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# Empty Species

class `sage.combinat.species.empty_species.``EmptySpecies`(min=None, max=None, weight=None)

  Bases: `sage.combinat.species.species.GenericCombinatorialSpecies`, `sage.structure.unique_representation.UniqueRepresentation`

  Returns the empty species. This species has no structure at all. It is the zero of the semi-ring of species.

  EXAMPLES:

      sage: X = species.EmptySpecies(); X
      Empty species
      sage: X.structures([]).list()
      []
      sage: X.structures([1]).list()
      []
      sage: X.structures([1,2]).list()
      []
      sage: X.generating_series().coefficients(4)
      [0, 0, 0, 0]
      sage: X.isotype_generating_series().coefficients(4)
      [0, 0, 0, 0]
      sage: X.cycle_index_series().coefficients(4)
      [0, 0, 0, 0]

  The empty species is the zero of the semi-ring of species. The following tests that it is neutral with respect to addition:

      sage: Empt  = species.EmptySpecies()
      sage: S = species.CharacteristicSpecies(2)
      sage: X = S + Empt
      sage: X == S    # TODO: Not Implemented
      True
      sage: (X.generating_series().coefficients(4) ==
      ...    S.generating_series().coefficients(4))
      True
      sage: (X.isotype_generating_series().coefficients(4) ==
      ...    S.isotype_generating_series().coefficients(4))
      True
      sage: (X.cycle_index_series().coefficients(4) ==
      ...    S.cycle_index_series().coefficients(4))
      True

  The following tests that it is the zero element with respect to multiplication:

      sage: Y = Empt*S
      sage: Y == Empt   # TODO: Not Implemented
      True
      sage: Y.generating_series().coefficients(4)
      [0, 0, 0, 0]
      sage: Y.isotype_generating_series().coefficients(4)
      [0, 0, 0, 0]
      sage: Y.cycle_index_series().coefficients(4)
      [0, 0, 0, 0]

  TESTS:

      sage: Empt  = species.EmptySpecies()
      sage: Empt2 = species.EmptySpecies()
      sage: Empt is Empt2
      True

`sage.combinat.species.empty_species.``EmptySpecies_class`

  alias of `EmptySpecies`

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