def __init__(self, K, ainvs):
self.__base_ring = K
self.__ainvs = tuple(map(K, ainvs))
self.a, self.d = self.__ainvs
P2 = ProjectiveSpace(2, K, names='xyz')
x, y, z = P2.coordinate_ring().gens()
a, d = self.ainvs()
f = a*x**2*z**2 + y**2*z**2 - z**4 - d*x**2*y**2
ProjectiveCurve_generic.__init__(self, P2, f)
def __init__(self, A, f):
r"""
See ``Conic`` for full documentation.
EXAMPLES:
::
sage: c = Conic([1, 1, 1]); c
Projective Conic Curve over Rational Field defined by x^2 + y^2 + z^2
"""
ProjectiveCurve_generic.__init__(self, A, f)
self._coefficients = [f[(2, 0, 0)], f[(1, 1, 0)], f[(1, 0, 1)], f[(0, 2, 0)], f[(0, 1, 1)], f[(0, 0, 2)]]
self._parametrization = None
self._diagonal_matrix = None
self._rational_point = None
def __init__(self, A, f):
r"""
See ``Conic`` for full documentation.
EXAMPLES:
::
sage: c = Conic([1, 1, 1]); c
Projective Conic Curve over Rational Field defined by x^2 + y^2 + z^2
"""
ProjectiveCurve_generic.__init__(self, A, f)
self._coefficients = [f[(2,0,0)], f[(1,1,0)], f[(1,0,1)],
f[(0,2,0)], f[(0,1,1)], f[(0,0,2)]]
self._parametrization = None
self._diagonal_matrix = None
self._rational_point = None
