Quartic curve constructor - Plane and Space Curves

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# Quartic curve constructor

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

  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

      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

  Python

      >>> 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