def __init__(self, parent, polynomial, check=True):
"""
Create an element of the quotient of a polynomial ring.
INPUT:
- ``parent`` - a quotient of a polynomial ring
- ``polynomial`` - a polynomial
- ``check`` - bool (optional): whether or not to
verify that x is a valid element of the polynomial ring and reduced
(mod the modulus).
"""
from sage.rings.polynomial.polynomial_quotient_ring import PolynomialQuotientRing_generic
from sage.rings.polynomial.polynomial_element import Polynomial
CommutativeRingElement.__init__(self, parent)
if check:
if not isinstance(parent, PolynomialQuotientRing_generic):
raise TypeError("parent must be a polynomial quotient ring")
if not isinstance(polynomial, Polynomial):
raise TypeError("polynomial must be a polynomial")
if not polynomial in parent.polynomial_ring():
raise TypeError(
"polynomial must be in the polynomial ring of the parent")
f = parent.modulus()
if polynomial.degree() >= f.degree() and polynomial.degree() >= 0:
try:
polynomial %= f
except AttributeError:
A = polynomial
B = f
R = A
P = B.parent()
Q = P(0)
X = P.gen()
while R.degree() >= B.degree():
S = P((R.leading_coefficient() / B.leading_coefficient()
)) * X**(R.degree() - B.degree())
Q = Q + S
R = R - S * B
polynomial = R
self._polynomial = polynomial
def __init__(self, parent, polynomial, check=True):
"""
Create an element of the quotient of a polynomial ring.
INPUT:
- ``parent`` - a quotient of a polynomial ring
- ``polynomial`` - a polynomial
- ``check`` - bool (optional): whether or not to
verify that x is a valid element of the polynomial ring and reduced
(mod the modulus).
"""
from sage.rings.polynomial.polynomial_quotient_ring import PolynomialQuotientRing_generic
from sage.rings.polynomial.polynomial_element import Polynomial
CommutativeRingElement.__init__(self, parent)
if check:
if not isinstance(parent, PolynomialQuotientRing_generic):
raise TypeError("parent must be a polynomial quotient ring")
if not isinstance(polynomial, Polynomial):
raise TypeError("polynomial must be a polynomial")
if not polynomial in parent.polynomial_ring():
raise TypeError("polynomial must be in the polynomial ring of the parent")
f = parent.modulus()
if polynomial.degree() >= f.degree() and polynomial.degree() >= 0:
try:
polynomial %= f
except AttributeError:
A = polynomial
B = f
R = A
P = B.parent()
Q = P(0)
X = P.gen()
while R.degree() >= B.degree():
S = P((R.leading_coefficient()/B.leading_coefficient())) * X**(R.degree()-B.degree())
Q = Q + S
R = R - S*B
polynomial = R
self._polynomial = polynomial