def bin_coeffs(n, start=None, stop=None, step=None):
def check_number(n):
if not isinstance(n, int):
raise TypeError("The number must be an integer.")
elif n < 0:
raise ValueError("The number must be positive.")
check_number(n)
if start is None:
start = 0
else:
check_number(start)
if start > n:
raise ValueError("'start' must be less than or equal to 'n'.")
if stop is None:
stop = n
else:
check_number(start)
if stop > n:
raise ValueError("'stop' must be less than or equal to 'n'.")
if start > stop:
if step is None:
step = -1
stop -= 1
k_range = list(range_(start, stop, -1))
else:
if step is None:
step = 1
stop += 1
k_range = list(range_(start, stop, 1))
coeffs = {0: 1, 1: n, n - 1: n, n: 1}
while start is not None:
for k in range_(start, stop, step):
start = None
try:
v = coeffs[k]
except KeyError:
try:
v = coeffs[k - 1] * (n - k + 1) / k
except KeyError:
try:
v = coeffs[k + 1] * (k + 1) / (n - k)
except KeyError:
v = comb_without_rep(n, k)
coeffs[k] = v
coeffs[n - k] = v
s = (yield v)
if s is not None:
check_number(s)
if s not in k_range:
raise ValueError("Sent value must be included in the "
"range (start, stop).")
start = s
break
def seq_without_rep(n, k):
if not isinstance(n, int) or not isinstance(k, int):
raise TypeError("Both numbers must be integers.")
elif n < 0 or k < 0:
raise ValueError("Both numbers must be non-negative integers.")
elif n < k:
raise ValueError("'n' must be bigger than 'k'")
return functools.reduce(operator.mul, range_(n, n - k, -1), 1)
def test_gcd(self):
self.assertEqual(gcd(0, 0), 1)
self.assertEqual(gcd(5, 0), 5)
self.assertEqual(gcd(0, 5), 5)
self.assertEqual(gcd(5, 5), 5)
self.assertEqual(gcd(5, 1), 1)
self.assertEqual(gcd(5, 0), 5)
self.assertEqual(gcd(33, 121), 11)
self.assertEqual(gcd(256, 160), 32)
self.assertEqual(gcd(256, -160), 32)
self.assertEqual(gcd(-256, 160), 32)
self.assertEqual(gcd(-256, -160), 32)
self.assertEqual(gcd(Polynomial("x2 - 2x + 1"),
Polynomial("x2 - 3x + 2")), Polynomial("x - 1"))
self.assertEqual(gcd(Polynomial("120x2y4z7t"), Polynomial("24xy5zhg")),
Polynomial("24xy4z"))
self.assertEqual(gcd(4, Polynomial("2x2 - 2x + 2")), 2)
self.assertEqual(gcd(Polynomial("4"), Polynomial("2x2 - 2x + 2")), 2)
self.assertEqual(gcd(fractions.Fraction(3, 2),
fractions.Fraction(21, 6)),
fractions.Fraction(1, 2))
self.assertEqual(gcd(1.2, 4.6), fractions.Fraction(1, 5))
self.assertEqual(gcd(1j, 2), 1)
self.assertEqual(gcd(fractions.Fraction(4, 2), 6), 2)
self.assertEqual(gcd(2.0, 6), 2)
self.assertEqual(gcd(-2.0, 6), 2)
self.assertEqual(gcd(fractions.Fraction(4),
Polynomial("2x2 - 2x + 2")), 2)
self.assertEqual(gcd(8j, 12j), 4j)
self.assertEqual(gcd(8j, 0), 8j)
self.assertEqual(gcd(Polynomial("x - 2"), Polynomial("x")),
Polynomial("1"))
self.assertEqual(gcd(30, 24, 54, 36), 6)
self.assertEqual(gcd(*(2 * x for x in range_(10))), 2)
self.assertEqual(gcd(Polynomial("x - 2") * "x - 1",
Polynomial("x - 1") ** 2,
Polynomial("y") * "x - 1",
Polynomial("x - 1")), "x - 1")
#self.assertEqual(gcd(Polynomial("2x - 4") * "x - 1",
# Polynomial("x - 1") ** 2 * 6,
# Polynomial("4y") * "x",
# Polynomial("2x - 2"),
# -2,
# fractions.Fraction(16, 4),
# 8.0,
# 16), 2)
self.assertRaises(TypeError, gcd, "3", 6)
self.assertRaises(TypeError, gcd, 3, "6")
self.assertRaises(TypeError, gcd, [3], "6")
self.assertRaises(TypeError, gcd, 3, 6, [])
self.assertRaises(TypeError, gcd, 3, 6, 9, 18, "")
self.assertRaises(TypeError, gcd, 3)
self.assertRaises(TypeError, gcd)
self.assertRaises(TypeError, gcd, 3, 6, pippo=3)
def is_complete(self, letter=None):
if letter is None:
return all(self.is_complete(l) for l in self.letters)
elif not is_letter_valid(letter):
raise ValueError("The letter must be a single letter from the "
"alphabet.")
elif letter not in self.letters:
return True
return set(self.all_letter_degrees[letter]) ==\
set(range_(self.max_degree_of_letter(letter) + 1))
def complete(self, letter=None):
if letter is None:
for l in self.letters:
self.complete(l)
return
elif not is_letter_valid(letter):
raise ValueError("The letter must be a single letter from the "
"alphabet.")
elif letter not in self.letters:
return
degrees = set(self.all_letter_degrees[letter])
for d in set(range_(self.max_degree_of_letter(letter))) - degrees:
self._monomials.append([0, {letter: d}])
self.sort()
def test_lcm(self):
self.assertEqual(lcm(0, 0), 0)
self.assertEqual(lcm(5, 0), 0)
self.assertEqual(lcm(0, 5), 0)
self.assertEqual(lcm(5, 5), 5)
self.assertEqual(lcm(5, 1), 5)
self.assertEqual(lcm(5, 0), 0)
self.assertEqual(lcm(33, 121), 363)
self.assertEqual(lcm(256, 160), 1280)
self.assertEqual(lcm(256, -160), 1280)
self.assertEqual(lcm(-256, 160), 1280)
self.assertEqual(lcm(-256, -160), 1280)
self.assertEqual(lcm(Polynomial("x2 - 2x + 1"),
Polynomial("x2 - 3x + 2")),
Polynomial("x - 1") ** 2 * "x - 2")
self.assertEqual(lcm(Polynomial("120x2y4z7t"), Polynomial("24xy5zhg")),
Polynomial("120x2y5z7hgt"))
self.assertEqual(lcm(4, Polynomial("2x2 - 2x + 2")),
Polynomial("4x2 - 4x + 4"))
self.assertEqual(lcm(Polynomial("4"), Polynomial("2x2 - 2x + 2")),
Polynomial("4x2 - 4x + 4"))
self.assertEqual(lcm(fractions.Fraction(3, 2),
fractions.Fraction(21, 6)),
fractions.Fraction(21, 2))
self.assertEqual(lcm(1.2, 4.6), fractions.Fraction(138, 5))
self.assertEqual(lcm(1j, 2), 2j)
self.assertEqual(lcm(fractions.Fraction(4, 2), 6), 6)
self.assertEqual(lcm(2.0, 6), 6)
self.assertEqual(lcm(-2.0, 6), 6)
self.assertEqual(lcm(fractions.Fraction(4),
Polynomial("2x2 - 2x + 2")),
Polynomial("4x2 - 4x + 4"))
self.assertEqual(lcm(Polynomial("x - 2"), Polynomial("x")),
Polynomial("x2 - 2x"))
self.assertEqual(lcm(32, 24, 54, 36), 864)
self.assertEqual(lcm(*(2 * x for x in range_(10))), 0)
self.assertEqual(lcm(*(2 * x for x in range_(1, 10))), 5040)
#self.assertEqual(lcm(Polynomial("x - 2") * "x - 1",
# Polynomial("x - 1") ** 2,
# Polynomial("y") * "x - 1",
# Polynomial("x - 1")),
# Polynomial("x - 1") ** 3 * "x - 2" * "y")
#self.assertEqual(lcm(Polynomial("2x - 4") * "x - 1",
# Polynomial("x - 1") ** 2 * 6,
# Polynomial("4y") * "x",
# Polynomial("2x - 2"),
# -2,
# fractions.Fraction(16, 4),
# 8.0,
# 16),
# Polynomial("x-1") ** 4 * "x-2" * "xy" * 3 * 2 ** 14)
self.assertRaises(TypeError, lcm, "3", 6)
self.assertRaises(TypeError, lcm, 3, "6")
self.assertRaises(TypeError, lcm, [3], "6")
self.assertRaises(TypeError, lcm, 3, 6, [])
self.assertRaises(TypeError, lcm, 3, 6, 9, 18, "")
self.assertRaises(TypeError, lcm, 3)
self.assertRaises(TypeError, lcm)
self.assertRaises(TypeError, lcm, 3, 6, pippo=3)
def str_divisors(x, abs_=True):
seq = range_(1, int(abs(x)) + 1)
if not abs_:
seq = itertools.chain(seq, (-x for x in seq))
return (str(d) for d in seq if not x % d)
