def _element_constructor_(self, x, check=True, reduce=True):
r"""
Construct an element of the divisor group.
EXAMPLES::
sage: A.<x, y> = AffineSpace(2, CC)
sage: C = Curve(y^2 - x^9 - x)
sage: DivZZ=C.divisor_group(ZZ)
sage: DivQQ=C.divisor_group(QQ)
sage: DivQQ( DivQQ.an_element() ) # indirect test
0
sage: DivZZ( DivZZ.an_element() ) # indirect test
0
sage: DivQQ( DivZZ.an_element() ) # indirect test
0
"""
if isinstance(x, Divisor_curve):
P = x.parent()
if P is self:
return x
elif P == self:
return Divisor_curve(x._data, check=False, reduce=False, parent=self)
else:
x = x._data
if isinstance(x, list):
return Divisor_curve(x, check=check, reduce=reduce, parent=self)
if x == 0:
return Divisor_curve([], check=False, reduce=False, parent=self)
else:
return Divisor_curve([(self.base_ring()(1), x)], check=False, reduce=False, parent=self)
def divisor(self, v, base_ring=None, check=True, reduce=True):
r"""
Return the divisor specified by ``v``.
.. WARNING::
The coefficients of the divisor must be in the base ring
and the terms must be reduced. If you set ``check=False``
and/or ``reduce=False`` it is your responsibility to pass
a valid object ``v``.
"""
return Divisor_curve(v, check=check, reduce=reduce, parent=self.divisor_group(base_ring))
def divisor(self, v, base_ring=None, check=True, reduce=True):
r"""
Return the divisor specified by ``v``.
.. WARNING::
The coefficients of the divisor must be in the base ring
and the terms must be reduced. If you set ``check=False``
and/or ``reduce=False`` it is your responsibility to pass
a valid object ``v``.
EXAMPLES::
sage: x,y,z = PolynomialRing(QQ, 3, names='x,y,z').gens()
sage: C = Curve(y^2*z - x^3 - 17*x*z^2 + y*z^2)
"""
return Divisor_curve(v, check=check, reduce=reduce, parent=self.divisor_group(base_ring))
