def extgcd(self, a, b):
"""
Return a tuple (u, v, d); they are the greatest common divisor
d of two given integers x and y and u, v such that
d = x * u + y * v.
"""
return tuple(map(Integer, gcd.extgcd(a, b)))
def extgcd(self, a, b):
"""
Return a tuple (u, v, d); they are the greatest common divisor
d of two given integers x and y and u, v such that
d = x * u + y * v.
"""
return tuple(map(Integer, gcd.extgcd(a, b)))
def testExtgcd(self):
u, v, d = gcd.extgcd(8, 11)
self.assertEqual(1, abs(d))
self.assertEqual(d, 8 * u + 11 * v)
#sf.bug 1924839
u, v, d = gcd.extgcd(-8, 11)
self.assertEqual(1, abs(d))
self.assertEqual(d, -8 * u + 11 * v)
u, v, d = gcd.extgcd(8, -11)
self.assertEqual(1, abs(d))
self.assertEqual(d, 8 * u - 11 * v)
u, v, d = gcd.extgcd(-8, -11)
self.assertEqual(1, abs(d))
self.assertEqual(d, -8 * u - 11 * v)
import nzmath.rational as rational
u, v, d = gcd.extgcd(rational.Integer(8), 11)
self.assertEqual(1, abs(d))
self.assertEqual(d, 8 * u + 11 * v)
def inverse(x, p):
"""
This function returns inverse of x for modulo p.
"""
x = x % p
y = gcd.extgcd(p, x)
if y[2] == 1:
if y[1] < 0:
r = p + y[1]
return r
else:
return y[1]
raise ZeroDivisionError("There is no inverse for %d modulo %d." % (x, p))
def inverse(x, n):
"""
This function returns inverse of x for modulo n.
"""
x = x % n
y = gcd.extgcd(n, x)
if y[2] == 1:
if y[1] < 0:
r = n + y[1]
return r
else:
return y[1]
raise ZeroDivisionError("There is no inverse for %d modulo %d." % (x, n))
def inverse(self):
t = gcd.extgcd(self.n, self.m)
if t[2] != 1:
raise ZeroDivisionError("No inverse of %s." % self)
return self.__class__(t[0], self.m)
def inverse(self):
t = gcd.extgcd(self.n, self.m)
if t[2] != 1:
raise ZeroDivisionError("No inverse of %s." % self)
return self.__class__(t[0], self.m)