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Add doctests to generating_series.py
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@mwhansen
mwhansen committed Jan 13, 2014
1 parent ed19baa commit 654a89d
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151 changes: 116 additions & 35 deletions src/sage/combinat/species/generating_series.py
View file
Original file line number Diff line number Diff line change
Expand Up @@ -194,14 +194,30 @@ def counts(self, n):

class FunctorialCompositionStream(SeriesStream):
def __init__(self, outer_series, inner_series, **kwds):
"""
A class for the stream of coefficients of the functorial
composition of two exponential generating series.
EXAMPLES::
sage: E = species.SetSpecies()
sage: E2 = E.restricted(min=2, max=3)
sage: WP = species.SubsetSpecies()
sage: P2 = E2*E
sage: g1 = WP.generating_series()
sage: g2 = P2.generating_series()
sage: s = g1.FunctorialCompositionStream(g1, g2, base_ring=g1.base_ring())
sage: [s[i] for i in range(10)]
[1, 1, 1, 4/3, 8/3, 128/15, 2048/45, 131072/315, 2097152/315, 536870912/2835]
"""
self._outer = outer_series
self._inner = inner_series
super(ExponentialGeneratingSeries.FunctorialCompositionStream, self).__init__(**kwds)

def compute(self, n):
"""
Returns a generator for the coefficients of the functorial
composition of self with y.
Computes the $n^{th}$ coefficient of this functorial
composition series.
EXAMPLES::
Expand Down Expand Up @@ -237,7 +253,7 @@ def functorial_composition(self, y):
EXAMPLES::
sage: G = species.SimpleGraphSpecies()
sage: g = G.generating_series()
sage: g = G.generating_series() # indirect doctest
sage: g._stream
<class 'sage.combinat.species.generating_series.FunctorialCompositionStream'>
sage: g.coefficients(10)
Expand Down Expand Up @@ -349,6 +365,22 @@ def coefficient_cycle_type(self, t):

class StretchStream(SeriesStream):
def __init__(self, stream, k, **kwds):
"""
A class for the coefficients of a "stretched" cycle index
series. See
:meth:`sage.combinat.species.generating_series.CycleIndexSeries.stretch`
for a definition.
EXAMPLES::
sage: from sage.combinat.species.generating_series import CycleIndexSeriesRing
sage: p = SymmetricFunctions(QQ).power()
sage: CIS = CycleIndexSeriesRing(QQ)
sage: f = CIS([0, p([1]), 2*p([1,1]),3*p([2,1]), 0])
sage: s = f.StretchStream(f._stream, 2, base_ring=f.base_ring())
sage: [s[i] for i in range(10)]
[0, 0, p[2], 0, 2*p[2, 2], 0, 3*p[4, 2], 0, 0, 0]
"""
self._stream = stream
self._k = k
super(CycleIndexSeries.StretchStream, self).__init__(children=[stream], **kwds)
Expand All @@ -375,6 +407,8 @@ def order_operation(self, a):

def compute(self, n):
"""
Computes the $n^{th}$ coefficient of the stretched stream.
EXAMPLES::
sage: from sage.combinat.species.generating_series import CycleIndexSeriesRing
Expand Down Expand Up @@ -443,6 +477,21 @@ def stretch(self, k):

class IsotypeGeneratingSeriesStream(SeriesStream):
def __init__(self, stream, **kwds):
"""
A class for the coefficients of the isotype generating
series given the corresponding cycle index series.
EXAMPLES::
sage: P = species.PermutationSpecies()
sage: cis = P.cycle_index_series()
sage: g = cis.IsotypeGeneratingSeriesStream(cis._stream, base_ring=cis.base_ring().base_ring())
sage: [g[i] for i in range(5)]
[1, 1, 2, 3, 5]
sage: itgs = cis.isotype_generating_series()
sage: [itgs[i] for i in range(5)]
[1, 1, 2, 3, 5]
"""
self._stream = stream
super(CycleIndexSeries.IsotypeGeneratingSeriesStream, self).__init__(children=[stream],
**kwds)
Expand Down Expand Up @@ -633,6 +682,8 @@ def multinv_builder(i):
@coerce_binop
def __div__(self, y):
"""
Division between two cycle index series.
TESTS::
sage: E = species.SetSpecies().cycle_index_series()
Expand All @@ -643,6 +694,24 @@ def __div__(self, y):

class FunctorialCompositionStream(SeriesStream):
def __init__(self, outer_series, inner_series, **kwds):
"""
A class for the coefficients of a cycle index series of a
functorial composition between two species.
EXAMPLES::
sage: E = species.SetSpecies()
sage: E2 = species.SetSpecies(size=2)
sage: WP = species.SubsetSpecies()
sage: P2 = E2*E
sage: P2_cis = P2.cycle_index_series()
sage: WP_cis = WP.cycle_index_series()
sage: s = WP_cis.FunctorialCompositionStream(WP_cis, P2_cis, base_ring=WP_cis.base_ring())
sage: [s[i] for i in range(4)]
[p[], p[1], p[1, 1] + p[2], 4/3*p[1, 1, 1] + 2*p[2, 1] + 2/3*p[3]]
sage: species.SimpleGraphSpecies().cycle_index_series().coefficients(4)
[p[], p[1], p[1, 1] + p[2], 4/3*p[1, 1, 1] + 2*p[2, 1] + 2/3*p[3]]
"""
self._outer = outer_series
self._inner = inner_series
super(CycleIndexSeries.FunctorialCompositionStream, self).__init__(**kwds)
Expand Down Expand Up @@ -702,7 +771,7 @@ def functorial_composition(self, g):
This is how it is implemented in :meth:`~sage.combinat.species.library.SimpleGraphSpecies`::
sage: S = species.SimpleGraphSpecies()
sage: cis = S.cycle_index_series()
sage: cis = S.cycle_index_series() # indirect doctest
sage: cis._stream
<class 'sage.combinat.species.generating_series.FunctorialCompositionStream'>
sage: cis.coefficients(5)
Expand Down Expand Up @@ -887,24 +956,23 @@ def _card(self, n):


class CompositionStream(LazyPowerSeries.CompositionStream):
"""
Returns a generator for the coefficients of the composition of this
cycle index series and the cycle index series y. This overrides the
the method defined in LazyPowerSeries.
def __init__(self, *args ,**kwds):
"""
A class for the coefficients of the composition of two
cycle index series.
EXAMPLES::
EXAMPLES::
sage: E = species.SetSpecies(); C = species.CycleSpecies()
sage: E_cis = E.cycle_index_series()
sage: g = E_cis(C.cycle_index_series())
sage: [g[i] for i in range(4)]
[p[], p[1], p[1, 1] + p[2], p[1, 1, 1] + p[2, 1] + p[3]]
"""
def __init__(self, *args ,**kwds):
sage: E = species.SetSpecies(); C = species.CycleSpecies()
sage: E_cis = E.cycle_index_series()
sage: g = E_cis(C.cycle_index_series())
sage: [g[i] for i in range(4)]
[p[], p[1], p[1, 1] + p[2], p[1, 1, 1] + p[2, 1] + p[3]]
"""
super(CycleIndexSeries.CompositionStream, self).__init__(*args, **kwds)
self._y_powers = PowerStream(self._inner)

def recursive_stream(self):
def tail_stream(self):
"""
Returns a stream whose tail is equal to the tail of this
composition stream.
Expand All @@ -918,7 +986,7 @@ def recursive_stream(self):
<class 'sage.combinat.species.generating_series.CompositionStream'>
sage: g.coefficients(4)
[p[], p[1], p[1, 1] + p[2], p[1, 1, 1] + p[2, 1] + p[3]]
sage: res = s.recursive_stream()
sage: res = s.tail_stream()
sage: [res[i] for i in range(1, 4)]
[p[1], p[1, 1] + p[2], p[1, 1, 1] + p[2, 1] + p[3]]
"""
Expand All @@ -929,17 +997,16 @@ def recursive_stream(self):

def _compose_term(self, p, y_powers):
"""
Returns the composition of one term in self with y.
Returns the composition of one term in the outer series
with the inner series.
INPUT:
- ``p`` - a term in self
- ``y_powers`` - a stream for the powers of y
starting with y
EXAMPLES::
sage: E = species.SetSpecies(); C = species.CycleSpecies()
Expand Down Expand Up @@ -970,23 +1037,39 @@ def _compose_term(self, p, y_powers):
return ListSumStream(res, base_ring=self._base_ring)

class WeightedCompositionStream(LazyPowerSeries.CompositionStream):
"""
Returns an iterator for the composition of this cycle index series
and the cycle index series of the weighted species y_species.
def __init__(self, outer, inner, inner_species, **kwds):
"""
A class for the coefficients of the composition of a
cycle index series and the cycle index series of the
weighted species.
EXAMPLES::
EXAMPLES::
sage: E = species.SetSpecies(); C = species.CycleSpecies()
sage: E_cis = E.cycle_index_series()
sage: g = E_cis.weighted_composition(C)
sage: [g[i] for i in range(4)]
[p[], p[1], p[1, 1] + p[2], p[1, 1, 1] + p[2, 1] + p[3]]
"""
def __init__(self, outer, inner, inner_species, **kwds):
sage: E = species.SetSpecies(); C = species.CycleSpecies()
sage: E_cis = E.cycle_index_series()
sage: g = E_cis.weighted_composition(C)
sage: [g[i] for i in range(4)]
[p[], p[1], p[1, 1] + p[2], p[1, 1, 1] + p[2, 1] + p[3]]
"""
self._inner_species = inner_species
super(CycleIndexSeries.WeightedCompositionStream, self).__init__(outer, inner, **kwds)

def recursive_stream(self):
def tail_stream(self):
"""
Returns a stream whose tail is equal to the tail of this
composition stream.
EXAMPLES::
sage: E = species.SetSpecies(); C = species.CycleSpecies()
sage: E_cis = E.cycle_index_series()
sage: g = E_cis.weighted_composition(C)._stream
sage: [g[i] for i in range(1, 4)]
[p[1], p[1, 1] + p[2], p[1, 1, 1] + p[2, 1] + p[3]]
sage: tail = g.tail_stream()
sage: [tail[i] for i in range(1, 4)]
[p[1], p[1, 1] + p[2], p[1, 1, 1] + p[2, 1] + p[3]]
"""
g = (self._weighted_compose_term(self._outer[i], self._inner_species)
for i in NN)
return SumGeneratorStream(g, base_ring=self._base_ring)
Expand All @@ -997,12 +1080,10 @@ def _weighted_compose_term(self, p, y_species):
INPUT:
- ``p`` - a term in self
- ``y_species`` - a species
EXAMPLES::
sage: E = species.SetSpecies(); C = species.CycleSpecies()
Expand Down
8 changes: 4 additions & 4 deletions src/sage/combinat/species/series_stream.py
View file
Original file line number Diff line number Diff line change
Expand Up @@ -533,7 +533,7 @@ def order_operation(self, a, b):
"""
return a*b

def recursive_stream(self):
def tail_stream(self):
"""
Returns a stream whose tail is equal to the tail of this
composition stream.
Expand All @@ -548,7 +548,7 @@ def recursive_stream(self):
<class 'sage.combinat.species.series_stream.CompositionStream'>
sage: [stream[i] for i in range(1, 5)]
[6, 24, 96, 384]
sage: f = stream.recursive_stream()
sage: f = stream.tail_stream()
sage: [f[i] for i in range(1, 5)]
[6, 24, 96, 384]
Expand All @@ -563,7 +563,7 @@ def compute(self, n):
Returns the $n^{th}$ coefficient of this composition stream.
If $n = 0$, then it will return the $0^{th}$ coefficient of
``self._outer``; otherwise, it will return the $n^th$ coefficient
of the stream defined by :meth:`recursive_stream`.
of the stream defined by :meth:`tail_stream`.
EXAMPLES::
Expand All @@ -583,7 +583,7 @@ def compute(self, n):
try:
res = self._res
except AttributeError:
res = self._res = self.recursive_stream()
res = self._res = self.tail_stream()
res[0]
return res[n]

Expand Down

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