Coverage for local/lib/python2.7/site-packages/sage/schemes/plane_quartics/quartic_constructor.py : 53%

""" 

Quartic curve constructor 

""" 

from __future__ import absolute_import 

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

# Copyright (C) 2006 David Kohel <kohel@maths.usyd.edu> 

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

# http://www.gnu.org/licenses/ 

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

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

from sage.rings.polynomial.multi_polynomial_element import is_MPolynomial 

from .quartic_generic import QuarticCurve_generic 

def 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 

TESTS:: 

sage: QuarticCurve(x**3+y**3) 

Traceback (most recent call last): 

... 

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

sage: QuarticCurve(x**4+y**4+z**3) 

Traceback (most recent call last): 

... 

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

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

sage: QuarticCurve(x**4+y**4) 

Traceback (most recent call last): 

... 

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

""" 

if not is_MPolynomial(F): 

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

P = F.parent() 

if not P.ngens() == 3: 

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

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

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

if not PP is None: 

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

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

else: 

PP = ProjectiveSpace(P) 

if check: 

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

return QuarticCurve_generic(PP, F)