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Package sage :: Package combinat :: Package species :: Module species :: Class GenericCombinatorialSpecies
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Class GenericCombinatorialSpecies

source code

                      object --+    
                               |    
structure.sage_object.SageObject --+
                                   |
                                  GenericCombinatorialSpecies
Known Subclasses:
CombinatorialSpecies, CompositionSpecies, CycleSpecies, FunctorialCompositionSpecies, LinearOrderSpecies, PartitionSpecies, PermutationSpecies, PositivePartSpecies, ProductSpecies, RestrictedSpecies, SetSpecies, SubsetSpecies, SumSpecies
Instance Methods [hide private]
 
__init__(self, structure_class)
x.__init__(...) initializes x; see x.__class__.__doc__ for signature		 source code
 
__repr__(self)
EXAMPLES:...		 source code
 
__add__(self, g)
Returns the sum of self and g.		 source code
 
sum(self, g)
Returns the sum of self and g.		 source code
 
__mul__(self, g)
Returns the product of self and g.		 source code
 
product(self, g)
Returns the product of self and g.		 source code
 
__call__(self, g)
EXAMPLES:...		 source code
 
composition(self, g)
EXAMPLES:...		 source code
 
functorial_composition(self, g)
Returns the functorial composition of self with g.		 source code
 
restricted(self, k)
EXAMPLES:...		 source code
 
structures(self, labels)
EXAMPLES: sage: F = CombinatorialSpecies() sage: F.structures([1,2,3]).list() Traceback (most recent call last): ...		 source code
 
isomorphism_types(self, labels)
EXAMPLES: sage: F = CombinatorialSpecies() sage: F.isomorphism_types([1,2,3]).list() Traceback (most recent call last): ...		 source code
 
__cmp__(self, x)
EXAMPLES:...		 source code
 
_check(self, n=5)
Returns True if the number of structures and isomorphism types generated is the same as the number found from the generating series.		 source code
 
positive_part(self)
EXAMPLES:...		 source code

Inherited from structure.sage_object.SageObject: __hash__, __new__, _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__, __reduce__, __reduce_ex__, __setattr__, __str__

Properties [hide private]

Inherited from object: __class__

Method Details [hide private]

__init__(self, structure_class)
(Constructor)

source code  
x.__init__(...) initializes x; see x.__class__.__doc__ for signature
Overrides: object.__init__
(inherited documentation)

__repr__(self)
(Representation operator)

source code  

EXAMPLES:
    sage: CombinatorialSpecies()
    Combinatorial species
Overrides: structure.sage_object.SageObject.__repr__

__add__(self, g)
(Addition operator)

source code  

Returns the sum of self and g.

EXAMPLES:
    sage: from sage.combinat.species.species import PermutationSpecies
    sage: P = PermutationSpecies()
    sage: F = P + P; F
    Sum of (Permutation species) and (Permutation species)
    sage: F.structures([1,2]).list()
    [[1, 2], [2, 1], [1, 2], [2, 1]]

sum(self, g)

source code  

Returns the sum of self and g.

EXAMPLES:
    sage: from sage.combinat.species.species import PermutationSpecies
    sage: P = PermutationSpecies()
    sage: F = P + P; F
    Sum of (Permutation species) and (Permutation species)
    sage: F.structures([1,2]).list()
    [[1, 2], [2, 1], [1, 2], [2, 1]]

__mul__(self, g)

source code  

Returns the product of self and g.

EXAMPLES:
    sage: from sage.combinat.species.species import PermutationSpecies
    sage: P = PermutationSpecies()
    sage: F = P * P; F
    Product of (Permutation species) and (Permutation species)

product(self, g)

source code  

Returns the product of self and g.

EXAMPLES:
    sage: from sage.combinat.species.species import PermutationSpecies
    sage: P = PermutationSpecies()
    sage: F = P * P; F
    Product of (Permutation species) and (Permutation species)

__call__(self, g)
(Call operator)

source code  

EXAMPLES:
    sage: from sage.combinat.species.species import SetSpecies
    sage: S = SetSpecies()
    sage: S(S)
    Composition of (Set species) and (Set species)

composition(self, g)

source code  

EXAMPLES:
    sage: from sage.combinat.species.species import SetSpecies
    sage: S = SetSpecies()
    sage: S(S)
    Composition of (Set species) and (Set species)

functorial_composition(self, g)

source code  

Returns the functorial composition of self with g.

EXAMPLES:
    sage: from sage.combinat.species.species import SetSpecies, SubsetSpecies
    sage: E = SetSpecies()
    sage: E2 = E.restricted(2)
    sage: WP = SubsetSpecies()
    sage: P2 = E2*E
    sage: G = WP.functorial_composition(P2)
    sage: G.isomorphism_type_generating_series().coefficients(5)
    [1, 1, 2, 4, 11]

restricted(self, k)

source code  

EXAMPLES:
    sage: from sage.combinat.species.species import PermutationSpecies
    sage: PermutationSpecies().restricted(3)
    Permutation species restricted to 3

structures(self, labels)

source code  

EXAMPLES:
    sage: F = CombinatorialSpecies()
    sage: F.structures([1,2,3]).list()
    Traceback (most recent call last):
    ...
    NotImplementedError

isomorphism_types(self, labels)

source code  

EXAMPLES:
    sage: F = CombinatorialSpecies()
    sage: F.isomorphism_types([1,2,3]).list()
    Traceback (most recent call last):
    ...
    NotImplementedError

__cmp__(self, x)
(Comparison operator)

source code  

EXAMPLES:
    sage: from sage.combinat.species.species import SingletonSpecies, EmptySetSpecies
    sage: S = SingletonSpecies()
    sage: E = EmptySetSpecies()
    sage: S == S
    True
    sage: S == E
    False

_check(self, n=5)

source code  

Returns True if the number of structures and isomorphism
types generated is the same as the number found from
the generating series.

EXAMPLES:
    sage: from sage.combinat.species.species import PartitionSpecies
    sage: P = PartitionSpecies()
    sage: P._check()
    True

positive_part(self)

source code  

EXAMPLES:
    sage: from sage.combinat.species.species import PartitionSpecies
    sage: P = PartitionSpecies().positive_part(); P
    Positive part of Partition species
    sage: P.isomorphism_type_generating_series().coefficients(5)
    [0, 1, 2, 3, 5]

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