def construction(self, forbid_frac_field=False):
"""
Returns the functorial construction of ``self``, namely,
completion of the rational numbers with respect a given prime.
Also preserves other information that makes this field unique
(e.g. precision, rounding, print mode).
INPUT:
- ``forbid_frac_field`` -- require a completion functor rather
than a fraction field functor. This is used in the
:meth:`sage.rings.padics.local_generic.LocalGeneric.change` method.
EXAMPLES::
sage: K = Qp(17, 8, print_mode='val-unit', print_sep='&')
sage: c, L = K.construction(); L
17-adic Ring with capped relative precision 8
sage: c
FractionField
sage: c(L)
17-adic Field with capped relative precision 8
sage: K == c(L)
True
We can get a completion functor by forbidding the fraction field::
sage: c, L = K.construction(forbid_frac_field=True); L
Rational Field
sage: c
Completion[17, prec=8]
sage: c(L)
17-adic Field with capped relative precision 8
sage: K == c(L)
True
TESTS::
sage: R = QpLC(13,(31,41))
sage: R._precision_cap()
(31, 41)
sage: F, Z = R.construction()
sage: S = F(Z)
sage: S._precision_cap()
(31, 41)
"""
from sage.categories.pushout import FractionField, CompletionFunctor
if forbid_frac_field:
extras = {
'print_mode': self._printer.dict(),
'type': self._prec_type(),
'names': self._names
}
if hasattr(self, '_label'):
extras['label'] = self._label
return (CompletionFunctor(self.prime(), self._precision_cap(),
extras), QQ)
else:
return FractionField(), self.integer_ring()
def construction(self):
r"""
Returns a pair ``(functor, parent)`` such that ``functor(parent)``
returns ``self``.
This is the construction of `\QQ` as the fraction field of `\ZZ`.
EXAMPLES::
sage: QQ.construction()
(FractionField, Integer Ring)
"""
from sage.categories.pushout import FractionField
from . import integer_ring
return FractionField(), integer_ring.ZZ
def construction(self):
"""
EXAMPLES::
sage: Frac(ZZ['x']).construction()
(FractionField, Univariate Polynomial Ring in x over Integer Ring)
sage: K = Frac(GF(3)['t'])
sage: f, R = K.construction()
sage: f(R)
Fraction Field of Univariate Polynomial Ring in t over Finite Field of size 3
sage: f(R) == K
True
"""
from sage.categories.pushout import FractionField
return FractionField(), self.ring()
def construction(self):
from sage.categories.pushout import FractionField
import integer_ring
return FractionField(), integer_ring.ZZ
