def inverse_modulo(representative, modulus):
"""
Return an element @c n such that @c n * representative has remainder one
if divided by @p modulus.
In residue class rings, this is the multiplicative inverse.
@exception ValueError if @p representative and @p modulus are not
relatively prime.
"""
inverse, ignore, gcd = extended_euclidean_algorithm( representative, modulus )
try:
relatively_prime = ( gcd == representative.__class__.one() )
except Exception:
relatively_prime = ( gcd == 1 )
if relatively_prime:
return inverse
else:
raise ValueError( "representative and modulus must be relatively prime" )
def multiplicative_inverse(self):
"""
Return an residue class (QuotientRing element) @c n such that
@c n * self is one().
@exception ZeroDivisionError if @p self is not a unit, that is, has
no multiplicative inverse.
"""
if not self.__remainder:
raise ZeroDivisionError
inverse, ignore, gcd = \
extended_euclidean_algorithm(self.__remainder, self._modulus)
if gcd == self._ring.one():
return self.__class__(inverse)
else:
message = "element has no inverse: representative and modulus " \
"are not relatively prime"
raise ZeroDivisionError(message)
def multiplicative_inverse(self):
"""
Return an residue class (QuotientRing element) @c n such that
@c n * self is one().
@exception ZeroDivisionError if @p self is not a unit, that is, has
no multiplicative inverse.
"""
if not self.__remainder:
raise ZeroDivisionError
inverse, ignore, gcd = \
extended_euclidean_algorithm( self.__remainder, self._modulus )
if gcd == self._ring.one():
return self.__class__( inverse )
else:
message = "element has no inverse: representative and modulus " \
"are not relatively prime"
raise ZeroDivisionError( message )
