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sagemath
GitHub Repository: sagemath/sagesmc
 Path: blob/master/src/sage/schemes/plane_quartics/quartic_constructor.py
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"""

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Quartic curve constructor

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"""

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#*****************************************************************************

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#  Copyright (C) 2006 David Kohel <[email protected]>

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#  Distributed under the terms of the GNU General Public License (GPL)

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#                  http://www.gnu.org/licenses/

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#*****************************************************************************

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from sage.schemes.projective.all import is_ProjectiveSpace, ProjectiveSpace

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from sage.rings.polynomial.multi_polynomial_element import is_MPolynomial

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from quartic_generic import QuarticCurve_generic

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def QuarticCurve(F, PP=None, check=False):

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    """

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    Returns the quartic curve defined by the polynomial F.

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    INPUT:

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    - F -- a polynomial in three variables, homogeneous of degree 4

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    - PP -- a projective plane (default:None)

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

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    EXAMPLES::

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        sage: x,y,z=PolynomialRing(QQ,['x','y','z']).gens()

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        sage: QuarticCurve(x**4+y**4+z**4)

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        Quartic Curve over Rational Field defined by x^4 + y^4 + z^4

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    TESTS::

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        sage: QuarticCurve(x**3+y**3)

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        Traceback (most recent call last):

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        ...

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        ValueError: Argument F (=x^3 + y^3) must be a homogeneous polynomial of degree 4

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        sage: QuarticCurve(x**4+y**4+z**3)

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        Traceback (most recent call last):

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        ...

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        ValueError: Argument F (=x^4 + y^4 + z^3) must be a homogeneous polynomial of degree 4

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        sage: x,y=PolynomialRing(QQ,['x','y']).gens()

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        sage: QuarticCurve(x**4+y**4)

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        Traceback (most recent call last):

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        ...

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        ValueError: Argument F (=x^4 + y^4) must be a polynomial in 3 variables

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    """

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    if not is_MPolynomial(F):

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        raise ValueError("Argument F (=%s) must be a multivariate polynomial"%F)

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    P = F.parent()

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    if not P.ngens() == 3:

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        raise ValueError("Argument F (=%s) must be a polynomial in 3 variables"%F)

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    if not(F.is_homogeneous() and F.degree()==4):

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        raise ValueError("Argument F (=%s) must be a homogeneous polynomial of degree 4"%F)

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    if not PP is None:

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        if not is_ProjectiveSpace(PP) and PP.dimension == 2:

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            raise ValueError("Argument PP (=%s) must be a projective plane"%PP)

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    else:

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        PP = ProjectiveSpace(P)

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    if check:

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        raise NotImplementedError("Argument checking (for nonsingularity) is not implemented.")

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    return QuarticCurve_generic(PP, F)

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