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7.3.15 mres (plural)

Syntax:
mres ( ideal_expression, int_expression )
mres ( module_expression, int_expression )
Type:
resolution
Purpose:
computes a minimal free resolution of an ideal or module M with the Groebner basis method. More precisely, let A=matrix(M), then mres computes a free resolution of where the columns of the matrix are a (possibly) minimal set of generators of . If the int expression k is not zero, then the computation stops after k steps and returns a resolution consisting of modules
mres(M,0) returns a resolution consisting of at most n+2 modules, where n is the number of variables of the basering. Let list L=mres(M,0); then L[1] consists of a minimal set of generators M, L[2] consists of a minimal set of generators for the first syzygy module of L[1], etc., until L[p+1], such that but L[p+1] (the first syzygy module of L[p]) is 0 (if the basering is not a qring).
Note:
Accessing single elements of a resolution may require that some partial computations have to be finished and may therefore take some time. Hence, assigning right away to a list is the recommended way to do it.
Example:
 
See ideal (plural); minres (plural); module (plural); nres (plural).


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