def sqrt(self):
"""
The square root of the number in the field.
Returns the value a \in F such that a*a = x.
If no such a exists, raises ValueError.
"""
if not self.is_square():
raise ValueError, "This number is not a square! (%s)" % str(self)
a = self.__class__(shanks_tonelli(self.value, self._base))
assert a * a == self
return a
def sqrt(self):
"""
The square root of the number in the field.
Returns the value a \in F such that a*a = x.
If no such a exists, raises ValueError.
"""
if not self.is_square():
raise ValueError, "This number is not a square! (%s)" % str(self)
a = self.__class__(shanks_tonelli(self.value, self._base))
assert a*a == self
return a
def test_shanks():
p = 37
for i in range(1, p):
n = i*i % p
st = shanks_tonelli(n, p)
assert st*st % p == n