= Fix Sage's Brill-Noether =

See the files

   * SAGE_ROOT/devel/sage/sage/schemes/plane_curves/projective_curve.py
   * SAGE_ROOT/devel/sage/sage/schemes/plane_curves/affine_curve.py

in the Sage install.   Note this in the funciton riemann_roch_space (in projective_curve.py):
{{{
        The following example illustrates that the Riemann-Roch space
        function in Singular doesn't *not* work correctly.
        
        ::
        
            sage: R.<x,y,z> = GF(5)[]
            sage: f = x^7 + y^7 + z^7
            sage: C = Curve(f); pts = C.rational_points()
            sage: D = C.divisor([ (3, pts[0]), (-1,pts[1]), (10, pts[5]) ])
            sage: C.riemann_roch_basis(D)    # output is random (!!!!)
            [x/(y + x), (z + y)/(y + x)]
        
        The answer has dimension 2 (confirmed via Magma). But it varies
        between 1 and quite large with Singular.
}}} 


 * Sage's [[http://trac.sagemath.org/sage_trac/ticket/8997|trac 8997]].

 * Singular's [[http://www.singular.uni-kl.de:8002/trac/ticket/153|trac 153]].

There is a [[daysff/curves|wiki page about general function fields issues in Sage]].