Python ntheory.primorial函数代码示例

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本文整理汇总了Python中sympy.ntheory.primorial函数的典型用法代码示例。如果您正苦于以下问题：Python primorial函数的具体用法？Python primorial怎么用？Python primorial使用的例子？那么恭喜您, 这里精选的函数代码示例或许可以为您提供帮助。

在下文中一共展示了primorial函数的4个代码示例，这些例子默认根据受欢迎程度排序。您可以为喜欢或者感觉有用的代码点赞，您的评价将有助于我们的系统推荐出更棒的Python代码示例。

示例1: test_generate

def test_generate():
    assert nextprime(-4) == 2
    assert nextprime(2) == 3
    assert nextprime(5) == 7
    assert nextprime(12) == 13
    assert nextprime(90) == 97
    assert nextprime(10**40) == (10**40 + 121)
    assert prevprime(3) == 2
    assert prevprime(7) == 5
    assert prevprime(13) == 11
    assert prevprime(97) == 89
    assert prevprime(10**40) == (10**40 - 17)
    assert list(primerange(2, 7)) == [2, 3, 5]
    assert list(primerange(2, 10)) == [2, 3, 5, 7]
    assert list(primerange(1050, 1100)) == [1051, 1061,
        1063, 1069, 1087, 1091, 1093, 1097]
    s = Sieve()
    for i in range(30, 2350, 376):
        for j in range(2, 5096, 1139):
            A = list(s.primerange(i, i + j))
            B = list(primerange(i, i + j))
            assert A == B
    s = Sieve()
    assert s[10] == 29

    assert nextprime(2, 2) == 5

    raises(ValueError, lambda: totient(0))

    raises(ValueError, lambda: reduced_totient(0))

    raises(ValueError, lambda: primorial(0))

    assert mr(1, [2]) is False

    func = lambda i: (i**2 + 1) % 51
    assert next(cycle_length(func, 4)) == (6, 2)
    assert list(cycle_length(func, 4, values=True)) == \
        [17, 35, 2, 5, 26, 14, 44, 50, 2, 5, 26, 14]
    assert next(cycle_length(func, 4, nmax=5)) == (5, None)
    assert list(cycle_length(func, 4, nmax=5, values=True)) == \
        [17, 35, 2, 5, 26]

开发者ID:JamesdeLisle，项目名称:sympy，代码行数:42，代码来源:test_generate.py

示例2: test_primorial

def test_primorial():
    assert primorial(1) == 2
    assert primorial(1, nth=0) == 1
    assert primorial(2) == 6
    assert primorial(2, nth=0) == 2
    assert primorial(4, nth=0) == 6

开发者ID:LuckyStrikes1090，项目名称:sympy，代码行数:6，代码来源:test_ntheory.py

示例3: test_factorint

def test_factorint():
    assert primefactors(123456) == [2, 3, 643]
    assert factorint(0) == {0: 1}
    assert factorint(1) == {}
    assert factorint(-1) == {-1: 1}
    assert factorint(-2) == {-1: 1, 2: 1}
    assert factorint(-16) == {-1: 1, 2: 4}
    assert factorint(2) == {2: 1}
    assert factorint(126) == {2: 1, 3: 2, 7: 1}
    assert factorint(123456) == {2: 6, 3: 1, 643: 1}
    assert factorint(5951757) == {3: 1, 7: 1, 29: 2, 337: 1}
    assert factorint(64015937) == {7993: 1, 8009: 1}
    assert factorint(2**(2**6) + 1) == {274177: 1, 67280421310721: 1}
    assert multiproduct(factorint(fac(200))) == fac(200)
    for b, e in factorint(fac(150)).items():
        assert e == fac_multiplicity(150, b)
    assert factorint(103005006059**7) == {103005006059: 7}
    assert factorint(31337**191) == {31337: 191}
    assert factorint(2**1000 * 3**500 * 257**127 * 383**60) == \
        {2: 1000, 3: 500, 257: 127, 383: 60}
    assert len(factorint(fac(10000))) == 1229
    assert factorint(12932983746293756928584532764589230) == \
        {2: 1, 5: 1, 73: 1, 727719592270351: 1, 63564265087747: 1, 383: 1}
    assert factorint(727719592270351) == {727719592270351: 1}
    assert factorint(2**64 + 1, use_trial=False) == factorint(2**64 + 1)
    for n in range(60000):
        assert multiproduct(factorint(n)) == n
    assert pollard_rho(2**64 + 1, seed=1) == 274177
    assert pollard_rho(19, seed=1) is None
    assert factorint(3, limit=2) == {3: 1}
    assert factorint(12345) == {3: 1, 5: 1, 823: 1}
    assert factorint(
        12345, limit=3) == {4115: 1, 3: 1}  # the 5 is greater than the limit
    assert factorint(1, limit=1) == {}
    assert factorint(0, 3) == {0: 1}
    assert factorint(12, limit=1) == {12: 1}
    assert factorint(30, limit=2) == {2: 1, 15: 1}
    assert factorint(16, limit=2) == {2: 4}
    assert factorint(124, limit=3) == {2: 2, 31: 1}
    assert factorint(4*31**2, limit=3) == {2: 2, 31: 2}
    p1 = nextprime(2**32)
    p2 = nextprime(2**16)
    p3 = nextprime(p2)
    assert factorint(p1*p2*p3) == {p1: 1, p2: 1, p3: 1}
    assert factorint(13*17*19, limit=15) == {13: 1, 17*19: 1}
    assert factorint(1951*15013*15053, limit=2000) == {225990689: 1, 1951: 1}
    assert factorint(primorial(17) + 1, use_pm1=0) == \
        {long(19026377261): 1, 3467: 1, 277: 1, 105229: 1}
    # when prime b is closer than approx sqrt(8*p) to prime p then they are
    # "close" and have a trivial factorization
    a = nextprime(2**2**8)  # 78 digits
    b = nextprime(a + 2**2**4)
    assert 'Fermat' in capture(lambda: factorint(a*b, verbose=1))

    raises(ValueError, lambda: pollard_rho(4))
    raises(ValueError, lambda: pollard_pm1(3))
    raises(ValueError, lambda: pollard_pm1(10, B=2))
    # verbose coverage
    n = nextprime(2**16)*nextprime(2**17)*nextprime(1901)
    assert 'with primes' in capture(lambda: factorint(n, verbose=1))
    capture(lambda: factorint(nextprime(2**16)*1012, verbose=1))

    n = nextprime(2**17)
    capture(lambda: factorint(n**3, verbose=1))  # perfect power termination
    capture(lambda: factorint(2*n, verbose=1))  # factoring complete msg

    # exceed 1st
    n = nextprime(2**17)
    n *= nextprime(n)
    assert '1000' in capture(lambda: factorint(n, limit=1000, verbose=1))
    n *= nextprime(n)
    assert len(factorint(n)) == 3
    assert len(factorint(n, limit=p1)) == 3
    n *= nextprime(2*n)
    # exceed 2nd
    assert '2001' in capture(lambda: factorint(n, limit=2000, verbose=1))
    assert capture(
        lambda: factorint(n, limit=4000, verbose=1)).count('Pollard') == 2
    # non-prime pm1 result
    n = nextprime(8069)
    n *= nextprime(2*n)*nextprime(2*n, 2)
    capture(lambda: factorint(n, verbose=1))  # non-prime pm1 result
    # factor fermat composite
    p1 = nextprime(2**17)
    p2 = nextprime(2*p1)
    assert factorint((p1*p2**2)**3) == {p1: 3, p2: 6}
    # Test for non integer input
    raises(ValueError, lambda: factorint(4.5))

开发者ID:LuckyStrikes1090，项目名称:sympy，代码行数:88，代码来源:test_ntheory.py

示例4: test_generate

def test_generate():
    from sympy.ntheory.generate import sieve
    sieve._reset()
    assert nextprime(-4) == 2
    assert nextprime(2) == 3
    assert nextprime(5) == 7
    assert nextprime(12) == 13
    assert prevprime(3) == 2
    assert prevprime(7) == 5
    assert prevprime(13) == 11
    assert prevprime(19) == 17
    assert prevprime(20) == 19

    sieve.extend_to_no(9)
    assert sieve._list[-1] == 23

    assert sieve._list[-1] < 31
    assert 31 in sieve

    assert nextprime(90) == 97
    assert nextprime(10**40) == (10**40 + 121)
    assert prevprime(97) == 89
    assert prevprime(10**40) == (10**40 - 17)

    assert list(sieve.primerange(10, 1)) == []
    assert list(sieve.primerange(5, 9)) == [5, 7]
    sieve._reset(prime=True)
    assert list(sieve.primerange(2, 12)) == [2, 3, 5, 7, 11]

    assert list(sieve.totientrange(5, 15)) == [4, 2, 6, 4, 6, 4, 10, 4, 12, 6]
    sieve._reset(totient=True)
    assert list(sieve.totientrange(3, 13)) == [2, 2, 4, 2, 6, 4, 6, 4, 10, 4]
    assert list(sieve.totientrange(900, 1000)) == [totient(x) for x in range(900, 1000)]
    assert list(sieve.totientrange(0, 1)) == []
    assert list(sieve.totientrange(1, 2)) == [1]

    assert list(sieve.mobiusrange(5, 15)) == [-1, 1, -1, 0, 0, 1, -1, 0, -1, 1]
    sieve._reset(mobius=True)
    assert list(sieve.mobiusrange(3, 13)) == [-1, 0, -1, 1, -1, 0, 0, 1, -1, 0]
    assert list(sieve.mobiusrange(1050, 1100)) == [mobius(x) for x in range(1050, 1100)]
    assert list(sieve.mobiusrange(0, 1)) == []
    assert list(sieve.mobiusrange(1, 2)) == [1]

    assert list(primerange(10, 1)) == []
    assert list(primerange(2, 7)) == [2, 3, 5]
    assert list(primerange(2, 10)) == [2, 3, 5, 7]
    assert list(primerange(1050, 1100)) == [1051, 1061,
        1063, 1069, 1087, 1091, 1093, 1097]
    s = Sieve()
    for i in range(30, 2350, 376):
        for j in range(2, 5096, 1139):
            A = list(s.primerange(i, i + j))
            B = list(primerange(i, i + j))
            assert A == B
    s = Sieve()
    assert s[10] == 29

    assert nextprime(2, 2) == 5

    raises(ValueError, lambda: totient(0))

    raises(ValueError, lambda: reduced_totient(0))

    raises(ValueError, lambda: primorial(0))

    assert mr(1, [2]) is False

    func = lambda i: (i**2 + 1) % 51
    assert next(cycle_length(func, 4)) == (6, 2)
    assert list(cycle_length(func, 4, values=True)) == \
        [17, 35, 2, 5, 26, 14, 44, 50, 2, 5, 26, 14]
    assert next(cycle_length(func, 4, nmax=5)) == (5, None)
    assert list(cycle_length(func, 4, nmax=5, values=True)) == \
        [17, 35, 2, 5, 26]
    sieve.extend(3000)
    assert nextprime(2968) == 2969
    assert prevprime(2930) == 2927
    raises(ValueError, lambda: prevprime(1))

开发者ID:KonstantinTogoi，项目名称:sympy，代码行数:78，代码来源:test_generate.py

注：本文中的sympy.ntheory.primorial函数示例由纯净天空整理自Github/MSDocs等源码及文档管理平台，相关代码片段筛选自各路编程大神贡献的开源项目，源码版权归原作者所有，传播和使用请参考对应项目的License；未经允许，请勿转载。

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Python ntheory.primorial函数代码示例

示例1: test_generate

示例2: test_primorial

示例3: test_factorint

示例4: test_generate

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