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Trac #17263: remove "optional - arb"
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@cheuberg
cheuberg committed Nov 29, 2015
1 parent 3a5f3f9 commit 9f3a647
Showing 1 changed file with 25 additions and 25 deletions.
50 changes: 25 additions & 25 deletions src/sage/combinat/fsm_fourier.pyx
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Expand Up @@ -396,28 +396,28 @@ def _reduce_resolution_(data, x_min, x_max, resolution):
EXAMPLES::
sage: from sage.combinat.fsm_fourier import _reduce_resolution_ # optional - arb
sage: _reduce_resolution_(((i/10, i) for i in range(10)), # optional - arb
sage: from sage.combinat.fsm_fourier import _reduce_resolution_
sage: _reduce_resolution_(((i/10, i) for i in range(10)),
....: 0, 1, 2)
[(0.0, 0, 4), (0.5, 5, 9)]
sage: _reduce_resolution_(((1 - i/10, i) for i in range(1, 11)), # optional - arb
sage: _reduce_resolution_(((1 - i/10, i) for i in range(1, 11)),
....: 0, 1, 2)
[(0.0, 6, 10), (0.5, 1, 5)]
sage: _reduce_resolution_(((0, 2), (0.2, 1), (0.4, 0), # optional - arb
sage: _reduce_resolution_(((0, 2), (0.2, 1), (0.4, 0),
....: (0.6, 1.5), (0.8, 3)), 0, 1, 2)
[(0.0, 0, 2), (0.5, 1.50000000000000, 3)]
sage: _reduce_resolution_([(0, 10)], # optional - arb
sage: _reduce_resolution_([(0, 10)],
....: 0, 1, 2)
[(0.0, 10, 10)]
TESTS::
sage: _reduce_resolution_([(1, 10)], # optional - arb
sage: _reduce_resolution_([(1, 10)],
....: 0, 1, 2)
Traceback (most recent call last):
...
ValueError: x values must be >= x_min and < x_max.
sage: _reduce_resolution_([(-1, 10)], # optional - arb
sage: _reduce_resolution_([(-1, 10)],
....: 0, 1, 2)
Traceback (most recent call last):
...
Expand Down Expand Up @@ -1173,14 +1173,14 @@ cdef class FSMFourierCache(SageObject):
f
sage: var('n')
n
sage: from sage.combinat.fsm_fourier import FSMFourier # optional - arb
sage: from sage.combinat.fsm_fourier import FSMFourier
sage: T = transducers.Recursion([
....: f(2*n + 1) == f(n) + 1,
....: f(2*n) == f(n),
....: f(0) == 0],
....: 2, f, n)
sage: F = FSMFourier(T) # optional - arb
sage: F.cache.fluctuation_empirical(10, 12) # optional - arb; tolerance 1e-12
sage: F = FSMFourier(T)
sage: F.cache.fluctuation_empirical(10, 12) # tolerance 1e-12
[(3.3219280948873626, -0.1609640474436813),
(3.4594316186372978, -0.18426126386410324)]
Expand All @@ -1192,8 +1192,8 @@ cdef class FSMFourierCache(SageObject):
sage: T.state(0).final_word_out = 1
sage: [T(i.bits()) for i in srange(3)]
[[1], [0, 1], [0, 0, 1]]
sage: F = FSMFourier(T) # optional - arb
sage: F.cache.fluctuation_empirical(1, 4) # optional - arb; tolerance 1e-12
sage: F = FSMFourier(T)
sage: F.cache.fluctuation_empirical(1, 4) # tolerance 1e-12
[(0.0, 1.0), (1.0, 1.0), (1.5849625007211563, 1.0)]
The following transducer has sum of output `\lfloor\log n\rfloor` for input `n`. ::
Expand All @@ -1204,17 +1204,17 @@ cdef class FSMFourierCache(SageObject):
sage: T.state(0).final_word_out = -1
sage: [sum(T(i.bits())) for i in srange(5)]
[-1, 0, 1, 1, 2]
sage: F = FSMFourier(T) # optional - arb
sage: F.e_T # optional - arb
sage: F = FSMFourier(T)
sage: F.e_T
1
sage: F.cache.fluctuation_empirical(1, 4) # optional - arb; tolerance 1e-12
sage: F.cache.fluctuation_empirical(1, 4) # tolerance 1e-12
[(0.0, -1.0),
(1.0, -1.5),
(1.5849625007211563, -1.5849625007211563)]
The parameter ``start`` must be positive::
sage: F.cache.fluctuation_empirical(0, 2) # optional - arb
sage: F.cache.fluctuation_empirical(0, 2)
Traceback (most recent call last):
...
ValueError: start must be positive.
Expand Down Expand Up @@ -1295,15 +1295,15 @@ cdef class FSMFourierCache(SageObject):
The following transducer has sum of output `1` for all input. ::
sage: from sage.combinat.fsm_fourier import FSMFourier # optional - arb
sage: from sage.combinat.fsm_fourier import FSMFourier
sage: T = Transducer([(0, 0, 0, 0), (0, 0, 1, 0)],
....: initial_states=[0],
....: final_states=[0])
sage: T.state(0).final_word_out = 1
sage: [T(i.bits()) for i in srange(3)]
[[1], [0, 1], [0, 0, 1]]
sage: F = FSMFourier(T) # optional - arb
sage: F.cache.fluctuation_fourier(2, 3, 2) # optional - arb; rel tolerance 1e-10
sage: F = FSMFourier(T)
sage: F.cache.fluctuation_fourier(2, 3, 2) # rel tolerance 1e-10
[(2.0, 0.9999999999999978), (2.5, 0.9999999999999991)]
"""
cdef double c0
Expand Down Expand Up @@ -2178,17 +2178,17 @@ class FSMFourier(SageObject):
EXAMPLES::
sage: from sage.combinat.fsm_fourier import FSMFourier # optional - arb
sage: from sage.combinat.fsm_fourier import FSMFourier
sage: function('f')
f
sage: var('n')
n
sage: F = FSMFourier(transducers.Recursion([ # optional - arb
sage: F = FSMFourier(transducers.Recursion([
....: f(2*n + 1) == f(n) + 1,
....: f(2*n) == f(n),
....: f(0) == 0],
....: 2, f, n))
sage: F.plot_fluctuation(8, 9, 2) # optional - arb
sage: F.plot_fluctuation(8, 9, 2)
Graphics object consisting of 2 graphics primitives
.. SEEALSO::
Expand Down Expand Up @@ -2243,18 +2243,18 @@ class FSMFourier(SageObject):
EXAMPLES::
sage: from sage.combinat.fsm_fourier import FSMFourier # optional - arb
sage: from sage.combinat.fsm_fourier import FSMFourier
sage: function('f')
f
sage: var('n')
n
sage: F = FSMFourier(transducers.Recursion([ # optional - arb
sage: F = FSMFourier(transducers.Recursion([
....: f(2*n + 1) == f(n) + 1,
....: f(2*n) == f(n),
....: f(0) == 0],
....: 2, f, n))
sage: dir = tmp_dir()
sage: F.plot_fluctuation_asymptote( # optional - arb
sage: F.plot_fluctuation_asymptote(
....: dir + "test", 8, 9, resolution=2)
.. SEEALSO::
Expand Down

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