def __init__(
self, number: int = None, *, tweaks: LilyPondTweakManager = None
) -> None:
if number is not None:
assert mathtools.is_positive_integer(number)
self._number = number
if tweaks is not None:
assert isinstance(tweaks, LilyPondTweakManager), repr(tweaks)
self._tweaks = LilyPondTweakManager.set_tweaks(self, tweaks)
def __init__(
self,
number: int = None,
*,
tweaks: typing.Union[typing.List[typing.Tuple],
LilyPondTweakManager] = None,
) -> None:
if number is not None:
assert mathtools.is_positive_integer(number)
self._number = number
self._tweaks = None
LilyPondTweakManager.set_tweaks(self, tweaks)
def factors(n):
"""
Gets prime factors less than or equal to ``n`` .
.. container:: example
>>> abjad.mathtools.factors(84)
[2, 2, 3, 7]
>>> for n in range(10, 20):
... print(n, abjad.mathtools.factors(n))
...
10 [2, 5]
11 [11]
12 [2, 2, 3]
13 [13]
14 [2, 7]
15 [3, 5]
16 [2, 2, 2, 2]
17 [17]
18 [2, 3, 3]
19 [19]
``n`` must be a positive integer.
Returns factors in increasing order.
Returns list of positive integers.
"""
from abjad import mathtools
if not mathtools.is_positive_integer(n):
message = "must be positive integer: {!r}."
message = message.format(n)
raise TypeError(message)
factor = 2
factors = []
while 1 < n:
if n % factor == 0:
factors.append(factor)
n = n / factor
else:
factor = factor + 1
return factors
def _yield_restricted_growth_functions(length):
"""
Yields restricted growth functions of ``length``.
.. container:: example
>>> rgfs = abjad.Enumerator._yield_restricted_growth_functions(4)
>>> for rgf in rgfs:
... rgf
...
(1, 1, 1, 1)
(1, 1, 1, 2)
(1, 1, 2, 1)
(1, 1, 2, 2)
(1, 1, 2, 3)
(1, 2, 1, 1)
(1, 2, 1, 2)
(1, 2, 1, 3)
(1, 2, 2, 1)
(1, 2, 2, 2)
(1, 2, 2, 3)
(1, 2, 3, 1)
(1, 2, 3, 2)
(1, 2, 3, 3)
(1, 2, 3, 4)
Returns restricted growth functions in lex order.
Returns generator of tuples.
"""
assert mathtools.is_positive_integer(length), repr(length)
last_rgf = list(range(1, length + 1))
rgf = length * [1]
yield tuple(rgf)
while not rgf == last_rgf:
for i, x in enumerate(reversed(rgf)):
stop = -(i + 1)
if x < max(rgf[:stop]) + 1:
first_part = rgf[:stop]
increased_part = [rgf[stop] + 1]
trailing_ones = i * [1]
rgf = first_part + increased_part + trailing_ones
yield tuple(rgf)
break
def all_are_positive_integers(argument):
"""
Is true when ``argument`` is an iterable collection of positive integers.
.. container:: example
>>> abjad.mathtools.all_are_positive_integers([1, 2, 3, 99])
True
>>> abjad.mathtools.all_are_positive_integers(17)
False
Returns true or false.
"""
from abjad import mathtools
try:
return all(mathtools.is_positive_integer(_) for _ in argument)
except TypeError:
return False
def factors(n):
"""
Gets prime factors less than or equal to ``n`` .
.. container:: example
>>> abjad.mathtools.factors(84)
[2, 2, 3, 7]
>>> for n in range(10, 20):
... print(n, abjad.mathtools.factors(n))
...
10 [2, 5]
11 [11]
12 [2, 2, 3]
13 [13]
14 [2, 7]
15 [3, 5]
16 [2, 2, 2, 2]
17 [17]
18 [2, 3, 3]
19 [19]
``n`` must be a positive integer.
Returns factors in increasing order.
Returns list of positive integers.
"""
from abjad import mathtools
if not mathtools.is_positive_integer(n):
message = 'must be positive integer: {!r}.'
message = message.format(n)
raise TypeError(message)
factor = 2
factors = []
while 1 < n:
if n % factor == 0:
factors.append(factor)
n = n / factor
else:
factor = factor + 1
return factors
def all_are_positive_integers(argument):
"""
Is true when ``argument`` is an iterable collection of positive integers.
.. container:: example
>>> abjad.mathtools.all_are_positive_integers([1, 2, 3, 99])
True
>>> abjad.mathtools.all_are_positive_integers(17)
False
Returns true or false.
"""
from abjad import mathtools
try:
return all(mathtools.is_positive_integer(_) for _ in argument)
except TypeError:
return False