def __init__(self, p, modulus, name=None):
"""
Create a finite field of characteristic `p` defined by the
polynomial ``modulus``, with distinguished generator called
``name``.
EXAMPLE::
sage: from sage.rings.finite_rings.finite_field_pari_ffelt import FiniteField_pari_ffelt
sage: R.<x> = PolynomialRing(GF(3))
sage: k = FiniteField_pari_ffelt(3, x^2 + 2*x + 2, 'a'); k
Finite Field in a of size 3^2
"""
n = modulus.degree()
if n < 2:
raise ValueError("the degree must be at least 2")
FiniteField.__init__(self, base=GF(p), names=name, normalize=True)
self._modulus = modulus
self._degree = n
self._kwargs = {}
self._gen_pari = modulus._pari_with_name(self._names[0]).ffgen()
self._zero_element = self.element_class(self, 0)
self._one_element = self.element_class(self, 1)
self._gen = self.element_class(self, self._gen_pari)
def __init__(self, p, modulus, name=None):
"""
Create a finite field of characteristic `p` defined by the
polynomial ``modulus``, with distinguished generator called
``name``.
EXAMPLE::
sage: from sage.rings.finite_rings.finite_field_pari_ffelt import FiniteField_pari_ffelt
sage: R.<x> = PolynomialRing(GF(3))
sage: k = FiniteField_pari_ffelt(3, x^2 + 2*x + 2, 'a'); k
Finite Field in a of size 3^2
"""
n = modulus.degree()
if n < 2:
raise ValueError("the degree must be at least 2")
FiniteField.__init__(self, base=GF(p), names=name, normalize=True)
self._modulus = modulus
self._degree = n
self._kwargs = {}
self._gen_pari = modulus._pari_with_name(self._names[0]).ffgen()
self._zero_element = self.element_class(self, 0)
self._one_element = self.element_class(self, 1)
self._gen = self.element_class(self, self._gen_pari)
def __init__(self, p, modulus, name=None):
"""
Create a finite field of characteristic `p` defined by the
polynomial ``modulus``, with distinguished generator called
``name``.
EXAMPLE::
sage: from sage.rings.finite_rings.finite_field_pari_ffelt import FiniteField_pari_ffelt
sage: R.<x> = PolynomialRing(GF(3))
sage: k = FiniteField_pari_ffelt(3, x^2 + 2*x + 2, 'a'); k
Finite Field in a of size 3^2
"""
import constructor
from sage.libs.pari.all import pari
from sage.rings.integer import Integer
from sage.structure.proof.all import arithmetic
proof = arithmetic()
p = Integer(p)
if ((p < 2)
or (proof and not p.is_prime())
or (not proof and not p.is_pseudoprime())):
raise ArithmeticError("p must be a prime number")
Fp = constructor.FiniteField(p)
if name is None:
name = modulus.variable_name()
FiniteField.__init__(self, base=Fp, names=name, normalize=True)
modulus = self.polynomial_ring()(modulus)
n = modulus.degree()
if n < 2:
raise ValueError("the degree must be at least 2")
self._modulus = modulus
self._degree = n
self._card = p ** n
self._kwargs = {}
self._gen_pari = pari(modulus).ffgen()
self._zero_element = self.element_class(self, 0)
self._one_element = self.element_class(self, 1)
self._gen = self.element_class(self, self._gen_pari)
def __init__(self, p, modulus, name=None):
"""
Create a finite field of characteristic `p` defined by the
polynomial ``modulus``, with distinguished generator called
``name``.
EXAMPLE::
sage: from sage.rings.finite_rings.finite_field_pari_ffelt import FiniteField_pari_ffelt
sage: R.<x> = PolynomialRing(GF(3))
sage: k = FiniteField_pari_ffelt(3, x^2 + 2*x + 2, 'a'); k
Finite Field in a of size 3^2
"""
import constructor
from sage.libs.pari.all import pari
from sage.rings.integer import Integer
from sage.structure.proof.all import arithmetic
proof = arithmetic()
p = Integer(p)
if ((p < 2) or (proof and not p.is_prime())
or (not proof and not p.is_pseudoprime())):
raise ArithmeticError("p must be a prime number")
Fp = constructor.FiniteField(p)
if name is None:
name = modulus.variable_name()
FiniteField.__init__(self, base=Fp, names=name, normalize=True)
modulus = self.polynomial_ring()(modulus)
n = modulus.degree()
if n < 2:
raise ValueError("the degree must be at least 2")
self._modulus = modulus
self._degree = n
self._card = p**n
self._kwargs = {}
self._gen_pari = pari(modulus).ffgen()
self._zero_element = self.element_class(self, 0)
self._one_element = self.element_class(self, 1)
self._gen = self.element_class(self, self._gen_pari)