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D.4.4.11 preComp
Procedure from library mprimdec.lib (see mprimdec_lib).
- Usage:
preComp(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:
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)=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)
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