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Package sage :: Package combinat :: Package root_system :: Module cartan_type :: Class CartanTypeFactory
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Class CartanTypeFactory

source code

                      object --+    
                               |    
structure.sage_object.SageObject --+
                                   |
                                  CartanTypeFactory
Instance Methods [hide private]
 
__call__(self, *args)
Returns an object corresponding to the Cartan type t.		 source code
 
samples(self, finite=False, affine=False, crystalographic=False)
Returns a sample of the implemented cartan types With finite=True resp.		 source code

Inherited from structure.sage_object.SageObject: __hash__, __new__, __repr__, _axiom_, _axiom_init_, _gap_, _gap_init_, _gp_, _gp_init_, _interface_, _interface_init_, _interface_is_cached_, _kash_, _kash_init_, _macaulay2_, _macaulay2_init_, _magma_, _magma_init_, _maple_, _maple_init_, _mathematica_, _mathematica_init_, _maxima_, _maxima_init_, _octave_, _octave_init_, _pari_, _pari_init_, _r_init_, _sage_, _singular_, _singular_init_, category, db, dump, dumps, plot, rename, reset_name, save, version

Inherited from object: __delattr__, __getattribute__, __init__, __reduce__, __reduce_ex__, __setattr__, __str__

Properties [hide private]

Inherited from object: __class__

Method Details [hide private]

__call__(self, *args)
(Call operator)

source code  

Returns an object corresponding to the Cartan type t.

INPUT:
[letter, rank]
where letter is one of 'A','B','C','D','E','F','G' and rank
is the rank. An alternative string notation is allowed.
A third optional parameter is permitted for affine
types. Reducible types may be entered by giving a list of
irreducible types or by a single string 

EXAMPLES:
    sage: CartanType(['A',4])
    ['A', 4]
    sage: CartanType("A4")
    ['A', 4]
    sage: CartanType(['A',2],['B',2])
    A2xB2
    sage: CartanType(['A',2],['B',2]).is_reducible()
    True
    sage: CartanType("A2xB2")
    A2xB2
    sage: CartanType("A2","B2") == CartanType("A2xB2")
    True
    sage: CartanType(['A',4,1])
    ['A', 4, 1]
    sage: CartanType(['A',4,1]).is_affine()
    True

samples(self, finite=False, affine=False, crystalographic=False)

source code  

Returns a sample of the implemented cartan types

With finite=True resp. affine=True, one can restrict to finite
resp. affine only cartan types

EXAMPLES:
    sage: CartanType.samples(finite=True)
    [['A', 1], ['A', 5], ['B', 5], ['C', 5], ['D', 5], ['E', 6], ['E', 7], ['E', 8], ['F', 4], ['G', 2], ['I', 5], ['H', 3], ['H', 4]]
    
    sage: CartanType.samples(affine=True)
    [['A', 1, 1], ['A', 5, 1], ['B', 5, 1], ['C', 5, 1], ['D', 5, 1], ['E', 6, 1], ['E', 7, 1], ['E', 8, 1], ['F', 4, 1], ['G', 2, 1], ['A', 2, 2], ['A', 10, 2], ['A', 9, 2], ['D', 5, 2], ['D', 4, 3], ['E', 6, 2]]
    
    sage: CartanType.samples()
    [['A', 1], ['A', 5], ['B', 5], ['C', 5], ['D', 5], ['E', 6], ['E', 7], ['E', 8], ['F', 4], ['G', 2], ['I', 5], ['H', 3], ['H', 4], ['A', 1, 1], ['A', 5, 1], ['B', 5, 1], ['C', 5, 1], ['D', 5, 1], ['E', 6, 1], ['E', 7, 1], ['E', 8, 1], ['F', 4, 1], ['G', 2, 1], ['A', 2, 2], ['A', 10, 2], ['A', 9, 2], ['D', 5, 2], ['D', 4, 3], ['E', 6, 2]]
    sage: CartanType.samples(crystalographic=True)
    [['A', 1], ['A', 5], ['B', 5], ['C', 5], ['D', 5], ['E', 6], ['E', 7], ['E', 8], ['F', 4], ['G', 2], ['A', 1, 1], ['A', 5, 1], ['B', 5, 1], ['C', 5, 1], ['D', 5, 1], ['E', 6, 1], ['E', 7, 1], ['E', 8, 1], ['F', 4, 1], ['G', 2, 1], ['A', 2, 2], ['A', 10, 2], ['A', 9, 2], ['D', 5, 2], ['D', 4, 3], ['E', 6, 2]]

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