예제 #1
0
def test_continued_fraction():
    raises(ValueError, lambda: cf_p(1, 0, 0))
    raises(ValueError, lambda: cf_p(1, 1, -1))
    assert cf_p(4, 3, 0) == [1, 3]
    assert cf_p(0, 3, 5) == [0, 1, [2, 1, 12, 1, 2, 2]]
    assert cf_p(1, 1, 0) == [1]
    assert cf_p(3, 4, 0) == [0, 1, 3]
    assert cf_p(4, 5, 0) == [0, 1, 4]
    assert cf_p(5, 6, 0) == [0, 1, 5]
    assert cf_p(11, 13, 0) == [0, 1, 5, 2]
    assert cf_p(16, 19, 0) == [0, 1, 5, 3]
    assert cf_p(27, 32, 0) == [0, 1, 5, 2, 2]
    assert cf_p(1, 2, 5) == [[1]]
    assert cf_p(0, 1, 2) == [1, [2]]
    assert cf_p(6, 7, 49) == [1, 1, 6]
    assert cf_p(3796, 1387, 0) == [2, 1, 2, 1, 4]
    assert cf_p(3245, 10000) == [0, 3, 12, 4, 13]
    assert cf_p(1932, 2568) == [0, 1, 3, 26, 2]
    assert cf_p(6589, 2569) == [2, 1, 1, 3, 2, 1, 3, 1, 23]

    def take(iterator, n=7):
        res = []
        for i, t in enumerate(cf_i(iterator)):
            if i >= n:
                break
            res.append(t)
        return res

    assert take(phi) == [1, 1, 1, 1, 1, 1, 1]
    assert take(pi) == [3, 7, 15, 1, 292, 1, 1]

    assert list(cf_i(S(17) / 12)) == [1, 2, 2, 2]
    assert list(cf_i(S(-17) / 12)) == [-2, 1, 1, 2, 2]

    assert list(cf_c([1, 6, 1, 8])) == [S(1), S(7) / 6, S(8) / 7, S(71) / 62]
    assert list(cf_c([2])) == [S(2)]
    assert list(cf_c([1, 1, 1, 1, 1, 1, 1])) == [
        S.One,
        S(2), S(3) / 2,
        S(5) / 3,
        S(8) / 5,
        S(13) / 8,
        S(21) / 13
    ]
    assert list(cf_c([1, 6, S(-1) / 2,
                      4])) == [S.One, S(7) / 6,
                               S(5) / 4, S(3) / 2]

    assert cf_r([1, 6, 1, 8]) == S(71) / 62
    assert cf_r([3]) == S(3)
    assert cf_r([-1, 5, 1, 4]) == S(-24) / 29
    assert (cf_r([0, 1, 1, 7, [24, 8]]) - (sqrt(3) + 2) / 7).expand() == 0
    assert cf_r([1, 5, 9]) == S(55) / 46
    assert (cf_r([[1]]) - (sqrt(5) + 1) / 2).expand() == 0
예제 #2
0
def test_continued_fraction():
    raises(ValueError, lambda: cf_p(1, 0, 0))
    raises(ValueError, lambda: cf_p(1, 1, -1))
    assert cf_p(4, 3, 0) == [1, 3]
    assert cf_p(0, 3, 5) == [0, 1, [2, 1, 12, 1, 2, 2]]
    assert cf_p(1, 1, 0) == [1]
    assert cf_p(3, 4, 0) == [0, 1, 3]
    assert cf_p(4, 5, 0) == [0, 1, 4]
    assert cf_p(5, 6, 0) == [0, 1, 5]
    assert cf_p(11, 13, 0) == [0, 1, 5, 2]
    assert cf_p(16, 19, 0) == [0, 1, 5, 3]
    assert cf_p(27, 32, 0) == [0, 1, 5, 2, 2]
    assert cf_p(1, 2, 5) == [[1]]
    assert cf_p(0, 1, 2) == [1, [2]]
    assert cf_p(6, 7, 49) == [1, 1, 6]
    assert cf_p(3796, 1387, 0) == [2, 1, 2, 1, 4]
    assert cf_p(3245, 10000) == [0, 3, 12, 4, 13]
    assert cf_p(1932, 2568) == [0, 1, 3, 26, 2]
    assert cf_p(6589, 2569) == [2, 1, 1, 3, 2, 1, 3, 1, 23]

    def take(iterator, n=7):
        res = []
        for i, t in enumerate(cf_i(iterator)):
            if i >= n:
                break
            res.append(t)
        return res

    assert take(phi) == [1, 1, 1, 1, 1, 1, 1]
    assert take(pi) == [3, 7, 15, 1, 292, 1, 1]

    assert list(cf_i(S(17)/12)) == [1, 2, 2, 2]
    assert list(cf_i(S(-17)/12)) == [-2, 1, 1, 2, 2]

    assert list(cf_c([1, 6, 1, 8])) == [S(1), S(7)/6, S(8)/7, S(71)/62]
    assert list(cf_c([2])) == [S(2)]
    assert list(cf_c([1, 1, 1, 1, 1, 1, 1])) == [S.One, S(2), S(3)/2, S(5)/3,
                                                 S(8)/5, S(13)/8, S(21)/13]
    assert list(cf_c([1, 6, S(-1)/2, 4])) == [S.One, S(7)/6, S(5)/4, S(3)/2]

    assert cf_r([1, 6, 1, 8]) == S(71)/62
    assert cf_r([3]) == S(3)
    assert cf_r([-1, 5, 1, 4]) == S(-24)/29
    assert (cf_r([0, 1, 1, 7, [24, 8]]) - (sqrt(3) + 2)/7).expand() == 0
    assert cf_r([1, 5, 9]) == S(55)/46
    assert (cf_r([[1]]) - (sqrt(5) + 1)/2).expand() == 0
예제 #3
0
def test_continued_fraction():
    raises(ValueError, lambda: cf_p(1, 0, 0))
    raises(ValueError, lambda: cf_p(1, 1, -1))
    assert cf_p(4, 3, 0) == [1, 3]
    assert cf_p(0, 3, 5) == [0, 1, [2, 1, 12, 1, 2, 2]]
    assert cf_p(1, 1, 0) == [1]
    assert cf_p(3, 4, 0) == [0, 1, 3]
    assert cf_p(4, 5, 0) == [0, 1, 4]
    assert cf_p(5, 6, 0) == [0, 1, 5]
    assert cf_p(11, 13, 0) == [0, 1, 5, 2]
    assert cf_p(16, 19, 0) == [0, 1, 5, 3]
    assert cf_p(27, 32, 0) == [0, 1, 5, 2, 2]
    assert cf_p(1, 2, 5) == [[1]]
    assert cf_p(0, 1, 2) == [1, [2]]
    assert cf_p(3796, 1387, 0) == [2, 1, 2, 1, 4]
    assert cf_p(3245, 10000) == [0, 3, 12, 4, 13]
    assert cf_p(1932, 2568) == [0, 1, 3, 26, 2]
    assert cf_p(6589, 2569) == [2, 1, 1, 3, 2, 1, 3, 1, 23]

    def take(iterator, n=7):
        res = []
        for i, t in enumerate(cf_i(iterator)):
            if i >= n:
                break
            res.append(t)
        return res

    assert take(phi) == [1, 1, 1, 1, 1, 1, 1]
    assert take(pi) == [3, 7, 15, 1, 292, 1, 1]
예제 #4
0
def test_continued_fraction():
    raises(ValueError, lambda: cf_p(1, 0, 0))
    raises(ValueError, lambda: cf_p(1, 1, -1))
    assert cf_p(4, 3, 0) == [1, 3]
    assert cf_p(0, 3, 5) == [0, 1, [2, 1, 12, 1, 2, 2]]
    assert cf_p(1, 1, 0) == [1]
    assert cf_p(3, 4, 0) == [0, 1, 3]
    assert cf_p(4, 5, 0) == [0, 1, 4]
    assert cf_p(5, 6, 0) == [0, 1, 5]
    assert cf_p(11, 13, 0) == [0, 1, 5, 2]
    assert cf_p(16, 19, 0) == [0, 1, 5, 3]
    assert cf_p(27, 32, 0) == [0, 1, 5, 2, 2]
    assert cf_p(1, 2, 5) == [[1]]
    assert cf_p(0, 1, 2) == [1, [2]]
    assert cf_p(3796, 1387, 0) == [2, 1, 2, 1, 4]
    assert cf_p(3245, 10000) == [0, 3, 12, 4, 13]
    assert cf_p(1932, 2568) == [0, 1, 3, 26, 2]
    assert cf_p(6589, 2569) == [2, 1, 1, 3, 2, 1, 3, 1, 23]

    def take(iterator, n=7):
        res = []
        for i, t in enumerate(cf_i(iterator)):
            if i >= n:
                break
            res.append(t)
        return res

    assert take(phi) == [1, 1, 1, 1, 1, 1, 1]
    assert take(pi) == [3, 7, 15, 1, 292, 1, 1]
예제 #5
0
def test_continued_fraction():
    assert cf_p(1, 1, 10, 0) == cf_p(1, 1, 0, 1)
    assert cf_p(1, -1, 10, 1) == cf_p(-1, 1, 10, -1)
    t = sqrt(2)
    assert cf((1 + t) * (1 - t)) == cf(-1)
    for n in [
            0, 2,
            Rational(2, 3),
            sqrt(2), 3 * sqrt(2), 1 + 2 * sqrt(3) / 5, (2 - 3 * sqrt(5)) / 7,
            1 + sqrt(2), (-5 + sqrt(17)) / 4
    ]:
        assert (cf_r(cf(n)) - n).expand() == 0
        assert (cf_r(cf(-n)) + n).expand() == 0
    raises(ValueError, lambda: cf(sqrt(2 + sqrt(3))))
    raises(ValueError, lambda: cf(sqrt(2) + sqrt(3)))
    raises(ValueError, lambda: cf(pi))
    raises(ValueError, lambda: cf(.1))

    raises(ValueError, lambda: cf_p(1, 0, 0))
    raises(ValueError, lambda: cf_p(1, 1, -1))
    assert cf_p(4, 3, 0) == [1, 3]
    assert cf_p(0, 3, 5) == [0, 1, [2, 1, 12, 1, 2, 2]]
    assert cf_p(1, 1, 0) == [1]
    assert cf_p(3, 4, 0) == [0, 1, 3]
    assert cf_p(4, 5, 0) == [0, 1, 4]
    assert cf_p(5, 6, 0) == [0, 1, 5]
    assert cf_p(11, 13, 0) == [0, 1, 5, 2]
    assert cf_p(16, 19, 0) == [0, 1, 5, 3]
    assert cf_p(27, 32, 0) == [0, 1, 5, 2, 2]
    assert cf_p(1, 2, 5) == [[1]]
    assert cf_p(0, 1, 2) == [1, [2]]
    assert cf_p(6, 7, 49) == [1, 1, 6]
    assert cf_p(3796, 1387, 0) == [2, 1, 2, 1, 4]
    assert cf_p(3245, 10000) == [0, 3, 12, 4, 13]
    assert cf_p(1932, 2568) == [0, 1, 3, 26, 2]
    assert cf_p(6589, 2569) == [2, 1, 1, 3, 2, 1, 3, 1, 23]

    def take(iterator, n=7):
        res = []
        for i, t in enumerate(cf_i(iterator)):
            if i >= n:
                break
            res.append(t)
        return res

    assert take(phi) == [1, 1, 1, 1, 1, 1, 1]
    assert take(pi) == [3, 7, 15, 1, 292, 1, 1]

    assert list(cf_i(Rational(17, 12))) == [1, 2, 2, 2]
    assert list(cf_i(Rational(-17, 12))) == [-2, 1, 1, 2, 2]

    assert list(cf_c(
        [1, 6, 1,
         8])) == [S.One,
                  Rational(7, 6),
                  Rational(8, 7),
                  Rational(71, 62)]
    assert list(cf_c([2])) == [S(2)]
    assert list(cf_c([1, 1, 1, 1, 1, 1, 1])) == [
        S.One,
        S(2),
        Rational(3, 2),
        Rational(5, 3),
        Rational(8, 5),
        Rational(13, 8),
        Rational(21, 13)
    ]
    assert list(cf_c(
        [1, 6, Rational(-1, 2),
         4])) == [S.One, Rational(7, 6),
                  Rational(5, 4),
                  Rational(3, 2)]

    assert cf_r([1, 6, 1, 8]) == Rational(71, 62)
    assert cf_r([3]) == S(3)
    assert cf_r([-1, 5, 1, 4]) == Rational(-24, 29)
    assert (cf_r([0, 1, 1, 7, [24, 8]]) - (sqrt(3) + 2) / 7).expand() == 0
    assert cf_r([1, 5, 9]) == Rational(55, 46)
    assert (cf_r([[1]]) - (sqrt(5) + 1) / 2).expand() == 0
    assert cf_r([-3, 1, 1, [2]]) == -1 - sqrt(2)