Root system data for (untwisted) type C affine

class sage.combinat.root_system.type_C_affine.CartanType(n)

Bases: sage.combinat.root_system.cartan_type.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

TESTS:

sage: TestSuite(ct).run()
ascii_art(label=<function <lambda> at 0x68cade8>)

Returns 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: sorted(c.edges())
[(0, 1, 2), (1, 0, 1), (1, 2, 1), (2, 1, 1), (2, 3, 1), (3, 2, 2)]

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