def _element_constructor_(self, x):
r"""
Coerce x into an element of this function field, possibly not canonically.
INPUT:
- ``x`` - the element
OUTPUT:
``x``, as an element of this function field
EXAMPLES::
sage: K.<t> = FunctionField(QQ)
sage: a = K._element_constructor_(K.maximal_order().gen()); a
t
sage: a.parent()
Rational function field in t over Rational Field
"""
if x.parent() is self._field:
return function_field_element.FunctionFieldElement_rational(self, x)
if isinstance(x, function_field_element.FunctionFieldElement):
return function_field_element.FunctionFieldElement_rational(self, self._field(x.element()))
if x.parent() is self.polynomial_ring():
return x[0]
return function_field_element.FunctionFieldElement_rational(self, self._field(x))
def _element_constructor_(self, f):
"""
EXAMPLES::
sage: R.<y> = FunctionField(QQ)
sage: R.maximal_order()._element_constructor_(y)
y
"""
# HUGE TODO: have to check that f is really in self!!
if f.parent() is self.fraction_field():
f = f.element()
elif f.parent() is self._ring:
return function_field_element.FunctionFieldElement_rational(
self, f)
return function_field_element.FunctionFieldElement_rational(
self, self._ring(f))