D.4.4.13 GTZopt

Procedure from library mprimdec.lib (see mprimdec_lib).

Usage:

GTZopt (N[, check]); module N[, module check]

Return:

list l
the minimal primary decomposition of the module N,
computed by a generalized and optimized version of
the algorithm of Gianny, Trager and Zacharias

Note:

if the parameter check is given, only components
not containing check are computed

Example:

LIB "mprimdec.lib";
ring r=0,(x,y,z),dp;
module N=x*gen(1)+ y*gen(2),
x*gen(1)-x2*gen(2);
list l=GTZopt(N);
l;
→ [1]:
→    [1]:
→       _[1]=x*gen(1)+y*gen(2)
→       _[2]=x*gen(2)-gen(1)
→    [2]:
→       _[1]=x2+y
→ [2]:
→    [1]:
→       _[1]=gen(2)
→       _[2]=x*gen(1)
→    [2]:
→       _[1]=x