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)
def QuarticCurve(F,PP=None,check=False):
"""
Returns the quartic curve defined by F.
"""
if not PP is None:
if not is_ProjectiveSpace(PP) and PP.dimension == 2:
raise TypeError, "Argument PP (=%s) must be a projective plane"%PP
elif not is_MPolynomial(F):
raise TypeError, \
"Argument F (=%s) must be a homogeneous multivariate polynomial"%F
else:
if not F.is_homogeneous():
"Argument F (=%s) must be a homogeneous polynomial"%F
P = F.parent()
if P.ngens() != 3:
"Argument F (=%s) must be a homogeneous multivariate polynomial in 3 variables"%F
PP = ProjectiveSpace(P)
if check:
raise TypeError, "Argument checking (for nonsingularity) is not implemented."
return QuarticCurve_generic(PP, F)
def QuarticCurve(F, PP=None, check=False):
"""
Returns the quartic curve defined by F.
"""
if not PP is None:
if not is_ProjectiveSpace(PP) and PP.dimension == 2:
raise TypeError, "Argument PP (=%s) must be a projective plane" % PP
elif not is_MPolynomial(F):
raise TypeError, \
"Argument F (=%s) must be a homogeneous multivariate polynomial"%F
else:
if not F.is_homogeneous():
"Argument F (=%s) must be a homogeneous polynomial" % F
P = F.parent()
if P.ngens() != 3:
"Argument F (=%s) must be a homogeneous multivariate polynomial in 3 variables" % F
PP = ProjectiveSpace(P)
if check:
raise TypeError, "Argument checking (for nonsingularity) is not implemented."
return QuarticCurve_generic(PP, F)