### 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 =matrix(M),then `nres` computes a free resolution of

  where the columns of the matrix are 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 .
  `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. ( in the notations from above).
`Note:`
  `nres` honours `degBound`.
`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 degBound; fres; hres; ideal; lres; module; mres; res; resolution; sres.

User manual for Singular version 4.4.1, 2025, generated by texi2html.