Divisor and Riemman Roch

[Gato]

help me please:


sage: F.<w>=GF(4,'w')
sage: R.<X,Y,Z> = 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]
(1 : w : 1)
sage: print pts[5]
(w : 1 : 1)
sage: D = C.divisor([ (2, pts[4]),(1, pts[5]) ])
sage: print C.riemann_roch_basis(D)
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)

/home/valpo/Descargas/sage-4.8/<ipython console> in <module>()

/home/valpo/Descargas/sage-4.8/local/lib/python2.6/site-packages/sage/structure/parent.so in sage.structure.parent.Parent.__getattr__ (sage/structure/parent.c:6249)()

AttributeError: 'ProjectiveCurve_finite_field' object has no attribute 'riemann_roch_basis'


why??

[David Joyner]

I think this means that the class ProjectiveCurve_finite_field does
not have the method
riemann_roch_basis implemented.

See http://www.sagemath.org/doc/constructions/algebraic_geometry.html
for examples.

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[Andrés Vargas]

but as I define it over the finite field GF(4)?

2012/6/15 David Joyner <wdjo...@gmail.com>

[Slumberland]

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  on a curve over a field , one can use Sage’s wrapperriemann_roch_basis of Singular’s implementation of the Brill Noether algorithm. Note that this wrapper currently only works when  is prime and the divisor  is supported on rational points.  

(from http://www.sagemath.org/doc/constructions/algebraic_geometry.html)

I checked your example, and got the same error.

I did two examples from the documentation.  The syntax was identical. They were on GF(5) and (7), and they worked.

Sorry I can't be of more assistance; this is new math for me.

Good luck.