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5.1.135 sres
Syntax:
sres ( ideal_expression, int_expression )
sres ( module_expression, int_expression )
Type:
- resolution
Purpose:
- computes a free resolution of an ideal or module with Schreyer's
method. The ideal, resp. module, has to be a standard basis.
More precisely, let M be given by a standard basis and
Then
sres
computes a free resolution of
If the int expression k is not zero then the computation stops after k steps
and returns a list of modules (given by standard bases)
sres(M,0)
returns a list of n modules where n is the number of variables of the basering.
Even if sres does not compute a minimal resolution, the betti
command gives the true betti numbers! In many cases of interest
sres is much faster than any other known method.
Let list L=sres(M,0); then L[1]=M is identical to the input,
L[2] is a standard basis with respect to the Schreyer ordering of
the first syzygy
module of L[1] , etc.
in the notations from above.)
Note:
- Accessing single elements of a resolution may require some partial
computations to be finished and may therefore take some time.
Example:
See
betti;
hres;
ideal;
int;
lres;
minres;
module;
mres;
res;
syz.
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