def createElement(self, seed):
"""
Create an element of the field.
"""
if isinstance(seed, int):
expansion = arith1.expand(seed, card(self.basefield))
return ExtendedFieldElement(
uniutil.FiniteFieldPolynomial(enumerate(expansion),
self.basefield), self)
elif seed in self.basefield:
return ExtendedFieldElement(
uniutil.FiniteFieldPolynomial([(0, seed)], self.basefield),
self)
elif seed in self:
# seed is in self, return only embedding
return self.zero + seed
elif (isinstance(seed, uniutil.FiniteFieldPolynomial)
and seed.getCoefficientRing() is self.basefield):
return ExtendedFieldElement(seed, self)
else:
try:
# lastly check sequence
return ExtendedFieldElement(
uniutil.FiniteFieldPolynomial(enumerate(seed),
self.basefield), self)
except TypeError:
raise TypeError("seed %s is not an appropriate object." %
str(seed))
def _random_irriducible(char, degree):
"""
Return randomly chosen irreducible polynomial of self.degree.
"""
cardinality = char**degree
basefield = FinitePrimeField.getInstance(char)
seed = bigrandom.randrange(1, char) + cardinality
cand = uniutil.FiniteFieldPolynomial(enumerate(
arith1.expand(seed, cardinality)),
coeffring=basefield)
while cand.degree() < degree or not cand.isirreducible():
seed = bigrandom.randrange(1, cardinality) + cardinality
cand = uniutil.FiniteFieldPolynomial(enumerate(
arith1.expand(seed, cardinality)),
coeffring=basefield)
_log.debug(cand.order.format(cand))
return cand
def _getZero(self):
"getter for zero"
if self._zero is None:
self._zero = ExtendedFieldElement(
uniutil.FiniteFieldPolynomial([], self.basefield), self)
return self._zero
def _getOne(self):
"getter for one"
if self._one is None:
self._one = ExtendedFieldElement(
uniutil.FiniteFieldPolynomial([(0, 1)], self.basefield), self)
return self._one