def testGeneratorEratosthenes(self):
g = prime.generator_eratosthenes(3)
self.assertEqual(2, g.next())
self.assertEqual(3, g.next())
self.assertRaises(StopIteration, g.next)
g = prime.generator_eratosthenes(541)
self.assertEqual(100, len([p for p in g]))
def _parse_seq(self, options):
"""
Parse 'options' to define trial sequaence.
"""
if 'start' in options and 'stop' in options:
if 'step' in options:
trials = bigrange.range(options['start'], options['stop'], options['step'])
else:
trials = bigrange.range(options['start'], options['stop'])
elif 'iterator' in options:
trials = options['iterator']
elif 'eratosthenes' in options:
trials = prime.generator_eratosthenes(options['eratosthenes'])
elif options['n'] < 1000000:
trials = prime.generator_eratosthenes(arith1.floorsqrt(options['n']))
else:
trials = prime.generator()
return trials
def class_formula(disc, uprbd):
"""
Return the approximation of class number 'h' with the given discriminant.
h = sqrt(|D|)/pi (1 - (D/p)(1/p))^{-1} where p is less than ubound.
"""
ht = math.sqrt(abs(disc)) / math.pi
ml = number_unit(disc) / 2
for factor in prime.generator_eratosthenes(uprbd):
ml = ml * (1 - (kronecker(disc, factor) / factor))**(-1)
return int(ht * ml + 0.5)
def class_formula(disc, uprbd):
"""
Return the approximation of class number 'h' with the given discriminant.
h = sqrt(|D|)/pi (1 - (D/p)(1/p))^{-1} where p is less than ubound.
"""
ht = math.sqrt(abs(disc)) / math.pi
ml = number_unit(disc) / 2
for factor in prime.generator_eratosthenes(uprbd):
ml = ml * (1 - (kronecker(disc, factor) / factor))**(-1)
return int(ht * ml + 0.5)
def _parse_seq(self, options):
"""
Parse 'options' to define trial sequaence.
"""
if 'start' in options and 'stop' in options:
if 'step' in options:
trials = bigrange.range(options['start'], options['stop'],
options['step'])
else:
trials = bigrange.range(options['start'], options['stop'])
elif 'iterator' in options:
trials = options['iterator']
elif 'eratosthenes' in options:
trials = prime.generator_eratosthenes(options['eratosthenes'])
elif options['n'] < 1000000:
trials = prime.generator_eratosthenes(
arith1.floorsqrt(options['n']))
else:
trials = prime.generator()
return trials
def stage1(n, bounds, C, Q):
"""
ECM stage 1 for factoring n.
The upper bound for primes to be tested is bounds.first.
It uses curve C and starting point Q.
"""
for p in _prime.generator_eratosthenes(bounds.first):
q = p
while q < bounds.first:
Q = mul(Q, p, C, n)
q *= p
g = _gcd.gcd(Q.z, n)
_log.debug("Stage 1: %d" % g)
return g
def stage1(n, bounds, C, Q):
"""
ECM stage 1 for factoring n.
The upper bound for primes to be tested is bounds.first.
It uses curve C and starting point Q.
"""
for p in _prime.generator_eratosthenes(bounds.first):
q = p
while q < bounds.first:
Q = mul(Q, p, C, n)
q *= p
g = _gcd.gcd(Q.z, n)
_log.debug("Stage 1: %d" % g)
return g
def perfect_power_detection(n):
"""
Return (m, k) if n = m**k.
Note that k is the smallest possible and m still can be a perfect
power; if n is not a perfect power, it returns (n, 1).
"""
f = arith1.log(n) + 1
y = DyadicRational(0, n).nroot(1, 3 + (f - 1) // 2 + 1)
for p in prime.generator_eratosthenes(f):
x = _is_kth_power(n, p, y, f)
if x != 0:
return (x, p)
return (n, 1)
def powerDetection(n, largest_exp=False):
"""
param positive integer n
param boolean largest_exp
return integer x, k s.t. n == x ** k
(2 <= k if exist else x, k == n, 1)
if largest_exp is true then return largest k
"""
from nzmath.prime import generator_eratosthenes as generator_eratosthenes
ge = generator_eratosthenes(log(n, 2))
for exp in ge:
power_root, power = floorpowerroot(n, exp, True)
if power == n:
if largest_exp:
x, k = powerDetection(power_root, True)
return x, k * exp
else:
return power_root, exp
return n, 1
def trialDivision(n, **options):
"""
Return a factor of given integer by trial division.
options can be either:
1) 'start' and 'stop' as range parameters.
2) 'iterator' as an iterator of primes.
If both options are not given, prime factor is searched from 2
to the square root of the given integer.
"""
# verbosity
verbose = options.get('verbose', False)
if not verbose:
_silence()
if 'start' in options and 'stop' in options:
if 'step' in options:
trials = list(
range(options['start'], options['stop'], options['step']))
else:
trials = list(range(options['start'], options['stop']))
elif 'iterator' in options:
trials = options['iterator']
elif n < 1000000:
trials = prime.generator_eratosthenes(arith1.floorsqrt(n))
else:
trials = prime.generator()
limit = arith1.floorsqrt(n)
for p in trials:
if limit < p:
break
if 0 == n % p:
if not verbose:
_verbose()
return p
if not verbose:
_verbose()
return 1
def trialDivision(n, **options):
"""
Return a factor of given integer by trial division.
options can be either:
1) 'start' and 'stop' as range parameters.
2) 'iterator' as an iterator of primes.
If both options are not given, prime factor is searched from 2
to the square root of the given integer.
"""
# verbosity
verbose = options.get('verbose', False)
if not verbose:
_silence()
if 'start' in options and 'stop' in options:
if 'step' in options:
trials = range(options['start'], options['stop'], options['step'])
else:
trials = range(options['start'], options['stop'])
elif 'iterator' in options:
trials = options['iterator']
elif n < 1000000:
trials = prime.generator_eratosthenes(arith1.floorsqrt(n))
else:
trials = prime.generator()
for p in trials:
if not (n % p):
if not verbose:
_verbose()
return p
if p ** 2 > n:
break
if not verbose:
_verbose()
return 1
