Root system data for (untwisted) type D affine

class sage.combinat.root_system.type_D_affine.CartanType(n)

Bases: sage.combinat.root_system.cartan_type.CartanType_standard_untwisted_affine, sage.combinat.root_system.cartan_type.CartanType_simply_laced

EXAMPLES:

sage: ct = CartanType(['D',4,1])
sage: ct
['D', 4, 1]
sage: ct._repr_(compact = True)
'D4~'

sage: ct.is_irreducible()
True
sage: ct.is_finite()
False
sage: ct.is_affine()
True
sage: ct.is_untwisted_affine()
True
sage: ct.is_crystallographic()
True
sage: ct.is_simply_laced()
True
sage: ct.classical()
['D', 4]
sage: ct.dual()
['D', 4, 1]

TESTS:

sage: TestSuite(ct).run()
ascii_art(label=<function <lambda> at 0x69081b8>)

Returns a ascii art representation of the extended Dynkin diagram

TESTS:

sage: print CartanType(['D',6,1]).ascii_art(label = lambda x: x+2)
  2 O       O 8
    |       |
    |       |
O---O---O---O---O
3   4   5   6   7

sage: print CartanType(['D',4,1]).ascii_art(label = lambda x: x+2)
    O 6
    |
    |
O---O---O
3   |4  5
    |
    O 2

sage: print CartanType(['D',3,1]).ascii_art(label = lambda x: x+2)
2
O-------+
|       |
|       |
O---O---O
5   3   4
dynkin_diagram()

Returns the extended Dynkin diagram for affine type D.

EXAMPLES:

sage: d = CartanType(['D', 6, 1]).dynkin_diagram()
sage: d
   0 O       O 6
     |       |
     |       |
 O---O---O---O---O
 1   2   3   4   5
 D6~
sage: sorted(d.edges())
[(0, 2, 1), (1, 2, 1), (2, 0, 1), (2, 1, 1), (2, 3, 1),
 (3, 2, 1), (3, 4, 1), (4, 3, 1), (4, 5, 1), (4, 6, 1), (5, 4, 1), (6, 4, 1)]

sage: d = CartanType(['D', 4, 1]).dynkin_diagram()
sage: d
    O 4
    |
    |
O---O---O
1   |2  3
    |
    O 0
D4~
sage: sorted(d.edges())
[(0, 2, 1),
 (1, 2, 1),
 (2, 0, 1),
 (2, 1, 1),
 (2, 3, 1),
 (2, 4, 1),
 (3, 2, 1),
 (4, 2, 1)]

sage: d = CartanType(['D', 3, 1]).dynkin_diagram()
sage: d
0
O-------+
|       |
|       |
O---O---O
3   1   2
D3~
sage: sorted(d.edges())
[(0, 2, 1), (0, 3, 1), (1, 2, 1), (1, 3, 1), (2, 0, 1), (2, 1, 1), (3, 0, 1), (3, 1, 1)]

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