Root system data for (untwisted) type C affine#
- class sage.combinat.root_system.type_C_affine.CartanType(n)#
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
- PieriFactors#
alias of
PieriFactors_type_C_affine
- ascii_art(label=<function CartanType.<lambda> at 0x7fded85b8ee0>, node=None)#
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
- dynkin_diagram()#
Returns the extended Dynkin diagram for affine type C.
EXAMPLES:
sage: c = CartanType(['C',3,1]).dynkin_diagram() sage: c O=>=O---O=<=O 0 1 2 3 C3~ sage: c.edges(sort=True) [(0, 1, 2), (1, 0, 1), (1, 2, 1), (2, 1, 1), (2, 3, 1), (3, 2, 2)]