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