Fixing issues with definition of Coxeter matrices.

src/sage/combinat/root_system/cartan_matrix.py

@@ -903,6 +903,65 @@ def is_indecomposable(self):
  # consider the empty matrix to be indecomposable
  return comp_num <= 1
 
+ @cached_method
+ def coxeter_matrix(self):
+ r"""
+ Return the Coxeter matrix for ``self``.
+
+ .. SEEALSO:: :meth:`CartanType_abstract.coxeter_matrix`
+
+ EXAMPLES::
+
+ sage: cm = CartanMatrix([[2,-5,0],[-2,2,-1],[0,-1,2]])
+ sage: cm.coxeter_matrix()
+ [ 1 -1 2]
+ [-1 1 3]
+ [ 2 3 1]
+ sage: ct = CartanType([['A',2,2], ['B',3]])
+ sage: ct.coxeter_matrix()
+ [ 1 -1 2 2 2]
+ [-1 1 2 2 2]
+ [ 2 2 1 3 2]
+ [ 2 2 3 1 4]
+ [ 2 2 2 4 1]
+ sage: ct.cartan_matrix().coxeter_matrix() == ct.coxeter_matrix()
+ True
+ """
+ scalarproducts_to_order = {0: 2, 1: 3, 2: 4, 3: 6}
+ from sage.combinat.root_system.coxeter_matrix import CoxeterMatrix
+ I = self.index_set()
+ n = len(I)
+ M = matrix.identity(ZZ, n)
+ for i in range(n):
+ for j in range(i+1,n):
+ val = self[i,j] * self[j,i]
+ val = scalarproducts_to_order.get(val, -1)
+ M[i,j] = val
+ M[j,i] = val
+ return CoxeterMatrix(M, index_set=self.index_set(), cartan_type=self)
+
+ @cached_method
+ def coxeter_diagram(self):
+ r"""
+ Construct the Coxeter diagram of ``self``.
+
+ .. SEEALSO:: :meth:`CartanType_abstract.coxeter_diagram`
+
+ EXAMPLES::
+
+ sage: cm = CartanMatrix([[2,-5,0],[-2,2,-1],[0,-1,2]])
+ sage: G = cm.coxeter_diagram(); G
+ Graph on 3 vertices
+ sage: G.edges()
+ [(0, 1, +Infinity), (1, 2, 3)]
+ sage: ct = CartanType([['A',2,2], ['B',3]])
+ sage: ct.coxeter_diagram()
+ Graph on 5 vertices
+ sage: ct.cartan_matrix().coxeter_diagram() == ct.coxeter_diagram()
+ True
+ """
+ return self.coxeter_matrix().coxeter_graph()
+
  def principal_submatrices(self, proper=False):
  """
  Return a list of all principal submatrices of ``self``.

src/sage/combinat/root_system/cartan_type.py

@@ -1631,7 +1631,6 @@ def cartan_matrix(self):
  from sage.combinat.root_system.cartan_matrix import CartanMatrix
  return CartanMatrix(self.dynkin_diagram())
 
- @cached_method
  def coxeter_diagram(self):
  """
  Return the Coxeter diagram for ``self``.
@@ -1655,19 +1654,7 @@ def coxeter_diagram(self):
  sage: CartanType(['A',2,2]).coxeter_diagram().edges()
  [(0, 1, +Infinity)]
  """
- from sage.rings.infinity import infinity
- scalarproducts_to_order = { 0: 2, 1: 3, 2: 4, 3: 6, 4: infinity }
- from sage.graphs.graph import Graph
- coxeter_diagram = Graph(multiedges=False)
- a = self.dynkin_diagram()
- I = self.index_set()
- coxeter_diagram.add_vertices(I)
- for i in I:
- for j in a.neighbors_out(i):
- # avoid adding the edge twice
- if not coxeter_diagram.has_edge(i,j):
- coxeter_diagram.add_edge(i,j, scalarproducts_to_order[a[i,j]*a[j,i]])
- return coxeter_diagram
+ return self.dynkin_diagram().coxeter_diagram()
 
  def is_crystallographic(self):
  """

src/sage/combinat/root_system/dynkin_diagram.py

@@ -805,6 +805,42 @@ def row(self, i):
  val = 2 if i not in self._odd_isotropic_roots else 0
  return [(i,val)] + [(j,-m) for (j, i1, m) in self.incoming_edges(i)]
 
+ @cached_method
+ def coxeter_diagram(self):
+ r"""
+ Construct the Coxeter diagram of ``self``.
+
+ .. SEEALSO:: :meth:`CartanType_abstract.coxeter_diagram`
+
+ EXAMPLES::
+
+ sage: cm = CartanMatrix([[2,-5,0],[-2,2,-1],[0,-1,2]])
+ sage: D = cm.dynkin_diagram()
+ sage: G = D.coxeter_diagram(); G
+ Graph on 3 vertices
+ sage: G.edges()
+ [(0, 1, +Infinity), (1, 2, 3)]
+
+ sage: ct = CartanType([['A',2,2], ['B',3]])
+ sage: ct.coxeter_diagram()
+ Graph on 5 vertices
+ sage: ct.dynkin_diagram().coxeter_diagram() == ct.coxeter_diagram()
+ True
+ """
+ from sage.rings.infinity import infinity
+ scalarproducts_to_order = {0: 2, 1: 3, 2: 4, 3: 6}
+ from sage.graphs.graph import Graph
+ coxeter_diagram = Graph(multiedges=False)
+ I = self.index_set()
+ coxeter_diagram.add_vertices(I)
+ for i in I:
+ for j in self.neighbors_out(i):
+ # avoid adding the edge twice
+ if not coxeter_diagram.has_edge(i,j):
+ val = scalarproducts_to_order.get(self[i,j]*self[j,i], infinity)
+ coxeter_diagram.add_edge(i,j, val)
+ return coxeter_diagram.copy(immutable=True)
+
 def precheck(t, letter=None, length=None, affine=None, n_ge=None, n=None):
  """
  EXAMPLES::

src/sage/combinat/root_system/type_reducible.py

@@ -266,10 +266,12 @@ def cartan_matrix(self, subdivide=True):
  [-1 2 0 0]
  [ 0 0 2 -1]
  [ 0 0 -2 2]
+ sage: ct.index_set() == ct.cartan_matrix().index_set()
+ True
  """
  from sage.combinat.root_system.cartan_matrix import CartanMatrix
  return CartanMatrix(block_diagonal_matrix([t.cartan_matrix() for t in self._types], subdivide=subdivide),
- cartan_type=self)
+ cartan_type=self, index_set=self.index_set())
 
  def dynkin_diagram(self):
  """