Package sage :: Package combinat :: Package crystals :: Module letters :: Class Letter

Class Letter

                      object --+        
                               |        
structure.sage_object.SageObject --+    
                                   |    
           structure.element.Element --+
                                       |
                                      Letter

Known Subclasses:: Crystal_of_letters_type_A_element, Crystal_of_letters_type_B_element, Crystal_of_letters_type_C_element, Crystal_of_letters_type_D_element, Crystal_of_letters_type_G_element, affine.AffineCrystalFromClassicalElement, affine.AffinizationFromAffineCrystalElement


A class for letters

Instance Methods

[hide private]

__init__(self, parent, value)
EXAMPLES:...

source code

parent(self)
Returns the parent of self.

source code

__repr__(self)
EXAMPLES:...

source code

__eq__(self, other)
EXAMPLES: sage: from sage.combinat.crystals.letters import Letter sage: parent1 = 1 # Any fake value ...

source code

__cmp__(self, other)
EXAMPLES:...

source code

Inherited from structure.element.Element: __ge__, __gt__, __hash__, __le__, __lt__, __ne__, __new__, __nonzero__, __reduce__, __rxor__, __xor__, _cmp_, _im_gens_, _repr_, _richcmp_, base_base_extend, base_base_extend_canonical_sym, base_extend, base_extend_canonical, base_extend_canonical_sym, base_extend_recursive, base_ring, category, is_zero, n, subs, substitute

Inherited from structure.element.Element (private): _coeff_repr, _is_atomic, _latex_coeff_repr, _make_new_with_parent_c, _set_parent

Inherited from structure.sage_object.SageObject: _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_, db, dump, dumps, plot, rename, reset_name, save, version

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

Properties

[hide private]

Inherited from object: __class__

Method Details

[hide private]

init(self, parent, value)
(Constructor)

source code


EXAMPLES:
    sage: from sage.combinat.crystals.letters import Letter
    sage: a = Letter(ZZ, 1)
    sage: a == loads(dumps(a))
    True

Overrides: structure.element.Element.__init__

parent(self)

source code


Returns the parent of self.

EXAMPLES:
    sage: from sage.combinat.crystals.letters import Letter
    sage: Letter(ZZ, 1).parent()
    Integer Ring

Overrides: structure.element.Element.parent

repr(self)
(Representation operator)

source code


EXAMPLES:
    sage: from sage.combinat.crystals.letters import Letter
    sage: Letter(ZZ, 1).__repr__()
    '1'

Overrides: structure.sage_object.SageObject.__repr__

eq(self, other)
(Equality operator)

source code


EXAMPLES:
    sage: from sage.combinat.crystals.letters import Letter
    sage: parent1 = 1  # Any fake value ...
    sage: parent2 = 2  # Any fake value ...
    sage: l11 = Letter(parent1, 1)
    sage: l12 = Letter(parent1, 2)
    sage: l21 = Letter(parent2, 1)
    sage: l22 = Letter(parent2, 2)
    sage: l11 == l11
    True
    sage: l11 == l12
    False
    sage: l11 == l21
    False

Overrides: structure.element.Element.__eq__

cmp(self, other)
(Comparison operator)

source code


EXAMPLES:
    sage: C = CrystalOfLetters(['A', 5])
    sage: C(1) < C(2)
    True
    sage: C(2) < C(1)
    False
    sage: C(2) > C(1)
    True
    sage: C(1) <= C(1)
    True

Overrides: structure.element.Element.__cmp__

Class Letter

__init__(self, parent, value) (Constructor)

parent(self)

__repr__(self) (Representation operator)

__eq__(self, other) (Equality operator)

__cmp__(self, other) (Comparison operator)

init(self, parent, value)
(Constructor)

repr(self)
(Representation operator)

eq(self, other)
(Equality operator)

cmp(self, other)
(Comparison operator)