Singular Manual: nres

  | ### 5.1.106 nres `Syntax:` `nres (` ideal_expression`,` int_expression `)` `nres (` module_expression`,` int_expression `)` `Type:` resolution `Purpose:` computes a free resolution of an ideal or module M which is minimized from the second module on (by the standard basis method). More precisely, let 166#166=matrix(M),then `nres` computes a free resolution of 169#169 165#165 where the columns of the matrix 166#166are the given set of generators of M. If the int expression k is not zero then the computation stops after k steps and returns a list of modules 170#170. `nres(M,0)` returns a list of n modules where n is the number of variables of the basering. Let `list L=nres(M,0);` then `L[1]=M` is identical to the input, `L[2]` is a minimal set of generators for the first syzygy module of `L[1]`, etc. ( 136#136in the notations from above). `Example:`
        ring r=31991,(t,x,y,z,w),ls;
        ideal M=t2x2+tx2y+x2yz,t2y2+ty2z+y2zw,
                t2z2+tz2w+xz2w,t2w2+txw2+xyw2;
        resolution L=nres(M,0);
        L;
      ==>  1      4      15      18      7      1
      ==> r <--  r <--  r <--   r <--   r <--  r
      ==>
      ==> 0      1      2       3       4      5
      ==> resolution not minimized yet
      ==>
See fres; hres; ideal; lres; module; mres; res; resolution; sres.

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