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()
-
PieriFactors
¶ alias of
PieriFactors_type_D_affine
-
ascii_art
(label=<function <lambda>>, node=None)¶ Return an 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)]
-