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D.4.14.14 zeroOpt

Procedure from library mprimdec.lib (see mprimdec_lib).

Usage:
zeroOpt (N[, check]); zero-dimensional module N[, module check]

Return:
list l
the minimal primary decomposition of a zero-dimensional module N, computed by a generalized and optimized version of the algorithm of Gianni, Trager and Zacharias

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

Example:
 
LIB "mprimdec.lib";
ring r=0,z,dp;
module N=z*gen(1),(z-1)*gen(2),(z+1)*gen(3);
list l=zeroOpt(N);
l;
==> [1]:
==>    [1]:
==>       _[1]=gen(1)
==>       _[2]=z*gen(2)-gen(2)
==>       _[3]=gen(3)
==>    [2]:
==>       _[1]=z-1
==> [2]:
==>    [1]:
==>       _[1]=z*gen(1)
==>       _[2]=gen(2)
==>       _[3]=gen(3)
==>    [2]:
==>       _[1]=z
==> [3]:
==>    [1]:
==>       _[1]=gen(1)
==>       _[2]=gen(2)
==>       _[3]=z*gen(3)+gen(3)
==>    [2]:
==>       _[1]=z+1