Root system data for (untwisted) type A affine#
- class sage.combinat.root_system.type_A_affine.CartanType(n)#
Bases:
CartanType_standard_untwisted_affine
EXAMPLES:
sage: ct = CartanType(['A',4,1]) sage: ct ['A', 4, 1] sage: ct._repr_(compact = True) 'A4~' 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() ['A', 4] sage: ct.dual() ['A', 4, 1] sage: ct = CartanType(['A', 1, 1]) sage: ct.is_simply_laced() False sage: ct.dual() ['A', 1, 1]
- PieriFactors#
alias of
PieriFactors_type_A_affine
- ascii_art(label=<function CartanType.<lambda> at 0x7f39823d75b0>, node=None)#
Return an ascii art representation of the extended Dynkin diagram.
EXAMPLES:
sage: print(CartanType(['A',3,1]).ascii_art()) 0 O-------+ | | | | O---O---O 1 2 3 sage: print(CartanType(['A',5,1]).ascii_art(label = lambda x: x+2)) 2 O---------------+ | | | | O---O---O---O---O 3 4 5 6 7 sage: print(CartanType(['A',1,1]).ascii_art()) O<=>O 0 1 sage: print(CartanType(['A',1,1]).ascii_art(label = lambda x: x+2)) O<=>O 2 3
- dual()#
Type \(A_1^1\) is self dual despite not being simply laced.
EXAMPLES:
sage: CartanType(['A',1,1]).dual() ['A', 1, 1]
- dynkin_diagram()#
Returns the extended Dynkin diagram for affine type A.
EXAMPLES:
sage: a = CartanType(['A',3,1]).dynkin_diagram() sage: a 0 O-------+ | | | | O---O---O 1 2 3 A3~ sage: a.edges(sort=True) [(0, 1, 1), (0, 3, 1), (1, 0, 1), (1, 2, 1), (2, 1, 1), (2, 3, 1), (3, 0, 1), (3, 2, 1)] sage: a = DynkinDiagram(['A',1,1]) sage: a O<=>O 0 1 A1~ sage: a.edges(sort=True) [(0, 1, 2), (1, 0, 2)]