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
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
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)