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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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