Root system data for (untwisted) type E affine

class sage.combinat.root_system.type_E_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(['E',6,1])
sage: ct
['E', 6, 1]
sage: ct._repr_(compact = True)
'E6~'

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()
['E', 6]
sage: ct.dual()
['E', 6, 1]

TESTS:

sage: TestSuite(ct).run()
ascii_art(label=<function <lambda> at 0x7f51a4ee9ed8>)

Returns a ascii art representation of the extended Dynkin diagram

EXAMPLES:

sage: print CartanType(['E',6,1]).ascii_art(label = lambda x: x+2)
        O 2
        |
        |
        O 4
        |
        |
O---O---O---O---O
3   5   6   7   8
sage: print CartanType(['E',7,1]).ascii_art(label = lambda x: x+2)
            O 4
            |
            |
O---O---O---O---O---O---O
2   3   5   6   7   8   9
sage: print CartanType(['E',8,1]).ascii_art(label = lambda x: x+1)
        O 3
        |
        |
O---O---O---O---O---O---O---O
2   4   5   6   7   8   9   1
dynkin_diagram()

Returns the extended Dynkin diagram for affine type E.

EXAMPLES:

sage: e = CartanType(['E', 6, 1]).dynkin_diagram()
sage: e
        O 0
        |
        |
        O 2
        |
        |
O---O---O---O---O
1   3   4   5   6
E6~
sage: sorted(e.edges())
[(0, 2, 1),
 (1, 3, 1),
 (2, 0, 1),
 (2, 4, 1),
 (3, 1, 1),
 (3, 4, 1),
 (4, 2, 1),
 (4, 3, 1),
 (4, 5, 1),
 (5, 4, 1),
 (5, 6, 1),
 (6, 5, 1)]

sage: e = CartanType(['E', 7, 1]).dynkin_diagram()
sage: e
            O 2
            |
            |
O---O---O---O---O---O---O
0   1   3   4   5   6   7
E7~
sage: sorted(e.edges())
[(0, 1, 1), (1, 0, 1), (1, 3, 1), (2, 4, 1), (3, 1, 1), (3, 4, 1),
 (4, 2, 1), (4, 3, 1), (4, 5, 1), (5, 4, 1), (5, 6, 1),
 (6, 5, 1), (6, 7, 1), (7, 6, 1)]
sage: e = CartanType(['E', 8, 1]).dynkin_diagram()
sage: e
        O 2
        |
        |
O---O---O---O---O---O---O---O
1   3   4   5   6   7   8   0
E8~
sage: sorted(e.edges())
[(0, 8, 1), (1, 3, 1), (2, 4, 1), (3, 1, 1), (3, 4, 1),
 (4, 2, 1), (4, 3, 1), (4, 5, 1), (5, 4, 1), (5, 6, 1),
 (6, 5, 1), (6, 7, 1), (7, 6, 1), (7, 8, 1), (8, 0, 1), (8, 7, 1)]

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