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Let be any
rational divisor on
. The algorithms of the
preceding sections finally allow to compute an
basis of
by the BrillNoether Algorithm (cf. Prop. 2.7):
 Input

,
list of closed places of
,
nonnegative integers , , s.th.
,
integers , , s.th.
.
 Output
 Vector space basis of
(in terms of rational
functions on ).
 Choose sufficiently large (for instance, according to
(3), above).
 Compute
,
, such that
. To do so, we compute an
basis for a vector
subspace of
complementary to
(cf. Section 2.4.4) and choose any element of this
basis (for instance, with the minimal number of monomials).
 Compute the effective divisor
(cf. Section 2.4.3).
 Compute an
basis
of a vector subspace of
complementary to
(cf. Section 2.4.4).
 Return the set of rational functions
.
Next: Example
Up: Computational Aspects
Previous: Computing bases of adjoint
Christoph Lossen
20010321