Quartic curve constructor

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

Return 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

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

x,y,z = PolynomialRing(QQ, ['x','y','z']).gens()
QuarticCurve(x**4 + y**4 + z**4)