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D.4.4.14 zeroOpt

Procedure from library mprimdec.lib (see section 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 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,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

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            User manual for Singular version 2-0-4, October 2002, generated by texinfo.