Root system data for Cartan types with marked nodes¶
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sage.combinat.root_system.type_marked.
AmbientSpace
¶ Ambient space for a marked finite Cartan type.
It is constructed in the canonical way from the ambient space of the original Cartan type.
EXAMPLES:
sage: L = CartanType(["F",4]).marked_nodes([1,3]).root_system().ambient_space(); L Ambient space of the Root system of type ['F', 4] with nodes (1, 3) marked sage: TestSuite(L).run()
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sage.combinat.root_system.type_marked.
CartanType
¶ A class for Cartan types with marked nodes.
INPUT:
ct
– a Cartan typemarked_nodes
– a list of marked nodes
EXAMPLES:
We take the Cartan type \(B_4\):
sage: T = CartanType(['B',4]) sage: T.dynkin_diagram() O---O---O=>=O 1 2 3 4 B4
And mark some of its nodes:
sage: T = T.marked_nodes([2,3]) sage: T.dynkin_diagram() O---X---X=>=O 1 2 3 4 B4 with nodes (2, 3) marked
Markings are not additive:
sage: T.marked_nodes([1,4]).dynkin_diagram() X---O---O=>=X 1 2 3 4 B4 with nodes (1, 4) marked
And trivial relabelling are honoured nicely:
sage: T = T.marked_nodes([]) sage: T.dynkin_diagram() O---O---O=>=O 1 2 3 4 B4
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sage.combinat.root_system.type_marked.
CartanType_affine
¶
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class
sage.combinat.root_system.type_marked.
CartanType_finite
(ct, marked_nodes)¶ Bases:
sage.combinat.root_system.type_marked.CartanType
,sage.combinat.root_system.cartan_type.CartanType_finite
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AmbientSpace
¶ Ambient space for a marked finite Cartan type.
It is constructed in the canonical way from the ambient space of the original Cartan type.
EXAMPLES:
sage: L = CartanType(["F",4]).marked_nodes([1,3]).root_system().ambient_space(); L Ambient space of the Root system of type ['F', 4] with nodes (1, 3) marked sage: TestSuite(L).run()
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affine
()¶ Return the affine Cartan type associated with
self
.EXAMPLES:
sage: B4 = CartanType(['B',4]).marked_nodes([1,3]) sage: B4.dynkin_diagram() X---O---X=>=O 1 2 3 4 B4 with nodes (1, 3) marked sage: B4.affine().dynkin_diagram() O 0 | | X---O---X=>=O 1 2 3 4 B4~ with nodes (1, 3) marked
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