15.2 Riemann-Roch spaces using Singular

Can you compute a basis of a Riemann-Roch space in Sage?

Unfortunately, the answer is ``no'' at the present time. The version of Singular currently used by Sage (version 3.0.2) has a Brill-Noether algorithm implementation (computing a basis of a Riemann-Roch space) which appears to be buggy. The rest of this section is included to illustrate the syntax once the bugs in brnoeth get worked out (or to help any developers wishing to work on this themselves).

To compute a basis for the Riemann-Roch space $ L(D)$ associated to a divisor $ D$ on a curve $ X$ over a field $ F$ , you can use Sage's ``wrapper'' riemann_roch_basis to Singular or Singular itself. Both are illustrated below.



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