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 FunctionFieldElement_rational(self, x)
if isinstance(x, FunctionFieldElement):
return FunctionFieldElement_rational(self,
self._field(x.element()))
if x.parent() is self.polynomial_ring():
return x[0]
return FunctionFieldElement_rational(self, self._field(x))
def _element_constructor_(self, f):
"""
Make ``f`` into an element of this order.
EXAMPLES::
sage: K.<y> = FunctionField(QQ)
sage: O = K.maximal_order()
sage: O._element_constructor_(y)
y
sage: O._element_constructor_(1/y)
Traceback (most recent call last):
...
ValueError: `1/y` is not a member of `Maximal order in Rational function field in y over Rational Field`
"""
if f.parent() is self.fraction_field():
if not f.denominator() in self.fraction_field(
).constant_base_field():
raise ValueError("`%s` is not a member of `%s`" % (f, self))
f = f.element()
from function_field_element import FunctionFieldElement_rational
return FunctionFieldElement_rational(self, self._ring(f))