コード例 #1
0
ファイル: test_ntheory.py プロジェクト: smichr/sympy-live
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
コード例 #2
0
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
コード例 #3
0
ファイル: test_ntheory.py プロジェクト: jcockayne/sympy-rkern
def test_factor():
    assert trial(1) == []
    assert trial(2) == [(2,1)]
    assert trial(3) == [(3,1)]
    assert trial(4) == [(2,2)]
    assert trial(5) == [(5,1)]
    assert trial(128) == [(2,7)]
    assert trial(720) == [(2,4), (3,2), (5,1)]
    assert factorint(123456) == [(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 pollard_rho(2**64+1, max_iters=1, seed=1) == 274177
    assert pollard_rho(19) is None
コード例 #4
0
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
コード例 #5
0
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))
コード例 #6
0
ファイル: test_ntheory.py プロジェクト: Visheshk/sympy
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}
コード例 #7
0
def get_divisor(num):
    print(f'get_divisor({num})', file=sys.stderr)
    return nt.pollard_rho(num)