예제 #1
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파일: orb.py 프로젝트: MShaffar19/PyQuantum
def L(l, n, rho):
    """Laguerre polynomial"""
    _L = 0.
    for i in range((n - l - 1) + 1):  # using a loop to do the summation
        _L += ((-i)**i * fac(n + l)**2. *
               rho**i) / (fac(i) * fac(n - l - 1. - i) * fac(2. * l + 1. + i))
    return _L
def R(r, n, l, z=1., a_0=1.):
    """Radial function"""
    rho = 2. * z * r / (n * a_0)
    _L = L(l, n, rho)
    _R = (2.*z/(n*a_0))**(3./2.)*sqrt(fac(n-l-1.)/\
         (2.*n*fac(n+l)**3.))*exp(-z/(n*a_0)*r)*rho**l*_L
    return _R
def Y_l_m(l,m,phi,theta):
    """Spherical harmonics"""
    eq = P_l_m(m,l,theta)
    if m>0:
        pe=re(exp(I*m*phi))*sqrt(2)
    elif m<0:
        pe=im(exp(I*m*phi))*sqrt(2)
    elif m==0:
        pe=1
    return abs(sqrt(((2*l+1)*fac(l-Abs(m)))/(4*pi*fac(l+Abs(m))))*pe*eq)
예제 #4
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파일: orb.py 프로젝트: MShaffar19/PyQuantum
def P_l(l, theta):  # valid for l greater than equal to zero
    """Legendre polynomial"""
    if l >= 0:
        eq = diff((cos(theta)**2 - 1)**l, cos(theta), l)
    else:
        print("l must be an integer equal to 0 or greater")
        raise ValueError
    return 1 / (2**l * fac(l)) * eq
예제 #5
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def test_factorint():
    assert sorted(factorint(123456).items()) == [(2, 6), (3, 1), (643, 1)]
    assert primefactors(123456) == [2, 3, 643]
    assert factorint(-16) == {-1:1, 2:4}
    assert factorint(2**(2**6) + 1) == {274177:1, 67280421310721:1}
    assert factorint(5951757) == {3:1, 7:1, 29:2, 337:1}
    assert factorint(64015937) == {7993:1, 8009:1}
    assert divisors(1) == [1]
    assert divisors(2) == [1, 2]
    assert divisors(3) == [1, 3]
    assert divisors(10) == [1, 2, 5, 10]
    assert divisors(100) == [1, 2, 4, 5, 10, 20, 25, 50, 100]
    assert divisors(101) == [1, 101]
    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(3,2) == {3: 1}
    assert factorint(12345) == {3: 1, 5: 1, 823: 1}
    assert factorint(12345, 3) == {12345: 1} # there are no factors less than 3
예제 #6
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def test_primeomega():
    assert primeomega(2) == 1
    assert primeomega(2 * 2) == 2
    assert primeomega(2 * 2 * 3) == 3
    assert primeomega(3 * 25) == primeomega(3) + primeomega(25)
    assert [primeomega(p) for p in primerange(1, 10)] == [1, 1, 1, 1]
    assert primeomega(fac(50)) == 108
    assert primeomega(2 ** 9941 - 1) == 1
    n = Symbol('n', integer=True)
    assert primeomega(n)
    assert primeomega(n).subs(n, 2 ** 31 - 1) == 1
    assert summation(primeomega(n), (n, 2, 30)) == 59
예제 #7
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def test_primeomega():
    assert primeomega(2) == 1
    assert primeomega(2 * 2) == 2
    assert primeomega(2 * 2 * 3) == 3
    assert primeomega(3 * 25) == primeomega(3) + primeomega(25)
    assert [primeomega(p) for p in primerange(1, 10)] == [1, 1, 1, 1]
    assert primeomega(fac(50)) == 108
    assert primeomega(2 ** 9941 - 1) == 1
    n = Symbol('n', integer=True)
    assert primeomega(n)
    assert primeomega(n).subs(n, 2 ** 31 - 1) == 1
    assert summation(primeomega(n), (n, 2, 30)) == 59
예제 #8
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def test_primenu():
    assert primenu(2) == 1
    assert primenu(2 * 3) == 2
    assert primenu(2 * 3 * 5) == 3
    assert primenu(3 * 25) == primenu(3) + primenu(25)
    assert [primenu(p) for p in primerange(1, 10)] == [1, 1, 1, 1]
    assert primenu(fac(50)) == 15
    assert primenu(2**9941 - 1) == 1
    n = Symbol("n", integer=True)
    assert primenu(n)
    assert primenu(n).subs(n, 2**31 - 1) == 1
    assert summation(primenu(n), (n, 2, 30)) == 43
예제 #9
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def test_factorint():
    assert sorted(factorint(123456).items()) == [(2, 6), (3, 1), (643, 1)]
    assert primefactors(123456) == [2, 3, 643]
    assert factorint(-16) == {-1: 1, 2: 4}
    assert factorint(2**(2**6) + 1) == {274177: 1, 67280421310721: 1}
    assert factorint(5951757) == {3: 1, 7: 1, 29: 2, 337: 1}
    assert factorint(64015937) == {7993: 1, 8009: 1}
    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, 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
예제 #10
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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}
    #issue 19683
    assert factorint(10**38 - 1) == {3: 2, 11: 1, 909090909090909091: 1, 1111111111111111111: 1}
    #issue 17676
    assert factorint(28300421052393658575) == {3: 1, 5: 2, 11: 2, 43: 1, 2063: 2, 4127: 1, 4129: 1}
    assert factorint(2063**2 * 4127**1 * 4129**1) == {2063: 2, 4127: 1, 4129: 1}
    assert factorint(2347**2 * 7039**1 * 7043**1) == {2347: 2, 7039: 1, 7043: 1}

    assert factorint(0, multiple=True) == [0]
    assert factorint(1, multiple=True) == []
    assert factorint(-1, multiple=True) == [-1]
    assert factorint(-2, multiple=True) == [-1, 2]
    assert factorint(-16, multiple=True) == [-1, 2, 2, 2, 2]
    assert factorint(2, multiple=True) == [2]
    assert factorint(24, multiple=True) == [2, 2, 2, 3]
    assert factorint(126, multiple=True) == [2, 3, 3, 7]
    assert factorint(123456, multiple=True) == [2, 2, 2, 2, 2, 2, 3, 643]
    assert factorint(5951757, multiple=True) == [3, 7, 29, 29, 337]
    assert factorint(64015937, multiple=True) == [7993, 8009]
    assert factorint(2**(2**6) + 1, multiple=True) == [274177, 67280421310721]

    assert factorint(fac(1, evaluate=False)) == {}
    assert factorint(fac(7, evaluate=False)) == {2: 4, 3: 2, 5: 1, 7: 1}
    assert factorint(fac(15, evaluate=False)) == \
        {2: 11, 3: 6, 5: 3, 7: 2, 11: 1, 13: 1}
    assert factorint(fac(20, evaluate=False)) == \
        {2: 18, 3: 8, 5: 4, 7: 2, 11: 1, 13: 1, 17: 1, 19: 1}
    assert factorint(fac(23, evaluate=False)) == \
        {2: 19, 3: 9, 5: 4, 7: 3, 11: 2, 13: 1, 17: 1, 19: 1, 23: 1}

    assert multiproduct(factorint(fac(200))) == fac(200)
    assert multiproduct(factorint(fac(200, evaluate=False))) == fac(200)
    for b, e in factorint(fac(150)).items():
        assert e == fac_multiplicity(150, b)
    for b, e in factorint(fac(150, evaluate=False)).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 len(factorint(fac(10000, evaluate=False))) == 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) == \
        {int(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))
    # test dict/Dict input
    sans = '2**10*3**3'
    n = {4: 2, 12: 3}
    assert str(factorint(n)) == sans
    assert str(factorint(Dict(n))) == sans
예제 #11
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def test_multiplicity_in_factorial():
    n = fac(1000)
    for i in (2, 4, 6, 12, 30, 36, 48, 60, 72, 96):
        assert multiplicity(i, n) == multiplicity_in_factorial(i, 1000)
예제 #12
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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))
예제 #13
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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(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) == \
           {19026377261L: 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, 'pollard_rho(4)')
    raises(ValueError, 'pollard_pm1(3)')
    raises(ValueError, '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}
예제 #14
0
"""
Created Nov 19, 2012

Author: Spencer Lyon

Project Euler Problem 34
"""
from sympy import factorial as fac
from time import time

start_time = time()

upper = fac(9) * 7

facs = [fac(i) for i in range(10)]

the_sum = 0
for x in xrange(3, upper + 1):
    if x == sum([facs[int(i)] for i in str(x)]):
        the_sum += x

print the_sum

running_time = time()
elapsed_time = running_time - start_time
print "Total Execution time is ", elapsed_time, "seconds"