Ticket #14001: trac_14001-coxeter_diagram_for_quiver_mutation_types.patch

sage/combinat/cluster_algebra_quiver/quiver_mutation_type.py

@@ -686 +686 @@
         """
         return self._rank
 
+    def coxeter_diagram(self):
+        """
+        Returns the Coxeter diagram of self.
+
+        EXAMPLES::
+            sage: mut_type = QuiverMutationType( ['A',5] ); mut_type
+            ['A', 5]
+            sage: mut_type.coxeter_diagram()
+            Coxeter diagram of rank 5
+
+            sage: mut_type = QuiverMutationType( ['A',[5,3],1] ); mut_type
+            ['A', [3, 5], 1]
+            sage: mut_type.coxeter_diagram()
+            Coxeter diagram of rank 8
+
+            sage: mut_type = QuiverMutationType(['A',3],['B',3]); mut_type
+            [ ['A', 3], ['B', 3] ]
+            sage: mut_type.coxeter_diagram()
+            Coxeter diagram of rank 6
+
+            sage: mut_type = QuiverMutationType(['A',3],['B',3],['X',6]); mut_type
+            [ ['A', 3], ['B', 3], ['X', 6] ]
+            sage: mut_type.coxeter_diagram()
+            Coxeter diagram of rank 12
+        """
+        G = Graph(self._graph)
+        for v1,v2,label in G.edges():
+            if type(label) in [list,tuple]: label = -prod(label)
+            elif label == 2: label = 4
+
+            if label is None:
+                G.set_edge_label(v1,v2,1)
+            elif label in [1,2]:
+                G.set_edge_label(v1,v2,label+2)
+            elif label == 3:
+                G.set_edge_label(v1,v2,4)
+            elif label == 4:
+                G.set_edge_label(v1,v2,infinity)
+            else:
+                raise ValueError, "Coxeter diagrams are not defined for quiver mutation types with edge labels (b,-c) such that b*c > 4"
+        return CoxeterDiagram(G)
+
+    def coxeter_matrix(self):
+        n = self._graph.order()
+        M = matrix(ZZ,[[2]*n]*n)
+        for v1,v2,label in self._graph.edge_iterator():
+            M[v1,v2] = M[v2,v1] = label
+        for i in xrange(n):
+            M[i,i] = 1
+        return M
+
     @cached_method
     def b_matrix(self):
         """
@@ -1939 +1990 @@
         comps = self.irreducible_components()
         return QuiverMutationType( [comp.dual() for comp in comps ] )
 
+class CoxeterDiagram(SageObject):
+    """
+    This is a very basic implementation of Coxeter diagrams. Is used in QuiverMutationType and should not be called directly.
+    """
+    def __init__(self, D):
+        """
+        INPUT:
+
+        - ``D`` -- is a graph without loops or two-cycles with integral edge labels 3 and bigger and +infinity
+
+            - QuiverMutationType
+            - tuple or list defining a proper quiver mutation type
+
+        EXAMPLES::
+            sage: QuiverMutationType(['A',4],['B',6])
+            [ ['A', 4], ['B', 6] ]
+        """
+        self._graph = Graph(D)
+
+    def __copy__(self):
+        """
+        """
+        return CoxeterDiagram(self._graph)
+
+    def __hash__(self):
+        return hash((tuple(self._graph.vertices()), tuple(self._graph.edge_iterator(self._graph.vertices()))))
+
+    def _repr_(self):
+        """
+        """
+        return "Coxeter diagram of rank %s"%len(self._graph.vertices())
+
+    def show(self):
+        G = Graph( self._graph )
+        for v1,v2,label in G.edge_iterator():
+            if label == 3:
+                G.set_edge_label(v1,v2,'')
+        G.show(edge_labels=True)
+
 def _construct_mutation_classes_by_rank( n ):
     r"""
     Returns a dict with keys being tuples representing regular QuiverMutationTypes
@@ -2169 +2259 @@
             M[v2,v1] = b
         if v2 < n:
             M[v1,v2] = a
-    return M
- No newline at end of file
+    return M