Coverage for local/lib/python2.7/site-packages/sage/schemes/plane_quartics/quartic_generic.py : 38%

""" 

Plane quartic curves over a general ring. These are generic genus 3 curves, 

as distinct from hyperelliptic curves of genus 3. 

EXAMPLES:: 

sage: PP.<X,Y,Z> = ProjectiveSpace(2, QQ) 

sage: f = X^4 + Y^4 + Z^4 - 3*X*Y*Z*(X+Y+Z) 

sage: C = QuarticCurve(f); C 

Quartic Curve over Rational Field defined by X^4 + Y^4 - 3*X^2*Y*Z - 3*X*Y^2*Z - 3*X*Y*Z^2 + Z^4 

""" 

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

# 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/ 

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

import sage.schemes.curves.projective_curve as projective_curve 

def is_QuarticCurve(C): 

""" 

Checks whether C is a Quartic Curve 

EXAMPLES:: 

sage: from sage.schemes.plane_quartics.quartic_generic import is_QuarticCurve 

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

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

sage: is_QuarticCurve(Q) 

True 

""" 

return isinstance(C, QuarticCurve_generic) 

class QuarticCurve_generic(projective_curve.ProjectivePlaneCurve): 

# DRK: Note that we should check whether the curve is 

def _repr_type(self): 

""" 

Return the representation of self 

EXAMPLES:: 

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

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

sage: Q._repr_type() 

'Quartic' 

""" 

return "Quartic" 

def genus(self): 

""" 

Returns the genus of self 

EXAMPLES:: 

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

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

sage: Q.genus() 

3 

""" 

return 3