5.1.85 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
$A_1$=matrix(M),
then nres computes a free resolution of
$coker(A_1)=F_0/M$
$$...\longrightarrow F_2 \buildrel{A_2}\over{\longrightarrow} F_1 \buildrel{A_1}\over{\longrightarrow} F_0\longrightarrow F_0/M\longrightarrow 0,$$

where the columns of the matrix
$A_1$
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
$M_i={\tt module}(A_i)$, i=1..k.

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.
(${\tt L[i]}=M_i$
in 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
hres;
ideal;
lres;
module;
mres;
res;
resolution;
sres.
<font size="-1">
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; User manual for <a href="http://www.singular.uni-kl.de/"><i>Singular</i></a> version 2-0-4, October 2002,
generated by <a href="http://www.gnu.org/software/texinfo/"><i>texi2html</i></a>.
</font>

</body>
</html>
