def _coerce_map_from_(self, R):
r"""
Return a coerce map from ``R`` to this field.
EXAMPLES::
sage: R.<t> = GF(5)[]
sage: K = R.fraction_field()
sage: L = K.function_field()
sage: f = K.coerce_map_from(L); f # indirect doctest
Isomorphism:
From: Rational function field in t over Finite Field of size 5
To: Fraction Field of Univariate Polynomial Ring in t over Finite Field of size 5
sage: f(~L.gen())
1/t
"""
from sage.rings.function_field.function_field import is_RationalFunctionField
if is_RationalFunctionField(R) and self.variable_name(
) == R.variable_name() and self.base_ring() is R.constant_base_field():
from sage.categories.all import Hom
parent = Hom(R, self)
from sage.rings.function_field.maps import FunctionFieldToFractionField
return parent.__make_element_class__(FunctionFieldToFractionField)(
parent)
return super(FractionField_1poly_field, self)._coerce_map_from_(R)
def _coerce_map_from_(self, R):
r"""
Return a coerce map from ``R`` to this field.
EXAMPLES::
sage: R.<t> = GF(5)[]
sage: K = R.fraction_field()
sage: L = K.function_field()
sage: f = K.coerce_map_from(L); f # indirect doctest
Isomorphism:
From: Rational function field in t over Finite Field of size 5
To: Fraction Field of Univariate Polynomial Ring in t over Finite Field of size 5
sage: f(~L.gen())
1/t
"""
from sage.rings.function_field.function_field import is_RationalFunctionField
if is_RationalFunctionField(R) and self.variable_name() == R.variable_name() and self.base_ring() is R.constant_base_field():
from sage.categories.all import Hom
parent = Hom(R, self)
from sage.rings.function_field.maps import FunctionFieldToFractionField
return parent.__make_element_class__(FunctionFieldToFractionField)(parent)
return super(FractionField_1poly_field, self)._coerce_map_from_(R)
def section(self):
r"""
Return a section of this map.
EXAMPLES::
sage: R.<x> = QQ[]
sage: R.fraction_field().coerce_map_from(R).section()
Section map:
From: Fraction Field of Univariate Polynomial Ring in x over Rational Field
To: Univariate Polynomial Ring in x over Rational Field
"""
from sage.categories.sets_with_partial_maps import SetsWithPartialMaps
from sage.all import Hom
parent = Hom(self.codomain(), self.domain(), SetsWithPartialMaps())
return parent.__make_element_class__(FractionFieldEmbeddingSection)(self)
def section(self):
r"""
Return a section of this map.
EXAMPLES::
sage: R.<x> = QQ[]
sage: R.fraction_field().coerce_map_from(R).section()
Section map:
From: Fraction Field of Univariate Polynomial Ring in x over Rational Field
To: Univariate Polynomial Ring in x over Rational Field
"""
from sage.categories.sets_with_partial_maps import SetsWithPartialMaps
from sage.all import Hom
parent = Hom(self.codomain(), self.domain(), SetsWithPartialMaps())
return parent.__make_element_class__(FractionFieldEmbeddingSection)(self)
