This is fine:
sage: C = Conic([1,1,-1])
sage: C
Projective Conic Curve over Rational Field defined by x^2 + y^2 - z^2
sage: C.rational_parameterization()
Scheme morphism:
From: Projective Space of dimension 1 over Rational Field
To: Projective Plane Curve over Rational Field defined by x^2 + y^2 - z^2
Defn: Defined on coordinates by sending (s : t) to
(s^2 - t^2 : 2*s*t : s^2 + t^2)
but this is not:
sage: C = Conic([1027986085027861747937 , 722974121783, -604305613931])
sage: C
Projective Conic Curve over Rational Field defined by
1027986085027861747937*x^2 + 722974121783*y^2 - 604305613931*z^2
sage: C.rational_parameterization()
Scheme morphism:
From: Projective Space of dimension 1 over Rational Field
To: Projective Plane Curve over Rational Field defined by
1027986085027861747937*x^2 + 722974121783*y^2 - 604305613931*z^2
Defn: Defined on coordinates by sending (s : t) to
(272561126856814943619672736316674281724159746275694018234 :
292362540189983749235664021894852879556406208063400253511743 :
483823403259473971100400534005871494692555156705)
since (1) the point displayed does not lie on the conic and (2) it's
only one point and the parametrization should involve quadratics in s
and t, not be constant.
Incidentally, the implementation calls Singular to do the work. I
don't know if Singular itself has this bug.
John
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