Root system data for (untwisted) type C affine¶
- class sage.combinat.root_system.type_C_affine.CartanType(n)[source]¶
Bases:
CartanType_standard_untwisted_affine
EXAMPLES:
sage: ct = CartanType(['C',4,1]) sage: ct ['C', 4, 1] sage: ct._repr_(compact = True) 'C4~' 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() False sage: ct.classical() ['C', 4] sage: ct.dual() ['C', 4, 1]^* sage: ct.dual().is_untwisted_affine() False
>>> from sage.all import * >>> ct = CartanType(['C',Integer(4),Integer(1)]) >>> ct ['C', 4, 1] >>> ct._repr_(compact = True) 'C4~' >>> ct.is_irreducible() True >>> ct.is_finite() False >>> ct.is_affine() True >>> ct.is_untwisted_affine() True >>> ct.is_crystallographic() True >>> ct.is_simply_laced() False >>> ct.classical() ['C', 4] >>> ct.dual() ['C', 4, 1]^* >>> ct.dual().is_untwisted_affine() False
- PieriFactors[source]¶
alias of
PieriFactors_type_C_affine
- ascii_art(label=None, node=None)[source]¶
Return a ascii art representation of the extended Dynkin diagram.
EXAMPLES:
sage: print(CartanType(['C',5,1]).ascii_art(label = lambda x: x+2)) O=>=O---O---O---O=<=O 2 3 4 5 6 7 sage: print(CartanType(['C',3,1]).ascii_art()) O=>=O---O=<=O 0 1 2 3 sage: print(CartanType(['C',2,1]).ascii_art()) O=>=O=<=O 0 1 2 sage: print(CartanType(['C',1,1]).ascii_art()) O<=>O 0 1
>>> from sage.all import * >>> print(CartanType(['C',Integer(5),Integer(1)]).ascii_art(label = lambda x: x+Integer(2))) O=>=O---O---O---O=<=O 2 3 4 5 6 7 >>> print(CartanType(['C',Integer(3),Integer(1)]).ascii_art()) O=>=O---O=<=O 0 1 2 3 >>> print(CartanType(['C',Integer(2),Integer(1)]).ascii_art()) O=>=O=<=O 0 1 2 >>> print(CartanType(['C',Integer(1),Integer(1)]).ascii_art()) O<=>O 0 1
- dynkin_diagram()[source]¶
Return the extended Dynkin diagram for affine type C.
EXAMPLES:
sage: c = CartanType(['C',3,1]).dynkin_diagram(); c # needs sage.graphs O=>=O---O=<=O 0 1 2 3 C3~ sage: c.edges(sort=True) # needs sage.graphs [(0, 1, 2), (1, 0, 1), (1, 2, 1), (2, 1, 1), (2, 3, 1), (3, 2, 2)]
>>> from sage.all import * >>> c = CartanType(['C',Integer(3),Integer(1)]).dynkin_diagram(); c # needs sage.graphs O=>=O---O=<=O 0 1 2 3 C3~ >>> c.edges(sort=True) # needs sage.graphs [(0, 1, 2), (1, 0, 1), (1, 2, 1), (2, 1, 1), (2, 3, 1), (3, 2, 2)]