trac #32805: unify use of weights

src/sage/graphs/generic_graph.py

@@ -4098,11 +4098,12 @@ def eulerian_circuit(self, return_vertices=False, labels=True, path=False):
             return edges
 
     def min_spanning_tree(self,
+                          by_weight=False,
                           weight_function=None,
+                          check_weight=True,
                           algorithm="Prim_Boost",
                           starting_vertex=None,
-                          check=False,
-                          by_weight=False):
+                          check=False):
         r"""
         Return the edges of a minimum spanning tree.
 
@@ -4115,6 +4116,9 @@ def min_spanning_tree(self,
 
         INPUT:
 
+        - ``by_weight`` -- boolean (default: ``False``); if ``True``, the edges
+          in the graph are weighted, otherwise all edges have weight 1
+
         - ``weight_function`` -- function (default: ``None``); a function that
           takes as input an edge ``(u, v, l)`` and outputs its weight. If not
           ``None``, ``by_weight`` is automatically set to ``True``. If ``None``
@@ -4123,8 +4127,8 @@ def min_spanning_tree(self,
           be used to transform the label into a weight (note that, if the weight
           returned is not convertible to a float, an error is raised)
 
-        - ``by_weight`` -- boolean (default: ``False``); if ``True``, the edges
-          in the graph are weighted, otherwise all edges have weight 1
+        - ``check_weight`` -- boolean (default: ``True``); whether to check that
+          the ``weight_function`` outputs a number for each edge.
 
         - ``algorithm`` -- string (default: ``"Prim_Boost"``); the algorithm to
           use in computing a minimum spanning tree of ``G``. The following
@@ -4296,85 +4300,80 @@ def min_spanning_tree(self,
             sage: g.min_spanning_tree(algorithm="Prim_Boost")
             Traceback (most recent call last):
             ...
-            ValueError: could not convert string to float:...
+            ValueError: the weight function cannot find the weight of...
             sage: g.min_spanning_tree(algorithm="Prim_fringe")
             Traceback (most recent call last):
             ...
-            ValueError: could not convert string to float:...
+            ValueError: the weight function cannot find the weight of...
             sage: g.min_spanning_tree(algorithm="Prim_edge")
             Traceback (most recent call last):
             ...
-            ValueError: could not convert string to float:...
+            ValueError: the weight function cannot find the weight of...
             sage: g.min_spanning_tree(algorithm="Kruskal")
             Traceback (most recent call last):
             ...
-            ValueError: could not convert string to float:...
+            ValueError: the weight function cannot find the weight of...
             sage: g.min_spanning_tree(algorithm="Filter_Kruskal")
             Traceback (most recent call last):
             ...
-            ValueError: could not convert string to float:...
+            ValueError: the weight function cannot find the weight of...
             sage: g.min_spanning_tree(algorithm="Kruskal_Boost")
             Traceback (most recent call last):
             ...
-            ValueError: could not convert string to float:...
+            ValueError: the weight function cannot find the weight of...
             sage: g.min_spanning_tree(algorithm="NetworkX")
             Traceback (most recent call last):
             ...
-            ValueError: could not convert string to float:...
+            ValueError: the weight function cannot find the weight of...
             sage: g.min_spanning_tree(algorithm="Boruvka")
             Traceback (most recent call last):
             ...
-            ValueError: could not convert string to float:...
+            ValueError: the weight function cannot find the weight of...
 
             sage: g = Graph([(0, 1, 1), (1, 2, [1, 2, 3])], weighted=True)
 
             sage: g.min_spanning_tree(algorithm="Prim_Boost")
             Traceback (most recent call last):
             ...
-            TypeError: float() argument must be a string or a... number...
+            ValueError: the weight function cannot find the weight of...
             sage: g.min_spanning_tree(algorithm="Prim_fringe")
             Traceback (most recent call last):
             ...
-            TypeError: float() argument must be a string or a... number...
+            ValueError: the weight function cannot find the weight of...
             sage: g.min_spanning_tree(algorithm="Prim_edge")
             Traceback (most recent call last):
             ...
-            TypeError: float() argument must be a string or a... number...
+            ValueError: the weight function cannot find the weight of...
             sage: g.min_spanning_tree(algorithm="Kruskal")
             Traceback (most recent call last):
             ...
-            TypeError: float() argument must be a string or a... number...
+            ValueError: the weight function cannot find the weight of...
             sage: g.min_spanning_tree(algorithm="Filter_Kruskal")
             Traceback (most recent call last):
             ...
-            TypeError: float() argument must be a string or a... number...
+            ValueError: the weight function cannot find the weight of...
             sage: g.min_spanning_tree(algorithm="Kruskal_Boost")
             Traceback (most recent call last):
             ...
-            TypeError: float() argument must be a string or a... number...
+            ValueError: the weight function cannot find the weight of...
             sage: g.min_spanning_tree(algorithm="NetworkX")
             Traceback (most recent call last):
             ...
-            TypeError: float() argument must be a string or a... number...
+            ValueError: the weight function cannot find the weight of...
 
             sage: graphs.EmptyGraph().min_spanning_tree()
             []
         """
         if not self.order():
             return []
-        if weight_function is not None:
-            by_weight = True
 
         # for weighted graphs
         if self.weighted():
             by_weight = True
 
-        if weight_function is None and by_weight:
-            def weight_function(e):
-                return 1 if e[2] is None else e[2]
-
-        if not by_weight:
-            weight_function = lambda e: 1
+        by_weight, weight_function = self._get_weight_function(by_weight=by_weight,
+                                                               weight_function=weight_function,
+                                                               check_weight=check_weight)
 
         wfunction_float = lambda e: float(weight_function(e))
 
@@ -4386,13 +4385,13 @@ def weight_function(e):
 
             if algorithm == "Kruskal":
                 from .spanning_tree import kruskal
-                return kruskal(g, wfunction=wfunction_float, check=check)
+                return kruskal(g, weight_function=wfunction_float, check_weight=False, check=check)
             if algorithm == "Filter_Kruskal":
                 from .spanning_tree import filter_kruskal
-                return filter_kruskal(g, weight_function=wfunction_float, check=check)
+                return filter_kruskal(g, weight_function=wfunction_float, check_weight=False, check=check)
             elif algorithm == "Boruvka":
                 from .spanning_tree import boruvka
-                return boruvka(g, wfunction=wfunction_float, check=check)
+                return boruvka(g, weight_function=wfunction_float, check_weight=False, check=check)
             else:
                 from sage.graphs.base.boost_graph import min_spanning_tree
                 return min_spanning_tree(g,