Hmmm. My comment seems to be hung up pending review. New member.
Everything you did was fine.
riemann_roch_basis only works for prime F:
To compute a basis of the Riemann-Roch space of a divisor [image: D] on a
> curve over a field [image: F], one can use Sage’s wrapper
> riemann_roch_basis o
but as I define it over the finite field GF(4)?
2012/6/15 David Joyner
> On Fri, Jun 15, 2012 at 1:18 PM, Gato wrote:
> > help me please:
> >
> >
> > sage: F.=GF(4,'w')
> > sage: R. = ProjectiveSpace(F,2)
> > sage: C = Curve(X^2*Y + w*Y^2*Z+ w^2*Z^2*X)
> > sage: print C
> > Projective Curve ove
On Fri, Jun 15, 2012 at 1:18 PM, Gato wrote:
> help me please:
>
>
> sage: F.=GF(4,'w')
> sage: R. = ProjectiveSpace(F,2)
> sage: C = Curve(X^2*Y + w*Y^2*Z+ w^2*Z^2*X)
> sage: print C
> Projective Curve over Finite Field in w of size 2^2 defined by X^2*Y +
> (w)*Y^2*Z + (w + 1)*X*Z^2
> sage: print
help me please:
sage: F.=GF(4,'w')
sage: R. = ProjectiveSpace(F,2)
sage: C = Curve(X^2*Y + w*Y^2*Z+ w^2*Z^2*X)
sage: print C
Projective Curve over Finite Field in w of size 2^2 defined by X^2*Y +
(w)*Y^2*Z + (w + 1)*X*Z^2
sage: print C.genus()
1
sage: pts = C.rational_points()
sage: print pts[4]
