At the moment the implementation of algebraic curves in Sage doesn't seem 
to be connected at all to the implementation of Function Fields. Is this 
intentional? It would seem to be useful to be able to, for example, get the 
function field from a curve. Also surely the Riemann-Roch basis function on 
projective curves should return elements of a function field and not, as it 
does currently, the field of fractions of k[X,Y,Z].

Thanks to the current global meltdown I am stuck at home with time on my 
hands so happy to try and tie together these two areas if there isn't a 
specific reason not to.
 

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