Usage:
<extend_ring J x S
Computes an approximation S to the smallest
subring S' of the total quotient ring of R.
the base ring of J, having
depth J S' >= 2. In certain cases this is
\sum_n H^0( O_X (n) ),
where X is the projective variety defined by the
base ring of j --- see below.
Parameters:
J = ideal in the ambient ring with respect
to which the 0 th local cohom is being
computed.
x = the name of the new variables to use
in defining S; MUST NOT CONFLICT WITH
THE NAMES OF VARIABLES IN THE BASE RING
OF J.
Output values:
S = R[ x[1], x[2], ... ]/K,
where R is the base ring of J and K is an ideal.
The base ring R of J may be a quotient ring.
The natural map f from R to S may be found by using
<imap f J S
;
The ring generated over R by the fractional
ideal Hom(J,R) is computed, under the
assumption that the first generator of
J given is a nonzerodivisor on R
(use NZD to check this.) S is set
equal to this new ring. S is created for
this purpose, using variables named
x[1]..x[n], where n is the number of
variables in R + the number of generators
computed for Hom(J,R).
If J is primary to the maximal ideal,
then S is a subring of
\sum H^0( O_X (m) ),
where X is the projective variety corresponding
to R -- the part annihilated by J mod R.
If in addition J annihilates
the first local cohomology
of R, and in particular if R (nvars R)-1
+ the degrees of the generators of J
are all >= the largest degree
occurring in the resolution
of R at the (nvars R)-1 th step, then
Hom(J, R) is the whole of this ring.