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PrimaryDecomposition0

primary decomposition of a 0-dimensional ideal

Syntax
PrimaryDecomposition0(I: IDEAL): LIST of IDEAL

Description
This function returns the primary decomposition of the 0-dimensional ideal I . (Monico-Robbiano-Kreuzer probabilistic algorithm, Gao-Wan-Wang finite characteristic algorithm)

Implemented by Elisa Palezzato and Anna M. Bigatti.

Example
/**/  Use QQ[x,y,z];
/**/  PD := PrimaryDecomposition0(ideal(x -z,  y^2 -1,  z^2));  PD;
[ideal(y +1,  x -z,  y^2 -1,  z^2),  ideal(y -1,  x -z,  y^2 -1,  z^2)]

/**/ [IdealOfGBasis(Q) | Q in PD];  // remove some redundant generators
[ideal(y +1,  x -z,  z^2),  ideal(y -1,  x -z,  z^2)]

/**/  Use ZZ/(2)[x,y,z];
/**/  PD := PrimaryDecomposition0(ideal(x +z,  y^2 +1,  z^2));  PD;
[ideal(x +z,  y^2 +1,  z^2)]
/**/ IsPrimary(PD[1]);
true


NOTE: this function behaved like PrimaryDecompositionCore0 up to version CoCoA-5.1.4.
See Also