def dynkin_diagram(self):
"""
Returns a Dynkin diagram for type B.
EXAMPLES::
sage: b = CartanType(['B',3]).dynkin_diagram()
sage: b
O---O=>=O
1 2 3
B3
sage: sorted(b.edges())
[(1, 2, 1), (2, 1, 1), (2, 3, 2), (3, 2, 1)]
sage: b = CartanType(['B',1]).dynkin_diagram()
sage: b
O
1
B1
sage: sorted(b.edges())
[]
"""
from dynkin_diagram import DynkinDiagram_class
n = self.n
g = DynkinDiagram_class(self)
for i in range(1, n):
g.add_edge(i, i + 1)
if n >= 2:
g.set_edge_label(n - 1, n, 2)
return g
def dynkin_diagram(self):
"""
Returns a Dynkin diagram for type B.
EXAMPLES::
sage: b = CartanType(['B',3]).dynkin_diagram()
sage: b
O---O=>=O
1 2 3
B3
sage: sorted(b.edges())
[(1, 2, 1), (2, 1, 1), (2, 3, 2), (3, 2, 1)]
sage: b = CartanType(['B',1]).dynkin_diagram()
sage: b
O
1
B1
sage: sorted(b.edges())
[]
"""
from dynkin_diagram import DynkinDiagram_class
n = self.n
g = DynkinDiagram_class(self)
for i in range(1, n):
g.add_edge(i, i + 1)
if n >= 2:
g.set_edge_label(n - 1, n, 2)
return g
def dynkin_diagram(self):
"""
Returns the extended Dynkin diagram for affine type C.
EXAMPLES::
sage: c = CartanType(['C',3,1]).dynkin_diagram()
sage: c
O=>=O---O=<=O
0 1 2 3
C3~
sage: sorted(c.edges())
[(0, 1, 2), (1, 0, 1), (1, 2, 1), (2, 1, 1), (2, 3, 1), (3, 2, 2)]
"""
n = self.n
if n == 1:
import cartan_type
res = cartan_type.CartanType(["A",1,1]).dynkin_diagram()
res._cartan_type = self
return res
from dynkin_diagram import DynkinDiagram_class
g = DynkinDiagram_class(self)
for i in range(1, n):
g.add_edge(i, i+1)
g.set_edge_label(n,n-1,2)
g.add_edge(0,1,2)
return g
def dynkin_diagram(self):
"""
Returns the extended Dynkin diagram for affine type B.
EXAMPLES::
sage: b = CartanType(['B',3,1]).dynkin_diagram()
sage: b
O 0
|
|
O---O=>=O
1 2 3
B3~
sage: sorted(b.edges())
[(0, 2, 1), (1, 2, 1), (2, 0, 1), (2, 1, 1), (2, 3, 2), (3, 2, 1)]
sage: b = CartanType(['B',2,1]).dynkin_diagram(); b
O=>=O=<=O
0 2 1
B2~
sage: sorted(b.edges())
[(0, 2, 2), (1, 2, 2), (2, 0, 1), (2, 1, 1)]
sage: b = CartanType(['B',1,1]).dynkin_diagram(); b
O<=>O
0 1
B1~
sage: sorted(b.edges())
[(0, 1, 2), (1, 0, 2)]
"""
import cartan_type
n = self.n
if n == 1:
res = cartan_type.CartanType(["A", 1, 1]).dynkin_diagram()
res._cartan_type = self
return res
if n == 2:
res = cartan_type.CartanType(["C", 2, 1]).relabel({
0: 0,
1: 2,
2: 1
}).dynkin_diagram()
res._cartan_type = self
return res
from dynkin_diagram import DynkinDiagram_class
g = DynkinDiagram_class(self)
for i in range(1, n):
g.add_edge(i, i + 1)
g.set_edge_label(n - 1, n, 2)
g.add_edge(0, 2)
return g
def dynkin_diagram(self):
"""
Returns the extended Dynkin diagram for affine type B.
EXAMPLES::
sage: b = CartanType(['B',3,1]).dynkin_diagram()
sage: b
O 0
|
|
O---O=>=O
1 2 3
B3~
sage: sorted(b.edges())
[(0, 2, 1), (1, 2, 1), (2, 0, 1), (2, 1, 1), (2, 3, 2), (3, 2, 1)]
sage: b = CartanType(['B',2,1]).dynkin_diagram(); b
O=>=O=<=O
0 2 1
B2~
sage: sorted(b.edges())
[(0, 2, 2), (1, 2, 2), (2, 0, 1), (2, 1, 1)]
sage: b = CartanType(['B',1,1]).dynkin_diagram(); b
O<=>O
0 1
B1~
sage: sorted(b.edges())
[(0, 1, 2), (1, 0, 2)]
"""
import cartan_type
n = self.n
if n == 1:
res = cartan_type.CartanType(["A",1,1]).dynkin_diagram()
res._cartan_type = self
return res
if n == 2:
res = cartan_type.CartanType(["C",2,1]).relabel({0:0, 1:2, 2:1}).dynkin_diagram()
res._cartan_type = self
return res
from dynkin_diagram import DynkinDiagram_class
g = DynkinDiagram_class(self)
for i in range(1, n):
g.add_edge(i, i+1)
g.set_edge_label(n-1, n, 2)
g.add_edge(0,2)
return g
def dynkin_diagram(self):
"""
Returns a Dynkin diagram for type G.
EXAMPLES::
sage: g = CartanType(['G',2]).dynkin_diagram()
sage: g
3
O=<=O
1 2
G2
sage: sorted(g.edges())
[(1, 2, 1), (2, 1, 3)]
"""
from dynkin_diagram import DynkinDiagram_class
g = DynkinDiagram_class(self)
g.add_edge(1, 2)
g.set_edge_label(2, 1, 3)
return g
def dynkin_diagram(self):
"""
Returns a Dynkin diagram for type G.
EXAMPLES::
sage: g = CartanType(['G',2]).dynkin_diagram()
sage: g
3
O=<=O
1 2
G2
sage: sorted(g.edges())
[(1, 2, 1), (2, 1, 3)]
"""
from dynkin_diagram import DynkinDiagram_class
g = DynkinDiagram_class(self)
g.add_edge(1,2)
g.set_edge_label(2,1,3)
return g
def dynkin_diagram(self):
"""
Returns the extended Dynkin diagram for type G.
EXAMPLES::
sage: g = CartanType(['G',2,1]).dynkin_diagram()
sage: g
3
O=<=O---O
1 2 0
G2~
sage: sorted(g.edges())
[(0, 2, 1), (1, 2, 1), (2, 0, 1), (2, 1, 3)]
"""
from dynkin_diagram import DynkinDiagram_class
g = DynkinDiagram_class(self)
g.add_edge(1, 2)
g.set_edge_label(2,1,3)
g.add_edge(0, 2)
return g
def dynkin_diagram(self):
"""
Returns a Dynkin diagram for type F.
EXAMPLES::
sage: f = CartanType(['F',4]).dynkin_diagram()
sage: f
O---O=>=O---O
1 2 3 4
F4
sage: sorted(f.edges())
[(1, 2, 1), (2, 1, 1), (2, 3, 2), (3, 2, 1), (3, 4, 1), (4, 3, 1)]
"""
from dynkin_diagram import DynkinDiagram_class
g = DynkinDiagram_class(self)
for i in range(1, 4):
g.add_edge(i, i+1)
g.set_edge_label(2,3,2)
return g
def dynkin_diagram(self):
"""
Returns a Dynkin diagram for type F.
EXAMPLES::
sage: f = CartanType(['F',4]).dynkin_diagram()
sage: f
O---O=>=O---O
1 2 3 4
F4
sage: sorted(f.edges())
[(1, 2, 1), (2, 1, 1), (2, 3, 2), (3, 2, 1), (3, 4, 1), (4, 3, 1)]
"""
from dynkin_diagram import DynkinDiagram_class
g = DynkinDiagram_class(self)
for i in range(1, 4):
g.add_edge(i, i + 1)
g.set_edge_label(2, 3, 2)
return g
def dynkin_diagram(self):
"""
Returns the extended Dynkin diagram for affine type F.
EXAMPLES::
sage: f = DynkinDiagram(['F', 4, 1])
sage: f
O---O---O=>=O---O
0 1 2 3 4
F4~
sage: sorted(f.edges())
[(0, 1, 1), (1, 0, 1), (1, 2, 1), (2, 1, 1), (2, 3, 2), (3, 2, 1), (3, 4, 1), (4, 3, 1)]
"""
from dynkin_diagram import DynkinDiagram_class
g = DynkinDiagram_class(self)
for i in range(1, 4):
g.add_edge(i, i + 1)
g.set_edge_label(2, 3, 2)
g.add_edge(0, 1)
return g
def dynkin_diagram(self):
"""
Returns the extended Dynkin diagram for affine type F.
EXAMPLES::
sage: f = DynkinDiagram(['F', 4, 1])
sage: f
O---O---O=>=O---O
0 1 2 3 4
F4~
sage: sorted(f.edges())
[(0, 1, 1), (1, 0, 1), (1, 2, 1), (2, 1, 1), (2, 3, 2), (3, 2, 1), (3, 4, 1), (4, 3, 1)]
"""
from dynkin_diagram import DynkinDiagram_class
g = DynkinDiagram_class(self)
for i in range(1, 4):
g.add_edge(i, i+1)
g.set_edge_label(2,3,2)
g.add_edge(0, 1)
return g
