Usage:
<cohomology i M j H
Computes the cohomology module
H = \sum_{n >= 0} H^i(M(n))
of the module M , regarded as
a coherent sheaf on projective space.
Parameters:
i>0 the index of the cohomology group
M a module
j>0 a sufficiently large integer (see below.)
Output values:
H = module.
H is computed as the truncation in degrees >=0
of the module Ext^i(J, M), where J is the ideal
generated by the jth powers of the variables in the
base ring of M.
For the answer to be guaranteed correct, it is enough
to have: All the syzygy modules of M are generated
in degrees <= j + numvars - 1.
Caveats:
Note that the answer returned is
TRUNCATED IN DEGREES >= 0 ! To get all of Ext^i(J, M)
use <cohomology1 i M j H instead. This is desirable, for
example, when computing H^0, or the first nonzero H^i with
i >= 0, but in general the low degree parts may not mean much.