Singular

D.4.16.11 preComp

Usage:

preComp(N,check[, ann]); modul N, module check, ideal ann

Return:

(l, check) list l, module check
the elements of l consists of a triple with
[1] of type module [2] and [3] of type ideal
s.th. the intersection of the modules is equal to the zero-dimensional module N, furthermore l[j][3]=annil(l[j][1]) if l[j][2]!=0 then the module l[j][1] is primary
with associated prime l[j][2],
and check=intersect(check, l[j][1]) is computed

Note:

only components not containing check are computed;
if ann is given, ann is used instead of annil(N)

LIB "mprimdec.lib";
ring r=0,z,lp;
module N=z*gen(1), (z+1)*gen(2);
N=std(N);
list l; module check;
(l, check)=preComp(N,freemodule(2));
l;
==> [1]:
==>    [1]:
==>       _[1]=z*gen(1)
==>       _[2]=gen(2)
==>    [2]:
==>       _[1]=z
==>    [3]:
==>       _[1]=z
==> [2]:
==>    [1]:
==>       _[1]=gen(1)
==>       _[2]=z*gen(2)+gen(2)
==>    [2]:
==>       _[1]=z+1
==>    [3]:
==>       _[1]=z+1
check;
==> check[1]=z*gen(1)
==> check[2]=z*gen(2)+gen(2)