Next: Computing a basis for
Up: Computational Aspects
Previous: Computing the divisors
Computing
bases of adjoint forms
Let
Monom denote the
monomial
basis for
, resp. the corresponding
vector of monomials. We represent a homogeneous
form
by the vector
such that
Monom. To compute
bases of adjoint forms as needed by the BrillNoether algorithm,
we apply the following algorithm:
 Input

,
list of closed places of (defined by ),
a positive integer,
nonnegative integers , , s.th.
,
nonnegative integers , , s.th.
.
 Output

basis of a subspace of
complementary to
(given in form of a matrix of coefficients w.r.t.
Monom).
 The subspace
of forms divisible by
. Compute the matrix
with
Monom Monom.
Note that
,
.
 The space .
For each closed place with
do the following:
Finally, concatenate the to obtain
with
and compute as the kernel of , that is
 Compute a complement of in . This can be done, for
instance, by using the lift command in SINGULAR.
Next: Computing a basis for
Up: Computational Aspects
Previous: Computing the divisors
Christoph Lossen
20010321