/**/ Use R ::= QQ[x,y,z];
/**/ PD := PrimaryDecompositionCore0(ideal(xz, y^21, z^2));
/**/ indent(PD);  decomposition is correct, but not certified
record[
IsCertified := false,
PrDec_I := [
ideal(16*y^2 +40*y*z +25*z^2 +32*y +40*z +16, x z, y^2 1, z^2),
ideal(16*y^2 +40*y*z +25*z^2 32*y 40*z +16, x z, y^2 1, z^2)
]
]
/**/ PrimaryDecomposition0(ideal(xz, y^21, z^2));
[ideal(y +1, x z, z^2), ideal(y 1, x z, z^2)]
/**/ Use ZZ/(2)[x,y,z];
/**/ PD := PrimaryDecompositionCore0(ideal(xz, y^21, z^2));
/**/ indent(PD);
record[
IsCertified := true,
PrDec_I := [ideal(x +z, y^2 +1, z^2)]
]
