Quartic curve constructor#

sage.schemes.plane_quartics.quartic_constructor.QuarticCurve(F, PP=None, check=False)#

Return the quartic curve defined by the polynomial F.


  • F – a polynomial in three variables, homogeneous of degree 4

  • PP – a projective plane (default: None)

  • check – whether to check for smoothness or not (default: False)


sage: x,y,z = PolynomialRing(QQ, ['x','y','z']).gens()
sage: QuarticCurve(x**4 + y**4 + z**4)
Quartic Curve over Rational Field defined by x^4 + y^4 + z^4