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)

<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>
