def point(self, v, check=True):
r"""
Constructs a point on ``self`` corresponding to the input ``v``.
If ``check`` is True, then checks if ``v`` defines a valid
point on ``self``.
If no rational point on ``self`` is known yet, then also caches the point
for use by ``self.rational_point()`` and ``self.parametrization()``.
EXAMPLES ::
sage: c = Conic([1, -1, 1])
sage: c.point([15, 17, 8])
(15/8 : 17/8 : 1)
sage: c.rational_point()
(15/8 : 17/8 : 1)
sage: d = Conic([1, -1, 1])
sage: d.rational_point()
(1 : 1 : 0)
"""
if is_Vector(v):
v = Sequence(v)
p = ProjectiveCurve_generic.point(self, v, check=check)
if self._rational_point is None:
self._rational_point = p
return p
def point(self, v, check=True):
r"""
Constructs a point on ``self`` corresponding to the input ``v``.
If ``check`` is True, then checks if ``v`` defines a valid
point on ``self``.
If no rational point on ``self`` is known yet, then also caches the point
for use by ``self.rational_point()`` and ``self.parametrization()``.
EXAMPLES ::
sage: c = Conic([1, -1, 1])
sage: c.point([15, 17, 8])
(15/8 : 17/8 : 1)
sage: c.rational_point()
(15/8 : 17/8 : 1)
sage: d = Conic([1, -1, 1])
sage: d.rational_point()
(-1 : 1 : 0)
"""
if is_Vector(v):
v = Sequence(v)
p = ProjectiveCurve_generic.point(self, v, check=check)
if self._rational_point is None:
self._rational_point = p
return p
