def __init__(self, poly, prec, print_mode, names, element_class):
"""
Initializes self
INPUTS::
- poly -- Polynomial defining this extension.
- prec -- The precision cap
- print_mode -- a dictionary with print options
- names -- a 4-tuple, (variable_name, residue_name,
unramified_subextension_variable_name, uniformizer_name)
- element_class -- the class for elements of this unramified extension.
EXAMPLES::
sage: R.<a> = Zq(27) #indirect doctest
"""
# base = poly.base_ring()
# if base.is_field():
# self._PQR = pqr.PolynomialQuotientRing_field(poly.parent(), poly, name = names)
# else:
# self._PQR = pqr.PolynomialQuotientRing_domain(poly.parent(), poly, name = names)
pAdicExtensionGeneric.__init__(self, poly, prec, print_mode, names, element_class)
self._res_field = GF(
self.prime_pow.pow_Integer_Integer(poly.degree()),
name=names[1],
modulus=poly.change_ring(poly.base_ring().residue_field()),
)
def __init__(self, poly, prec, print_mode, names, element_class):
"""
Initializes self
INPUT:
- poly -- Polynomial defining this extension.
- prec -- The precision cap
- print_mode -- a dictionary with print options
- names -- a 4-tuple, (variable_name, residue_name,
unramified_subextension_variable_name, uniformizer_name)
- element_class -- the class for elements of this unramified extension.
EXAMPLES::
sage: R.<a> = Zq(27) #indirect doctest
"""
#base = poly.base_ring()
#if base.is_field():
# self._PQR = pqr.PolynomialQuotientRing_field(poly.parent(), poly, name = names)
#else:
# self._PQR = pqr.PolynomialQuotientRing_domain(poly.parent(), poly, name = names)
pAdicExtensionGeneric.__init__(self, poly, prec, print_mode, names,
element_class)
self._res_field = GF(self.prime_pow.pow_Integer_Integer(poly.degree()),
name=names[1],
modulus=poly.change_ring(
poly.base_ring().residue_field()))
def __init__(self, poly, prec, print_mode, names, element_class):
"""
Initializes self.
EXAMPLES::
sage: A = Zp(7,10)
sage: S.<x> = A[]
sage: B.<t> = A.ext(x^2+7) #indirect doctest
"""
pAdicExtensionGeneric.__init__(self, poly, prec, print_mode, names, element_class)
def __init__(self, poly, prec, print_mode, names, element_class):
"""
Initializes self.
EXAMPLES::
sage: A = Zp(7,10)
sage: S.<x> = A[]
sage: B.<t> = A.ext(x^2+7) #indirect doctest
"""
pAdicExtensionGeneric.__init__(self, poly, prec, print_mode, names,
element_class)