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PrimaryDecomposition0

primary decomposition of a 0-dimensional ideal

Syntax
PrimaryDecomposition0(I: IDEAL): RECORD of 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) It will be improved and extended in future versions of CoCoA.

Implementation by Elisa Palezzato.

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

See Also