D.4.4.9 splitting

Procedure from library mprimdec.lib (see mprimdec_lib).

Usage:

splitting(N[,check[, ann]]); module 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:

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

Example:

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)=splitting(N);
l;
→ [1]:
→    [1]:
→       _[1]=gen(2)
→       _[2]=z*gen(1)
→    [2]:
→       _[1]=z
→    [3]:
→       _[1]=z
→    [4]:
→       _[1]=z
→ [2]:
→    [1]:
→       _[1]=gen(1)
→       _[2]=z*gen(2)+gen(2)
→    [2]:
→       _[1]=z+1
→    [3]:
→       _[1]=z+1
→    [4]:
→       _[1]=z+1
check;
→ check[1]=z*gen(2)+gen(2)
→ check[2]=z*gen(1)