS::
 
             sage: S = ClusterQuiver(['A',4])
-            sage: S.interact()                                                          # optional - sage.plot sage.symbolic
+            sage: S.interact()                                                          # needs sage.plot sage.symbolic
             ...VBox(children=...
         """
         return cluster_interact(self, fig_size, circular, kind="quiver")
@@ -717,7 +720,7 @@ def save_image(self, filename, circular=False):
 
             sage: Q = ClusterQuiver(['F',4,[1,2]])
             sage: import tempfile
-            sage: with tempfile.NamedTemporaryFile(suffix=".png") as f:                 # optional - sage.plot sage.symbolic
+            sage: with tempfile.NamedTemporaryFile(suffix=".png") as f:                 # needs sage.plot sage.symbolic
             ....:     Q.save_image(f.name)
         """
         graph_plot = self.plot(circular=circular)
@@ -742,7 +745,7 @@ def qmu_save(self, filename=None):
 
             sage: Q = ClusterQuiver(['F',4,[1,2]])
             sage: import tempfile
-            sage: with tempfile.NamedTemporaryFile(suffix=".qmu") as f:                 # optional - sage.plot sage.symbolic
+            sage: with tempfile.NamedTemporaryFile(suffix=".qmu") as f:                 # needs sage.plot sage.symbolic
             ....:     Q.qmu_save(f.name)
 
         Make sure we can save quivers with `m != n` frozen variables, see :trac:`14851`::
@@ -751,7 +754,7 @@ def qmu_save(self, filename=None):
             sage: T1 = S.principal_extension()
             sage: Q = T1.quiver()
             sage: import tempfile
-            sage: with tempfile.NamedTemporaryFile(suffix=".qmu") as f:                 # optional - sage.plot sage.symbolic
+            sage: with tempfile.NamedTemporaryFile(suffix=".qmu") as f:                 # needs sage.plot sage.symbolic
             ....:     Q.qmu_save(f.name)
         """
         M = self.b_matrix()