# Quartic curve constructor¶

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

Returns the quartic curve defined by the polynomial F.

INPUT:

• 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)

EXAMPLES:

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